350-Year-Old Newton's Puzzle Solved By 16-Year-Old

First time accepted submitter johnsnails writes "A German 16-year-old, Shouryya Ray, solved two fundamental particle dynamic theories posed by Sir Isaac Newton, which until recently required the use of powerful computers. He worked out how to calculate exactly the path of a projectile under gravity and subject to air resistance. Shouryya solved the problem while working on a school project. From the article: 'Mr Ray won a research award for his efforts and has been labeled a genius by the German media, but he put it down to "curiosity and schoolboy naivety." "When it was explained to us that the problems had no solutions, I thought to myself, 'well, there's no harm in trying,'" he said.'"

Comments

That Moment

[Rie Beam]

We all had that moment in school when a teacher would pose an "impossible" problem, thought to ourselves "Well, they've never faced ME before!", spent a few minutes toying with it and finally giving up. This kid...did not.

Kudos all around! The rest of your life will, unfortunately, now no longer live up to something you accomplished when you were 16.

Re:That Moment

[__aaltlg1547]

There are two things impressive about this. One is the fact that you mention, that the kid did not give up until he had the solution and was smart enough to solve a problem that stumped every mathemetician for 350 years. The second is that people still try to solve difficult analytic problems at all instead of just turning it into a computing problem.

I don't know which surprises me more.

Re:That Moment

[mwvdlee]

The rest of your life will, unfortunately, now no longer live up to something you accomplished when you were 16.

Imagine the freedom of no longer having to live up to anybody's expectations. ;)

Re:That Moment

[chill]

Germany still produces some rays of light.

To be accurate... he was born in India and moved to Germany with his family at age 12. He did not speak a word of German when he arrived.

While credit must be given to the German school system, I think most of his accomplishment comes from him and possibly his family.

Re:That Moment

[Anonymous Coward]

While credit must be given to the German school system

Must it? The school system could be garbage and still have the occasional intelligent person go through it. Perhaps it's not the school system that must be given credit, but something else (like the child himself, for instance).

Re:That Moment

[rvw]

Germany still produces some rays of light.

To be accurate... he was born in India and moved to Germany with his family at age 12. He did not speak a word of German when he arrived.

While credit must be given to the German school system, I think most of his accomplishment comes from him and possibly his family.

And maybe from not being in Europe or the western world the first twelve years of his life, adopting beliefs or creating a mental attitude that stuff like this cannot be done. And I'm not criticizing the Germans.

Re:That Moment

[Anonymous Coward]

Computing tends to be a brute force analysis of all the possible inputs. That doesn't work well for NP hard problems and is often impossible with problems dealing with infinity... Not all problems are solvable by computers yet and instead need the analytical approach. Also computers may not find the most elegant solutions, for example there are problems which have been solved but required the invention of a new type of math to do so.

Re:That Moment

[epine]

The rest of your life will, unfortunately, now no longer live up to something you accomplished when you were 16.

Imagine the freedom of no longer having to live up to anybody's expectations. ;)

Better yet, he doesn't have an Erdos number less than his age, so he can still hope for a normal sex life.

Re:That Moment

[Chris Mattern]

Analytic solutions are far superior to computed approximations. They are far easier to calculate--computers have made computed approximations far easier, but most of the time that doesn't mean that they're *easy*--only that they're now possible. Being able to obtain the answer in a small fraction of the time is still a big advantage. They are more precise and do not require initial parameters. And they provide much greater understanding and insight into the underlying phenomenon. There is no surprise at all that people are still looking for analytic solutions.

Re:That Moment

[jthill]

Yeah, well, this never happened to him before!

I mean, I get you, but I think when you have to start asking "what produced _this_ guy?!??" all bets are off.

Re:That Moment

[Anonymous Coward]

I know a quote in Spanish that says something like "As they didn't know it was impossible, they did it" ("Como no sabían que era imposible, lo hicieron").

Re:That Moment

[Anonymous Coward]

He should have copy righted the work, so he would not need to accomplish anything else just like artists

Re:That Moment

[K. S. Kyosuke]

Computing tends to be a brute force analysis of all the possible inputs.

Hello? We've had symbolic computing ever since 1960's. There are many software tools today to assist mathematicians with creating and verifying proofs (e.g, Coq is probably the best known one). What's wrong with using them? Not to do that would be like using a pencil and paper instead of typing when you're preparing a publication – I'd think that brain power and time should be used constructively.

Re:That Moment

[Anonymous Coward]

If he solved it, then WHAT IS THE SOLUTION?! There is no link, no nothing, and we are apparently to trust this lame emotional article with no factual content. I'm surprised nobody else raised this point.

Re:That Moment

[mikael]

More likely , one or more of his parents is a mathematics lecturer/teacher. They would know about the resources available. At least he would have needed to what the problem was and what kind of notation was required to solve it.

Re:That Moment

[EMN13]

Possibly relevant here (in some minor way) is that thinking in a foreign language allows people to be more rational.

Re:That Moment

[LifesABeach]

Ha! Inventing a new mathmatical system in order to solve a problem is cheating!

But it works.

Re:That Moment

[mwvdlee]

How about just ANY sex life?

Re:That Moment

[Deadstick]

You can solve any problem if you define it the way you want...for example, my wife once took a drafting course from a guy who said he'd made fools of centuries of mathematicians by trisecting an angle. Of course, his solution was an approximation, but he conveniently left out "theoretically exact" as part of the definition of a constructive solution. He said he was working on squaring the circle, too...

I'd reserve your hosannas until this kid's magic formula gets published, along with a formal statement of the problem.

Re:That Moment

[trout007]

It depends on what you are trying to do. I'm a mechanical engineer and engineering is all about good enough. You have to economize resources to get a job done. While solving a dynamics problem analytically may give you more understanding into the solution it does take take to work out real world multidimensional problems. Numerical solutions to differential equations are very useful. I would have preferred to spend more time in Diff Eq setting up problems than solving problems analytically.

Re:That Moment

[iamhassi]

There are two things impressive about this. One is the fact that you mention, that the kid did not give up until he had the solution and was smart enough to solve a problem that stumped every mathemetician for 350 years. The second is that people still try to solve difficult analytic problems at all instead of just turning it into a computing problem.

I don't know which surprises me more.

^^^^ This.

I think the most impressive part is that even though we hear all the time about "X-teen year old invents BLAH" we're like "Great!" but secretly think "BIG Deal! Who can't invent something? How is that challenging, really? Oh look their dad's an electrical engineer that works at XYZ... hmmmm....." but this 16-year-old actually solved something that the best mathematicians on Earth haven't been able to solve for 350 years.

Major kudos kid! Only way that can be topped is if a teen cures cancer, aids or doubles productive lifespan.

Re:That Moment

[Intrepid imaginaut]

Business wise I'd type, fiction wise I prefer to use pen and paper.

Re:That Moment

[iamhassi]

Also he solved it without mooching off a company for 2 months (and still having nothing to show for it) or asking for $500,000! No $$$$ up front and he still brought results! This 16 yr old will go far, I would happily donate to this kid's next .... whatever he wants to do, since he's already earned it in my opinion.

Re:That Moment

[am 2k]

Analytic solutions are far superior to computed approximations. They are far easier to calculate--computers have made computed approximations far easier, but most of the time that doesn't mean that they're *easy*--only that they're now possible. Being able to obtain the answer in a small fraction of the time is still a big advantage.

Have fun with solving the Navier-Stokes equations then ;)

Re:That Moment

[skipdallas]

And you know this how? Even if what you say turns out to be true, this young man has made a lasting name for himself in mathematics.

Re:That Moment

[Anonymous Coward]

I just wanted to say that I LOVE Coq.

Re:That Moment

[ArundelCastle]

What's wrong with using them? Not to do that would be like using a pencil and paper instead of typing when you're preparing a publication – I'd think that brain power and time should be used constructively.

It's not a matter of the tool is wrong. It's a matter that assuming one tool is always best is wrong.
Your premise is based on: using a computer is easier and better for 100% of humans. That's not true. Allow me to introduce you to my parents. Allow me to introduce you to senior engineers who can craft new formulas on a whiteboard faster than juniors can wake their laptops.

Different areas of the brain are involved with the act of handwriting than with touch typing or pecking. Make LCARS speech recognition a reality and we have a winner. Solving problems that stump otherwise intelligent humans for *hundreds* of years, *clearly* requires some creatively alternate use of the brain, and not Microsoft Clippy. ("I see you're trying to solve an unprovable theorem, would you like to Quit without Saving?") I don't even need to cite sources that say poor UIs slow people down. That's how it is. Computers add cruft, otherwise there wouldn't be a market for applications that remove distractions when writing.

...like using a pencil and paper instead of typing when you're preparing a publication...

Poor analogy. Publication implies mass reproduction and distribution. An *author* can write however they want to form their ideas, the result is the same. How the idea gets distributed is irrelevant to the core point. (Also there are such things as shorthand.)

Re:That Moment

[ArundelCastle]

A common mistake that people make when trying to design something completely foolproof is to underestimate the ingenuity of complete fools. (Douglas Adams)

Re:That Moment

[Cryophallion]

Perhaps he should watch this TED video to feel better about it all:
Elizabeth Gilbert: A new way to think about creativity
http://www.youtube.com/watch?feature=player_embedded&v=86x-u-tz0MA

Re:That Moment

[tixxit]

The article states the father taught him calculus when he was 6. However, his father also says the kid passed his understanding a while ago and he doesn't understand the math used to solve this problem. Seems like the father was responsible for instilling a curiosity and some foundations, but after that it's all just this kid. You gotta give him credit.

Re:That Moment

[solidraven]

Yeah, cause right now it doesn't sound all that impressive.
Fact is that any engineering student who took fluid dynamics has had to solve similar problems like "A ball > was shot out of a cannon > into a gas with next properties: >. Calculate ... ." At least I remember I had to do that, and I'm not even a mechanical engineering major... So unless he found some super exact way to do it I'm not very impressed. And even if he found a very exact way to do it I'm still not impressed, it just means he bothered to waste more time on it and decided to not simplify irrelevant factors.
Same with an object hitting a wall, you can go as far in calculating that on paper as you want. It's just questionable if there's a point to it cause the analytic solutions are often very generalised and useless for actual modelling of physical systems.
In fact exact analytic modelling of physical systems sort of became a joke with us EEs. Cause you always end up using statistical physics when dealing with semiconductors or very gross over simplifications; Like using Kirchoff and Ohm instead of Maxwell's equations. And at the point where you introduce statistics and probability into a problem -as is always the case with very complex realistic modelling- you can just as well use a computer program to verify the solution. The computer is less prone to errors (if configured correctly), faster and will be able to visually represent the results without having to spend hours of additional work. The resulting time is better spent sniffing solder fumes, playing minesweeper on logic analysers, working on your own personal projects in the lab, drinking coffee, ...
Conclusion: Either the article must be mentioning something very wrong or this is another case of blowing up a highschool student's achievements to make a feel good story.

Re:That Moment

[fast turtle]

The simple answer is "Bias" in the programming. Everyone has a bias of some type and as this kid proved once again, there are many different ways to look at a problem as he hadn't yet reached the "Impossible stage" of thinking. Once Ossification of the thinking process sets in, everyone begins to add more and more bias (assumptions) to what they're doing based upon past experience/knowledge, which is why it is so important to encourage kids to look at the world with wide eye innocence.

Re:That Moment

[gd2shoe]

Ha! Inventing a new mathmatical system in order to solve a problem is cheating! But it works.

Not only is it cheating, it's tradition. We have many great branches of mathematics because of it.

Re:That Moment

[mikael]

Agreed. He could just have got bored and just learned a bit to keep his parents happy. But he managed to do sonething new and get a paper published in a maths journal. He will probably becone a MIT maths professor.

Re:That Moment

[K. S. Kyosuke]

is your software proven to be fault-free?

is your hardware proven to be fault-free? (have you ever read the list of errata for a modern CPU?)

if your software puts out a human readable (and verifiable) form of the proof everything is fine, if not you can only talk about probabilities not about proof.

First, you have to ask the same thing about mathematicians' brains and abilites (organic HW and SW). Second, of course that a proof assistant has to be able to print out a trace of the reasoning process. That's the whole point (or one of them).

Re:That Moment

[Jstlook]

Just had to point out how appropriate this xkcd is:
http://xkcd.com/447/

Re:That Moment

[whit3]

>Have fun writing...algorithms for those if you can't work out analytical solutions

Truth. It's easy to write code, but only a good little
computable-on-back-of-an-envelope test case will give
me confidence in it. I've found errors that were hidden
four decimals down in my brute-force algorithms.

Re:That Moment

[Karellen]

In fact, Newton did this himself.

I recall a story of some mathematical puzzle or hypothesis which had been unsolved by a number of mathematicians for many years. It was brought to Newton's attention, whereupon over the course of a few days (maybe a weekend?) he invented a new branch of mathematics and solved the puzzle. He published his results anonymously, but no-one was fooled and immediately (if somewhat resignedly) congratulated Newton on his genius (again).

Can't remember the hypothesis or the resulting branch of mathematics though.

Re:That Moment

[Anonymous Coward]

No. Analytically solution are definitely of theoretical interests, but they are not necessarily the best way to compute something. Simple example : the roots 4th degree polynomials. Due to floating point oddities, the analytic roots will yield inaccurate results, compared to numerical approaches, say Laguerre method.

Re:That Moment

[cavreader]

It's people like this kid who pop-up very rarely in the world that will eventually improve our mathematical understanding and all the technology based on advanced mathematics. That's a positive thing.

Re:That Moment

[gmhowell]

Also he solved it without mooching off a company for 2 months (and still having nothing to show for it) or asking for $500,000! No $$$$ up front and he still brought results! This 16 yr old will go far, I would happily donate to this kid's next .... whatever he wants to do, since he's already earned it in my opinion.

As far as Ted Kacinsky? Don't count your chickens before they're hatched. Let the kid live his life.

Re:That Moment

[Pseudonym]

I love ISABELLE myself, but hey, whatever floats your sequent.

Re:That Moment

[Pseudonym]

Analytic solutions are not necessarily easier to calculate.

Analytic solutions tend to involve special functions for which the computer can only compute an approximation anyway. Have you ever tried to write code to evaluate the error function over the entire domain of floating point numbers? (Yes, I know, it's now in the standard library; ten years ago, it wasn't.) That's one of the easier ones.

Even if there are no special functions, analytic solutions are still often harder to calculate if the problem is big enough. Think of solving systems of linear equations, one of the standard workhorses of numeric programming. We're talking really big ones; hundreds of thousands of equations in hundreds of thousands of unknowns or bigger. In the real world, this problem would almost certainly be solved using successive approximations, even though high school students know how to solve them analytically.

Finally, and most importantly, the problem statement is usually an approximation. Take the OP as an example. What this kid almost certainly solved was an analytic solution to the problem of a particle in a gravitational field with linear air resistance. Well, air resistance is not linear. At low velocities, and for projectiles with a sufficiently small cross-section, it's close enough. But it's still an approximation.

The advantages of analytic solutions are almost always not computational. What they buy you is understanding. The methods of obtaining the solution, and the form of the final equations, often reveal some deep insights about the problem. For many situations, that's far more valuable. And it's certainly something that no computer can give you.

Re:That Moment

[gardyloo]

I suspect you're thinking of the brachistochrone problem, posed by Johann Bernoulli in 1696, and solved the next day by Newton (also by several other mathematical giants of the time, very quickly).

Re:That Moment

[Darinbob]

Computing has too much brute force to it very often. Sure you could do it the hard way and when things take too long you just claim you need more memory and a faster CPU (sort of like Word). Whereas if you have the formula you can do it very quickly instead even on a slow computer. When you get off of the dumbed down desktop computer people still care about how long stuff takes to run.

Re:That Moment

[dcollins117]

Methinks this article is more about the boundless potential of human creativity when applied to technological problem solving, and not so much ballistics.

Re:That Moment

[dcollins117]

You must be new here.

Re:That Moment

[fluffy99]

Analytic solutions are far superior to computed approximations. They are far easier to calculate--computers have made computed approximations far easier, but most of the time that doesn't mean that they're *easy*--only that they're now possible. Being able to obtain the answer in a small fraction of the time is still a big advantage.

Have fun with solving the Navier-Stokes equations then ;)

For most engineering problems, you don't need the exact answer. You just need a sufficiently accurate one. For NS, the trick was recognizing which terms were tiny and throwing them out. Who cares if your answer is 0.000001% off if it means reducing the equation down to 4 parts that can be easily solved on paper.

Re:That Moment

[brillow]

I've known enough scientists from enough countries to know that if there is a culture which has intellectual ossification, its not Germany. In fact, the western world has a research enterprise in place which is of much higher caliber than the rest of the world. It may be because the western world has been intellectually liberated for much longer than the rest of the world.

Re:That Moment

[schroedingers_hat]

There's also the fact that teaching methods and notation are technologies and improve over time.
Try doing complex EM calculations purely in component form some time, or do your taxes in roman numerals or ancient greek notation -- or without 0.
If you had to spend a lot of time learning how to use trig tables for multiplication I'd wager you would have much more trouble/less time for learning algebra.

Re:That Moment

[thereitis]

Unfortunately in the past I have found the problems that actually are impossible to be the most interesting, like infinite compression and free energy. :)

Re:That Moment

[locrien]

It's not how big your Coq is; It's how you use it.

Re:That Moment

[gazbo]

I imagine that using trig tables for multiplication would hold you back, yes.

Re:That Moment

[HuguesT]

Good luck solving NS in the presence of turbulence.

Re:That Moment

[galaad2]

I'd reserve your hosannas until this kid's magic formula gets published, along with a formal statement of the problem.

the formula has already been published, here: https://www.jugend-forscht.de/images/1MAT_67_download.jpg
(photo of the formula taken on May 18th)

article source:
https://www.jugend-forscht.de/index.php/projectsearch/detail/6038.4568
and
http://www.jufo-dresden.de/projekt/teilnehmer/matheinfo/m1

i can't find the full paper yet though, but on reddit some users claim that the formula works in Maple
e.g.
http://www.reddit.com/r/worldnews/comments/u7551/teen_solves_newtons_300yearold_riddle_an/c4szejb

where f is constant on the path the particle makes in the space of velocities:
f:=(g^2 /(2*u^2 ) + a*(g/2)*(v*sqrt(u^2 +v^2 )/(u^2 ) + arcsinh(v/u)));

Re:That Moment

[Carewolf]

What's wrong with using them?

They are not helpful. Automatic proof, or automatic proof-verification is a research field, and has been so for decades, and has still YET to come up with something helpful to anyone doing real mathematical proofs. They have only barely reached the ability to help with play-thing problems handed to high school students, and even them the computer generated result (or input), is obtuse and stupid - not helpful in any way.

Re:That Moment

[treeves]

Didn't Einstein come up with tensors to work out general relativity?

Re:That Moment

[treeves]

I suspect he meant log tables. Be a human slide rule.

Re:That Moment

[treeves]

I disagree with his point in any case.

Re:That Moment

[kwoff]

Einstein had learned about [tensors], with great difficulty, from the geometer Marcel Grossmann.

Re:That Moment

[VendingMenace]

There are three things to say to this:

First, saying that he was just "lucky" is ridiculous. There have been several decades, at least, during which children were taught algebra as a matter of course. In those decades, no one else solved this problem. Please recognize that this solution required a brilliant moment of insight -- aka genius -- in order to solve. Does this mean that he will ALWAYS have these insights? No. But that doesn't mean that this was not, in itself, a work of genius.

Second, even if he never has another moment of genius, he is still pretty damn smart. AND he is willing to work hard. I would rather hire a smart, hard working person, than someone that tries to denigrate this hard work as "lucky." In fact, I would probably rather hire that guy than a true genius that wasn't willing to work hard.

Third, what, exactly, do you think we should idolize people for? We give out medals of honor for a single act of bravery. Should we say, "Meh, sure that guy did something awesome, but he probably won't save another whole platoon on his own again"? Or, for the Pulitzer Prize, do we say "Sure this is the best book this year, but he probably won't write the best book of NEXT year"? Even Nobel prizes are given out for a single discovery and a single (or just a few) papers. I would say that this kid deserves recognition. Just because you haven't done anything as awesome in your life, doesn't mean that we shouldn't recognize people that do.

Re:That Moment

[postbigbang]

That's what peer review is for, to vet the reasoning process and therefore, the crux of the domain of the output and its veracity. My experience is that people that are trained in long hand-drawn proofs are more comfortable with that process, while those comfy with the limitations of various processors, languages, FPUs and modes of expression will use those.

Tools: mind first, medium second.

Re:That Moment

[roman_mir]

aren't you happy now that you didn't forget to hit that "Post Anonymously" check box?

Re:That Moment

[qu33ksilver]

Yes, in 8th standard I learnt that to solve equations having 'n' unknowns, you need at least 'n' equations. I tried to solve an equation having 2 variables using only that equation. I tried for around half-hour and left. Wonder if it would have been solved if the boy tried it !!

Re:That Moment

[Zordak]

Also, his real name is Asok and he can grow a third arm when facing an impossible deadline.

Re:That Moment

[gl4ss]

Also he solved it without mooching off a company for 2 months (and still having nothing to show for it) or asking for $500,000! No $$$$ up front and he still brought results! This 16 yr old will go far, I would happily donate to this kid's next .... whatever he wants to do, since he's already earned it in my opinion.

the squatter got investment.. ..and this teenager was probably mooching off home anyways, like most kids do.

anyhow, if you want to mooch off, I'll bet you 100 bucks the aol squatter would have preferred german social security to aols free showers.

Re:That Moment

[Anonymous Coward]

I just wanted to say that I LOVE Coq.

Coq sucks.

Somehow, I think you have that backwards.

Re:That Moment

[drcesteffen]

The actual problem statement for most of us is how to solve math problems while simultaneously making money proportional to the usefulness or proportional to the time spent on this problem and other unsuccessful problem attempts. Otherwise, we end up going out of business.

Re:That Moment

[shadowofwind]

Minor counter-example....5th order polynomials have exact solutions, but truncation and cancellation error makes calculation difficult when they are close together. A comparably well implemented interative solver is actually about the same speed, and more stable. Not that this invalidates the countless other situations where analytic solutions are better.

Re:That Moment

[fluffy99]

Good luck getting really accurate FEA results in turbulent flow as well. I do testing on large scale models to validate the predictions created using computational models. More often than not, the models are not very accurate and they end up 'adjusting' the models to match the actual results.

Re:That Moment

[doppe1]

Well I'm a physicist, and I usually don't believe any numerical solution unless I have an analytical solution to an approximation of the numerical problem which I can compare the numerical solution to. Analytical solutions provide extremely useful benchmarks for verifying and validating numerical solutions.

Re:That Moment

[MPAndonee]

We all had that moment in school when a teacher would pose an "impossible" problem, thought to ourselves "Well, they've never faced ME before!", spent a few minutes toying with it and finally giving up.

Not necessarily true.

I remember sitting in class, in High School, maybe Junior High, and asked such a problem, and being the only one in a class of 45+ able to solve it,

BTW, my solution was unique, as in, the teacher had never seen it before. So, yeah, what Shouryya Ray did was VERY IMPRESSIVE, but, solving problems at 16? My mind was very agile back then. I've lost a lot since then.

Re:That Moment

[__aaltlg1547]

Agreed. I'd much rather have an analytic solution, or even a formulaic approximation. Sometimes approximations are quite good and come in the form of an upper bound and a lower bound so you can calculate not only about the right answer, but an absolute limit on the error in the answer. It's quite common to find approximate solutions for problems with no (known) analytic answer that are very accurate for large x and others that are very accurate for small x. As an engineer, I'm reasonably satisfied with such a solution, but there's nothing like an analytic answer that's valid for all ranges of all the variables.

Re:That Moment

[__aaltlg1547]

I think the most impressive part is that even though we hear all the time about "X-teen year old invents BLAH" we're like "Great!" but secretly think "BIG Deal! Who can't invent something? How is that challenging, really? Oh look their dad's an electrical engineer that works at XYZ... hmmmm....." but this 16-year-old actually solved something that the best mathematicians on Earth haven't been able to solve for 350 years. Major kudos kid! Only way that can be topped is if a teen cures cancer, aids or doubles productive lifespan.

Major achievements in medicine are achieved more by sweat than brilliance and never by 16 year old kids because it takes years to carry out such the experiments and 11 year olds don't have the wherewithal let alone the permission to carry out biological experiments on humans. If a 16 year old cures cancer, we won't know it until he's thirty and then we'll wonder about the validity of any claim that he came up with the idea when he was 16.

Re:That Moment

[schroedingers_hat]

I meant trig tables.
Also I would be interested to hear a rebuttal rather than simply 'I disagree'. Perhaps the multiplication example was a bad one as it wouldn't hold you back much with, but I know how hard it is to follow an EM textbook written in component form (I managed to grab one written just after the turn of the last century).
I'd imagine trying to understand exponentiation, or differential equations using greek numeral notation or without any explicit concept of e or logarithms (you can still solve x' = x using series) would be similarly difficult and cause the same sort of difficulties that special functions (erf, bessel functions etc) cause (or worse) for many contemporary students.

Re:That Moment

[schroedingers_hat]

always notice the mistake after hitting submit: 'hold you back much with basic algebra as you could use small/integer coefficients'

Re:That Moment

[TheMathemagician]

Good luck getting your theorem prover to prove the Poincare conjecture. Why not prove the Riemann hypothesis too when you've finished. These proof checkers are useful for error-free symbolic manipulation but when a mathematician proves a new fundamental theorem it's not the proof which is important. It's the new tools/concepts he had to create to get there. As an earlier poster mentioned, teams of mathematicians have been working for years to break down and simplify Perelman's proof into simpler chunks. Also the "pathfinders" for a proof usually don't find the most elegant method and others (who couldn't have come up with the original proof) are able to simplify and improve it.

Re:That Moment

[jitenderkhurana]

can u pls share me the objective and puzzle solved by Shourya. I will be very thankful to you. I am new to this site so dont know much about its working. I did nt find even any way to send any msg to other users.

Re:That Moment

[Idbar]

Well, if there was an analytic solution to the integral of a Gaussian you wouldn't need these calculations you're talking about.

And even then having an analytical solution to the problem can give you clues about analytical approximations as well, which in turn would make the computations faster.

Re:That Moment

[treeves]

I disagreed because I assume , from what you wrote, that using trig tables for multiplication, is but one method of several that is taught, not the only method, and learning more than one way to do something is better than learning just one way, since it gives you flexibility, and you can pick the one that's best for you, and it just gives you insight into other things.
I admit I did not know about the use of trig identities to do multiplication that you linked to. That's interesting and I'm glad you taught me something!

Re:That Moment

[Thuktun]

I just wanted to say that I LOVE Coq.

Coq sucks.

Somehow, I think you have that backwards.

Not in Soviet Russia.

Re:That Moment

[Thuktun]

I suspect you're thinking of the brachistochrone problem, posed by Johann Bernoulli in 1696, and solved the next day by Newton (also by several other mathematical giants of the time, very quickly).

Sounds a bit like crowdsourcing to me.

Re:That Moment

[mr_mischief]

I can double the productive hours during your lifespan: get the hell off of /. ;-)

Explain the mind of a genius?

[Anonymous Coward]

Can someone who worked with geniuses and child prodigies before explain to me how their brains allow for learning calculus at 6?

Arithmetic at 1-2, Algebra at 3-4, basics of Calc at 5-6? What's the progression? It's not that I don't believe the guy, it's just that that is a rather large volume of information to pack into life, when there are basic skills like toilet training and such. I'm having a tough time imagining the time scale.

Now, if he said calculus by 10-11, I'd believe that. In the US, from K-12, almost all of it is repetition where you learn to add and subtract for the first month of every school year for some reason. If they cut out the crap for the smart kids, I could easily see calculus by 12 for competent kids. But 6? It seems difficult.

Re:Explain the mind of a genius?

[xtal]

Concepts of mathematics (calculus) are actually very simple.

Most confuse the trivia of solving problems (knowing many rules) and how to apply them with understanding of basic mathematical principles.

Teach your kid about 'x' and abstract thinking in relation to rates of change. The rest follows quite naturally. (IMO).

Re:Explain the mind of a genius?

[LingNoi]

With all these things the kid probably started at 6 and got it all wrong rather then claim to be able to understand it at 6. Otherwise I think he's full of shit.

Re:Explain the mind of a genius?

[Anonymous Coward]

Everything that precedes calc, besides trig, is super easy and a smart kid can soak it up in a few months.

Re:Explain the mind of a genius?

[dysan27]

I'll bet you that any 6 year old can solve the problem of where a ballistic projectile will be, even accounting for air resistance, in real time without a computer.

Don't believe me? Toss them a ball. The rest is just notation.

Re:Explain the mind of a genius?

[St.Creed]

10% is about the number going to university straight off high school where I live, so it's "smart kids" I think, and not geniuses. I'm pretty sure none in my yeargroup were geniuses, although there were some scary smart kids in the mix (and we were already a selection of less than 1%, doing a beta science study).

Re:Explain the mind of a genius?

[ebcdic]

No. The problem is to determine the trajectory from the initial position and velocity. A human tracks the ball as it moves, which is a completely different problem.

Re:Explain the mind of a genius?

[maxwell demon]

"If they cut out the crap for the smart kids, I could easily see calculus by 12 for competent kids. But 6? It seems difficult."

Last time I checked, the AP Calculus course was taken only by about 10% of high school students in the US.

So I would say that Calculus by 12 is something for geniuses, not simply "smart kids".

So if you learn something the majority of people doesn't bother to learn, you're automatically a genius?

Re:Explain the mind of a genius?

[2.7182]

I was not a prodigy, but a really smart kid who was in many environments with prodigies or near prodigies.

My experience has been that most pre-teen children with this history don't understand the material very well, and there tends to be a lot of exaggeration about it. Smart kids are good at mimicking things and that is all that is really need to "do" the first year or two of college math.

Occasionally, but very occasionally you get someone really young who later goes on to do decent, or even more rarely great things, like Norbert Wiener or Terry Tao. But I would like to hear those people give their opinions of the depth of their understanding at that age.

I knew Nadine Kowalsky, who in HS would essentially just remember everything she heard in class and got 100 on every exam. (She wasn't the only one though. I knew a number of other people like that though that didn't do as well as Nadine did.) She later went on to get a Ph.D. from Chicago and published her thesis in the Annals of Math. That is a journal most mathematicians can't get a paper in. Like publishing in Nature or Science. Nadine was the real deal, but sadly she died of cancer not long after finishing her Ph.D. But I don't believe that Nadine was doing calculus until she was 15. And that was certainly on purpose. She, and her parents apparently, knew what was a good idea to do, and not to do, with a super smart kid. (This last sentence is conjecture on my part.)

But I think most cases of pre-teens you hear about are really not what they are made out to be. Once you get to 12 or 13 those, I think things do change a lot.

Re:Explain the mind of a genius?

[Lumpy]

I was doing advanced Geometry and Algebra at age 8, yes I'm a slow fool compared to this kid. but it's mostly the quality of teachers (his dad) and the willingness to keep giving a kid what they want and challenging them.

The american school system is designed to DISCOURAGE this. Smart kids are told to be happy with the A they got without trying. If they challenge their teachers knowledge they are told they are wrong. Mostly because Grade-High-school education in the USA is simply following a lesson out of a book and not teaching it from an expert. the Gym teacher teaches computer class, The English teacher teaches Chemistry, and all of it creates a ho hum boring as hell experience for the children.

Here in the USA we do NOT want geniuses, we want good factory and office workers. Mediocre will not challenge authority.

yes I am jaded at the education system here. I was one of them that got bad grades because the teachers were idiots. I challenged my math teacher who could not believe that a kid can do multiplication and simple geometry in his head. I proved it on several occasions, but I was given failing grades for not doing the busywork of writing it all out. Plus I refused to learn his technique. It sucked and was harder than what I was using that came from college text books. So I ended up being a pissed off moody kid hating the education system because all I saw was idiots and morons trying to tell me they knew more than Me and I knew that they were wrong. I was reading at a 14th grade level when I was 12 years old. I read 1984 and understood the concepts and hidden meanings. I was devouring Vonnegut with a passion. I was told that the books were "too grown up for me" Everyone talked down to me and all it did was piss me off.

Sadly I did not have rich parents, so I had to suffer through the waste of time that the American Public School system is. College I slept through and aced it, at least they were not morons requiring me to turn in worthless busy work. It was in college where I ran into real education, educators that actually knew what they were talking about and would actually hold a discussion with me and help me learn more.

This is the problem here in the USA. If you are smart, you have a sack put over your head to slow you down to match the rest of the other students.

Re:Explain the mind of a genius?

[WCguru42]

Catching a ball is a feedback mechanism. See where the ball is, compare to where the ball was, move (hands or feet, depending on how far off you are). Repeat as necessary.

Re:Explain the mind of a genius?

[gremlinuk]

Of course it's a different problem.

The first is a prediction from a known initial state, the second is an exercise in analytical approximation that just means you have to get your hands to reach the same position in space and time as the ball, based upon a continuous stream of information of ever-increasing accuracy about the relationship between said hands and the ball over time.

Wildly different exercises.

Re:Explain the mind of a genius?

[russotto]

Concepts of mathematics (calculus) are actually very simple.

Most confuse the trivia of solving problems (knowing many rules) and how to apply them with understanding of basic mathematical principles.

This isn't just integral calculus, though; it's differential equations. Finding an analytic solution to a nonlinear differential equation is often difficult, sometimes (provably) impossible.

Re:Explain the mind of a genius?

[xtal]

The principles of differential equations are also simple and there are many simple physical systems that can be used to demonstrate them in a way that is easy to grasp. Even by relatively young children.

The idea is not to confuse the understanding of principles with their applications, as those can be (and are) horribly complex.

Math is not hard. Math is very elegant and simple. Much like language, the same words that are in children's books also comprise the classics.

Re:Explain the mind of a genius?

[drinkypoo]

Here in the USA we do NOT want geniuses, we want good factory and office workers. Mediocre will not challenge authority.

I've shared this and I'll share it again (and again...) but when I was in third grade I had an asshole, authoritarian teacher who I believe was only at my school for a couple of years. He was a lazy, arrogant, abusive asshole. When one was done with one's work one was to literally lay one's head down on one's desk and wait quietly for the other children to finish. I was in trouble on numerous occasions for "looking at the other children". I wrote so many lines I had wrist problems before I ever owned a computer or even discovered masturbation.

Sadly I did not have rich parents, so I had to suffer through the waste of time that the American Public School system is.

I went to a private school for a couple of years, before my parents broke up and there wasn't enough money because my dad was a deadbeat. I was about to be learning algebra, I was learning Spanish (I had great retention back then, and I never forgot some of the words I learned back then... though "ferrocarril" does have a fantastic ring to it, no?) and so on. Then I was placed literally into kindergarten due to my age and went from actually learning at a satisfying pace to being told lies about American colonization, making flags out of construction paper and placing Dead-President's-Head's stickers on them, and the like. After a year of that I spent two weeks in first grade before being bumped up to second, where I was still doing work inferior to what I'd been doing in my previous school.

This is the problem here in the USA. If you are smart, you have a sack put over your head to slow you down to match the rest of the other students.

Especially if you are smart, but your parents are dysfunctional and can't teach you how to blend in because they know fuck-all about how social situations work.

College I slept through and aced it, at least they were not morons requiring me to turn in worthless busy work.

Alas, I discovered life about the same time I went to college for the first time and besides, by that time I was prejudiced against education. What really shat upon my educational aspirations at that time, though, was a counselor who suggested I take a fully practical case load and save my electives for later. If I could remember who that was, I would send them a picture of my asshole right now. Hated it. Made school just a big bore of a chore. Most counselors don't give one tenth of one fuck about you as a person or even as a student, you're just a convenient unit that can be used to fill out slightly empty classes. What, am I bitter? Why do you ask?

Now I have a two-year degree from going back to school much later, but it wasn't convenient for me to matriculate to a four-year at the time and now what do I do with this extra piece of paper? It's too crisp to be good bumwad.

Re:Explain the mind of a genius?

[mikael]

Path of a projectile at the Earth's surface without air resistance in a uniform gravitational field is a parabola (or quadratic curve). Go into Earth orbut and you also get ellipse curves.

Air resistance would slow horizontal and vertical velocity by a fraction per unit of time, so I would guess that it is an integral of a power sequence.

Re:Explain the mind of a genius?

[2.7182]

Yes, it is a venerable math joke you've made. I've been hearing colleagues call it the Anus of Mathematics for 30 years now. It does publish great papers, but does require something of a personal connection to get into. Something remarkable you don't hear about in the press ever. Same for The Proceedings of the National Academy of Sciences, and a few others. But no big deal now. The internet is a great equalizer, although you'll get a better raise if you publish in the Annals, or better job offers.

Re:Explain the mind of a genius?

[Dolphinzilla]

I have to agree with your comment about learning DE, I failed differential equations the first time I took the class (a D-grade) I was taking engineering course work at the time that required them - and what they actaully "meant" clicked in an electrical networks class - when I took the class again (my university had a 1 time grade forgiveness policy) I got an A - it seemed trivial and simple the second time around in a different context. I general I have mathematics makes mroe sense to me personally when I can relate it to a real world problem - Mathematics taught as rote learning is a horrible thing - some of us can't do it that way....

Re:Explain the mind of a genius?

[TheDarkMaster]

"Here in the USA we do NOT want geniuses, we want good factory and office workers. Mediocre will not challenge authority."

Exactly. And I tell you, is the same thing here in Brazil.

Re:Explain the mind of a genius?

[the gnat]

...it does publish great papers, but does require something of a personal connection to get into... Same for The Proceedings of the National Academy of Sciences

Actually, this isn't so true of PNAS any more. One of the previous editors decided in the late 1990s to raise the quality prestige of the journal by accepting more papers through a traditional peer-review route, as opposed to NAS members "communicating" or "contributing" articles (which would often have minimal peer review). This was very successful, and now most articles in PNAS get in through the front door, and they're slowly eliminating the back doors. The overall quality is pretty good - not as high-impact as Science or Nature or some of the top specialty journals, but it's definitely a journal that researchers are excited about publishing in if they can't get into the top tier. The fact that they're not part of Elsevier or one of the other big commercial publishers, and their open-access fee is very reasonable, is an added bonus. (Disclaimer: I've published there, so I'm not entirely unbiased.)

Now, as with any journal, knowing the right people always helps - sadly, this is true at any level.

Re:Explain the mind of a genius?

[plover]

Exactly. As a kid, I had a dog that understood when I threw a ball up on the roof of our garage, which caused it to disappear from her sight, that it would roll along the slope of the roof and and reappear further down the roofline. She actually got fairly good at predicting where the ball would reappear, repositioning herself along its path over time so she would meet it at its eventual drop point. Does that mean my dog understood calculus, or solved Newton's problem? Well, she recognized a pattern and was able to apply a repeatable solution.

That tells me that the brain is capable of recognizing complex patterns around us, and is actually already very capable of deriving and applying practical solutions. ("So easy a dog could do it.") Applying abstract mathematical models to them, however, is not so easy.

What I'd be most interested in in this whole saga is "what methods did his father use to teach him math?" Obviously they were highly effective.

Re:Explain the mind of a genius?

[plover]

I have evidence to the contrary. As I posted above, I had a dog that would watch me throw a ball onto a sloped roof, where it left her sight. It then rolled along the slope of the roof in an arc and returned to sight a few seconds later, further down the roofline. She became quite good at positioning herself under the spot where the ball would eventually reemerge and drop to her.

It obviously doesn't mean she understood the calculus or formal proofs. It does demonstrate that mammalian brains are capable of taking in some facts of movement and making predictions based on them. It's not all that surprising in a dog. They are descended from animals that hunt cooperatively in packs, where they learn that some of the pack will drive prey out, and others know to run ahead to where the prey will likely flee to, even though they aren't always following them with their eyes.

Re:Explain the mind of a genius?

[plover]

Yes, I'm much more interested in the story of how his dad taught him so well and effectively than I am in the solution itself.

And while I'm sorry you had such a crappy experience in public school, you might be heartened to know that not all public schools are equally horseshit as the ones you were unfortunate enough to attend. We have some absolutely stellar schools around us here, with teachers that actually care, and they try hard to challenge the kids to reach above their "expected potential". Not every school, mind you, but many of the ones in our district are excellent. I think it helps to have schools large enough to have multiple classes per grade level, which means they can offer a whole class or two of remedial addition to the kids who need that, several classes of algebra and trig to the majority of students, and a class of calc 1 and calc 2 to the kids who want that challenge.

Sadly, I know that your story is far too common. I have a friend who grew up in California public schools, then due to family circumstances had to take his senior year of high school in a Kentucky school. He went from an 11th grade pre-calc class to basic math in 12th grade, complete with scarily stupid students and teachers. (I don't know where in Kentucky he was.) With no challenges in school, (and suddenly being dropped into a foster family situation,) he found himself in the classic teenage rebellion scenario, and discovered plenty of ways to get into trouble. It was fortunate for him that he had only one year to suffer through the bad school before he got into a college, which certainly helped him get his life back on track.

Private schools aren't always the answer either, by the way. There are some well known parochial schools around here that deliver some pretty mediocre educations.

So my advice is don't judge all public schools based solely on your own experience. Like most other things in life there are good ones and bad ones out there, and any responsible parent needs to be very selective where their kids go.

Re:Explain the mind of a genius?

[tomhath]

Most confuse the trivia of solving problems (knowing many rules) and how to apply them with understanding of basic mathematical principles.

I wish I had mod points for you. IMHO, the biggest problem students face when learning mathematics is teachers who don't really understand the basic principles (or don't know how to teach them), so instead they spend weeks and months teaching and testing boring trivia.

Re:Explain the mind of a genius?

[abigsmurf]

The number of times I read rants against (maths) teachers for holding back students and then halfway through it they drop "just because I don't show my working!" bombshell.

Teachers are doing this for your benefit, not theirs. If you can hand in your homework with just the answers and get them all correct, great, but if you hand in the homework and get some wrong, the teacher won't have any idea where you went wrong, whether you used the wrong method when solving it or if you just made a simple error with the arithmetic. 99.9% of kids, even the ones who think they don't need to show their working because they know to do it, will at some pointstruggle with something and need help.

The UK exam system drills this into you pretty early, only 1 mark out of 3 or 4 being awarded for the correct answer, the rest being awarded for the method used. By the time you get to A-level (High school) maths, you're even given the answer beforehand and asked to "show that x = 5".

Ultimately the working out is usually more important in maths than the answer. You won't win a Fields medal for "Fermat's late theorem : it was correct. The end"

Re:Explain the mind of a genius?

[acid06]

I'm also from Brazil and I share the feeling... sadly, I think it's the same thing everywhere in the world.
I guess we're entering the next Dark Ages of knowledge...

Re:Explain the mind of a genius?

[ChrisMaple]

No criticism of you, I also failed to realize that I could educate myself if I chose to do so. For a bright, ambitious child with access to an adequate library, teachers are superfluous.

Re:Explain the mind of a genius?

[mattpalmer1086]

I think that you're absolutely correct in that mathematics requires some kind of actual grasp of the relationships being expressed by the maths.

For you it had to be something you could relate to a real world problem. I'm almost the opposite - I have to get something distilled down to pure abstract relationships before I feel I really get it. But either way, you have to do some work and understand what is being expressed by the maths.

I studied cryptography a while ago, and I had some difficulty working through the maths. I got really stuck at one point in the course material and had to ask for help. The professor responded that they'd fudged that part of the maths a bit to avoid confusing people, and they didn't think anyone would get that far into the maths. He also gave a perfectly clear explanation of the source of my confusion - providing the missing bit of information about the relationships involved in the math.

I was left amazed at the realisation that most people pass this stuff without actually understanding it in any real way.

Re:Explain the mind of a genius?

[JeffAtl]

A major league outfielder (baseball) can determine where the ball is going to land without having to constantly adjust. He still has to visually track it to make fine adjustments since it is relatively small and very fast moving - just arriving at the spot wouldn't be enough to catch it. Visually tracking also allows correction for dynamic atmospheric conditions.

A basketball player is also able to predict with very close precision where his jump shot will land.

Re:Explain the mind of a genius?

[JonySuede]

I never learn how to do it manually, but I did understand i:.
At that time I was in an EE school where a TI-92 was mandatory, the teachers selected problems unsolvable by the analytic solver of the calculator but solvable if you applied theirs successive discriminants method. I therefore implemented the techniques and outputted the reasoning and the text I had to wrote to answer to those questions. It took me 15 minutes to finish the exam. The professor surprised by the time I took to complete his 3 hours exam, took a red pen out of his pocket and to his sad surprise everything was right; there was no red on my answer sheets.

He asked me how I accomplished that. I then told him about my software and he then said that I should really consider leaving EE for CS and asked me not to copy my program as it would require the university to redo a big part of their curriculum. I kept my end of the deal and he was right as I eventually got bored by EE and I effectively went into CS a year later...

Re:Explain the mind of a genius?

[funfail]

1- I asked that stupid bitch what is be the length of the the hypotenuse of a triangle that have a 45 degrees slope, a side measuring 3cm and a side measuring 4cm, the answer is evidently 5cm...

This is an impossible triangle.

Re:Explain the mind of a genius?

[Deadstick]

being humiliated by the dumb bitch teaching to 1st graders who thought that I was retarded.

If you told her you could get a 45-degree slope on a 3-4-5 triangle, perhaps she was onto something.

Re:Explain the mind of a genius?

[dcollins117]

A basketball player is also able to predict with very close precision where his jump shot will land.

... unless they've played for the Charlotte Bobcats...

Re:Explain the mind of a genius?

[Rich0]

I wrote so many lines I had wrist problems before I ever owned a computer or even discovered masturbation.

I hear you, but the one nice thing about growing up just at the dawn of the personal computing age was that I asked my teacher if I could type my lines instead (on the computer), and they said, "sure." Ah, Command-V on a 128k Mac running MacWrite...

Re:Explain the mind of a genius?

[brillow]

I think you're right. Mozart was not a genius, and arguably not a prodigy. He was however raised in a house of means by the greatest musical pedagogue of his age who started teaching him music before the kid could talk. I've been teaching long enough (and not very long at all) to realize that any kid could be taught to do these things if they were raised in a stable home and taught intensively for many years. This kid doing this is no more impressive to me than 13 year old Chinese kids on the pommel horse. Any kid can be turned into a highly talented person (in a more or less limited skill-set) if they are given a lifetime of intensive and focused education in a healthy and stable environment.

There are drawbacks though, as the kids immense mathematical powers came at the cost of good judgement in the area of facial hair.
http://www.vip.it/wp-content/uploads/2012/05/Shouryya-Ray-256x300.jpg

Re:Explain the mind of a genius?

[dbIII]

I was doing advanced Geometry and Algebra at age 8

Martin Gardner's puzzles in old copies of Scientific American got me to that point as well (and I'm definitely no genius and had to work hard at University), approached the correct way a lot of things are simple enough for an interested 8 year old to understand. I was luckier with the education system (a public system far better funded than the US ones) and most of the teachers were prepared to actively challenge students that had passed beyond the coursework so that nobody sat around bored for too long. For example, the "fast" kids in grade 7 were sent down to the remedial classes to help other children with their reading, which also had the side effect of improving their ability to read aloud. Some classes of course sucked and the way calculus was taught just did not work.

Re:Explain the mind of a genius?

[dbIII]

Not many people are "self-starters", and most that are got some inspiration to be that way from somewhere. Also you have to know where to start and get some breadth of knowlege instead of just the details of that one cool thing.

Re:Explain the mind of a genius?

[chrismcb]

Concepts of mathematics (calculus) are actually very simple.

Teach your kid about 'x' and abstract thinking in relation to rates of change. The rest follows quite naturally. (IMO).

Sure, if you can figure out the "relation to rates of change" thing, then calculus is simple. BUT that is the hard part. That is something most people just can' grasp.Shoot most people have a problem grasping the concept of this 'x' thing, let alone its derivative. Throw in the fact that a derivative is different than most everything else you've learned in math, and it becomes a difficult concept.
The same way pointers are beyond most peoples understanding. If you understand it, its simple. But getting someone to understand it is the hard part.

Re:Explain the mind of a genius?

[chrismcb]

Here in the USA we do NOT want geniuses, we want good factory and office workers. Mediocre will not challenge authority.

Life isn't a big conspiracy theory. I had some great public teachers that tried to push my. The problem isn't that USA doesn't want geniuses, the problem is having the resources to deal with them. You have 35 students to teach, who will teach, the 1 or 2 at either end of the bell? Or the 25-30 in the middle of the class?

Re:Explain the mind of a genius?

[chrismcb]

Teachers are doing this for your benefit, not theirs.

They are doing this to make sure you don't cheat. My teachers told me to "show my work." "I did!" I wrote down everything that needed to be written down... Or I would solve it a way differently than I taught it. "Well how do we know you did the work?" Uhmmm perhaps because I scored the highest score on the annual national math test? Who else am I going to copy from?
It wasn't about helping you... it was about making sure you didn't cheat.

Re:Explain the mind of a genius?

[treeves]

Mozart's ability to compose was not something he got from Leopold, although perhaps playing the piano was. How many of Leopold's compositions have you heard? Not one of them comes close to what Wolfgang would do. True that would not have had the chance to develop without the his father's push to make him a great pianist. But many have been pushed to play the piano by their parents and how few have gone on to compose anything like the 41st Symphony.

Re:Explain the mind of a genius?

[tehcyder]

Mozart was not a genius, and arguably not a prodigy.

Well, if he wasn't then neither has anyone else ever been.

Re:Explain the mind of a genius?

[tehcyder]

I was one of them that got bad grades because the teachers were idiots.

Yeah, we get a lot of people like you on slashdot.

It arises from a combination of high intelligence and Asperger's, which means basic social skills like not annoying your fucking teachers by being a smart arse are absent.

Re:Explain the mind of a genius?

[tehcyder]

No criticism of you, I also failed to realize that I could educate myself if I chose to do so. For a bright, ambitious child with access to an adequate library, teachers are superfluous.

Yes, because the world's biggest library (the internet) has produced an abundance of self taught geniuses.

Re:Explain the mind of a genius?

[tehcyder]

Teachers are doing this for your benefit, not theirs.

They are doing this to make sure you don't cheat. My teachers told me to "show my work." "I did!" I wrote down everything that needed to be written down... Or I would solve it a way differently than I taught it. "Well how do we know you did the work?" Uhmmm perhaps because I scored the highest score on the annual national math test? Who else am I going to copy from? It wasn't about helping you... it was about making sure you didn't cheat.

I'm sure your helpful and cheerful attitude won you many friends and admirers amongst the staff.

Re:Explain the mind of a genius?

[drinkypoo]

We've all got it hard.

Yeah, you're so broke you can't afford to log into slashdot. I feel for you man, here's a quarter, get a nickname.

Re:Explain the mind of a genius?

[sco08y]

I'll bet you that any 6 year old can solve the problem of where a ballistic projectile will be, even accounting for air resistance, in real time without a computer.

Don't believe me? Toss them a ball. The rest is just notation.

They don't have a general solution. Most small kids will have trouble catching a pop fly.

But by your measure, they also have such a solid understanding of linguistics that they can parse a sentence and compose a grammatical sentence in response, on the fly.

The human neuroskeletal system has some heuristics that are a substantial partial solution to that class of problems. In particular, how to recognize a parabolic arc. Training allows one to develop a technique to "cover" a projectile coming in from further away such that the parabolic arc can't be determined.

The rest isn't "just notation", it's application to other domains.

And you can see that, even without getting into notation, they can't apply the solution more generally. Most 6 year olds would have trouble, for instance, even teaching another person how to speak or catch a ball, beyond their built-in instincts to play and socialize. And it's only years of study before someone can become an effective baseball coach. And if you want to beat other teams, you probably need specialists who have really studied ballistics and medicine so that they can develop better techniques for catching projectiles.

Re:Explain the mind of a genius?

[sco08y]

Absolutely, the method *is* the math. You're also required to show your work to prevent cheating, which is what most ranters are probably doing.

Re:Explain the mind of a genius?

[qu33ksilver]

Just one question- What do you do now ??

Re:Explain the mind of a genius?

[gl4ss]

I guess playing piano would fit to what you described.

but Mozart did a lot more than just playing piano, since the reason people remember Mozart is mainly instructions on what to play on a bunch of instruments. You can train "any kid"(not true either btw) to play Mozarts compositions but it's pretty hard to train anyone to compose his material.

the picture looks pretty unreal/weird.

Re:Explain the mind of a genius?

[shadowofwind]

I'd be surprised if the dog couldn't hear the ball rolling on the roof. Not that a dog wouldn't be able to do that trick without that, it makes it a lot easier.

Re:Explain the mind of a genius?

[AnonyMouseCowWard]

You know, most of it is not because of your education system, but because of your parents/environment?

I also was doing algebra at age 8. How many schools, or school systems, teach that at that age? It's not an American problem at all. The fact that kid was taught calculus at age 6 only means he had great parents, and there is no way he was taught the math necessary for solving his problem in school.

Now granted your school experience might have sucked, and having to apply and write down a technique for multiplication that you can do in your head is annoying, but that is also the point of giving you an education. Sure, the school system wants to produce good workers... because good workers fit in the society. If you were able to understand it, why wouldn't you apply it? Because you had a better way? What's wrong with understand the "bad" techniques? If you are open to understanding _all_ possible methods, that means you're a bright and intelligent person that is a curious about the world, in other words, someone worth teaching to. If you go back to your shell because you think you're special... well, that failing is yours, not the school system's.

If you want your school system to cater to the top 5%, or the bottom 5%, consider attending special schools. If you don't have the money, consider learning on your own, like that Shouryya Ray kid. The public school system is there to make sure everyone is given a fair chance and a standard basic education, not for the geniuses to have special treatment.

Now, on the other hand, if you want to start a debate on how to improve on the education system, let me propose a starting point: use tiers for public schools, with admission exams. Top students get into the top tier, but all schools are funded publicly. Would that work for you?

Re:Explain the mind of a genius?

[the gnat]

I was under the impression that you paid PNAS to publish your work because it was shit that you couldn't get published in a real journal.

This was very frequently true until the last decade or so. In fact, there were always some very good papers in PNAS, but there was also a lot more junk. Peter Duesberg, probably the most famous (and most reputable, until he went crazy) scientist to argue that HIV does not cause AIDS, is (or was) notorious for contributing an article to PNAS every year - since he was already an NAS member since the 1980s, they had to let him publish there. Since the editor who made the switch to direct submission, Nick Cozarelli, was a colleague of Duesberg's at Berkeley, I wouldn't be surprised if there's a direct link here.

Anyway, if the article says "communicated by" or "contributed by", that means it got in through the back door. Not all of these articles are crap, but many don't deserve to be there. According to the PNAS web site, 90% of articles submitted, and 79% of those published, are direct submission. I believe the "communication" route is now closed, but it is still possible to contact an NAS member directly and ask if he/she is willing to be an editor, in which case the footnotes will mention that the editor was "pre-arranged". The difference from before is that the peer review is more rigorous and the editorial board has veto power. I've done it both ways (as a minor co-author), and while I'd obviously feel better about getting in the front door, I can understand why we went directly to an NAS member in one case. Academic politics is a bitch.

Re:Explain the mind of a genius?

[Carnildo]

The american school system is designed to DISCOURAGE this.

No, it just sounds like you got some crappy teachers. There are some reasons why there are more crappy teachers around than they should be, but it is not some scheme to hold back smart people. The administrators don't sit around saying, "Gee, we aren't doing enough to hamper smart kids,"

No, it's designed to discourage this. By testing out of a couple of math courses and then taking Algebra II and Geometry at the same time, my younger brother completed the school district's highest-level math course (Advanced Placement calculus) in 10th grade (thus forcing the school district to pay for two years of university math instruction). The next year, the school district changed the prerequisite structure in the math program to make it impossible to take AP calc before 12th grade.

Re:Explain the mind of a genius?

[CSMoran]

No criticism of you, I also failed to realize that I could educate myself if I chose to do so. For a bright, ambitious child with access to an adequate library, teachers are superfluous.

Yes, because the world's biggest library (the internet) has produced an abundance of self taught geniuses.

It hasn't, but doesn't this simply reflect small numbers of "bright, ambitious children"?

terrible article

[Anonymous Coward]

The article itself is mathless. It doesn't tell you what the solution was, or even present the exact problem that was solved.

Re:terrible article

[sco08y]

The article itself is mathless. It doesn't tell you what the solution was, or even present the exact problem that was solved.

And running a search for the kid's name turns up the same article fifty fucking times over. Google did some work on link farms... they need to do some work deduping / despamming press releases.

Re:terrible article

[johnsnails]

Yeh Im sorry about the article, thats why i submitted to /. wanted other people to weigh in on the discussion, and maybe find some better links.

Re:terrible article

[Anonymous Coward]

With all due respect to this brilliant student, I wouldn't worry too much about that - the problem isn't actually solved until its been peer- reviewed and thd other mathematicians agree that his approach is correct.

Re:terrible article

[PolygamousRanchKid]

The answer was 42 . . . now what was the question?

Re:terrible article

[Anonymous Coward]

Indeed. The German title of his work is "Analytische Lösung von zwei ungelösten fundamentalen Partikeldynamikproblemen", and his Wikipedia (!) article says something about linear damping and collisions, but I have not been able to find his "paper", neither of the homepage of his school nor anywhere else. It almos seems like there is something to hide.

Re:terrible article

[TapeCutter]

News.com is one step away from the onion, in the wrong direction.

Re:terrible article

[ObsessiveMathsFreak]

You are right. This article is awful, conveying no sense of the nature of the problem or its complexity, and giving no idea of the solution at all.

The only equations I'm aware of for a falling particle subject to air resistance take the form

m v' = -mg -a*v-b*v^2

which is a constant coefficient Riccati differential equation for the velocity v. I'm reasonably sure this would have an analytic solution.

Maybe complications arise in the 2D motion case, or perhaps the problem includes a particle which is also spinning. Maybe the drag terms take more complicated forms. I don't know. The article is pretty dreadful to be honest.

Re:terrible article

[Smurf]

That's "Analytische lösung von zwei ungelösten fundamentalen Partikeldynamikproblemen" or, in English, "Analytical solution of two fundamental unsolved problems of particle dynamics".

But that doesn't seem to be a paper published in a peer-review journal, but rather the title slide of a presentation he gave on March 1, presumably when when he received the Jugend Forscht ("Young Researchers") award.

And the kid is Indian, not German (as long as we can tell from the article).

And this is a problem in Physics, not in Mathematics. It shocks me that people get that mixed up.

And the kid looks 30 years old, but I would never hold that against him.

Re:terrible article

[jairob]

How does Slashdot accept such a crappy post?!

Re:terrible article

[TubeSteak]

Google did some work on link farms... they need to do some work deduping / despamming press releases.

Google News has a decent deduping system going on.
Google Search... not at all.

Also, the kid's name is Shouryya Ray
Not Shouryya Ra[missing letter here]

Re:terrible article

[ralphdaugherty]

How does Slashdot accept such a crappy post?!

I believe they welcome this stuff with open arms, and add an obscure summary with sensational headline to boot.

And slashdotters tear it aprt even while complaining. Win-win for everyone.

Re:terrible article

[AmberBlackCat]

Perhaps Google should index the three sources every news site gets its articles from, and filter out all of the copies on sites who buy their articles.

Re:terrible article

[Anonymous Coward]

The one dimensional equation given does have an analytic solution (and in fact it isn't very hard, just a little intricate to integrate).

As you rightly suggest, it is the two dimensional problem that is a lot harder. As far as I know there is no exact solution; though perhaps Mr. Ray has found one. Indeed, Herman Goldstine in his magisterial "The Computer from Pascal to von Neumann" states that the reason why Americans during the war worked on computers was primarily to find solutions to this problem, so that artillery could be properly aimed.

Re:terrible article

[Asic Eng]

It's possible that he has dual citizenship, but that seems unlikely given that he only arrived in Germany 4 years ago and didn't speak any German at the time. 4 years would be a bit short for him to receive citizenship otherwise.

None of the German newspaper articles I found refer to him as German, so I'm inclined to think it's simply an error in the article.

Re:terrible article

[Anonymous Coward]

This isn't just your ordinary "kid solved fundamental problem" article that you see every other month. This is the politically correct version, implying that diverse (a.k.a. non-white) immigration is good for non-diverse countries. Really, I'm surprised that people on Slashdot are criticizing it. Looks like political correctness is finally falling apart.

Re:terrible article

[jordan314]

I was pretty disappointed that Slashdot wouldn't find the equation for this. I ended up finding it on reddit: http://www.reddit.com/r/worldnews/comments/u7551/teen_solves_newtons_300yearold_riddle_an/c4sxd91

Re:terrible article

[equex]

r/askscience is probably a place most slashdotters wanna go when they've read all the slashvertisments.

Re:terrible article

[sco08y]

Yeh Im sorry about the article, thats why i submitted to /. wanted other people to weigh in on the discussion, and maybe find some better links.

I think it was a fair submission. I'm just annoyed at the copy-pasta policies of many news outlets.

I thought these were pretty much known already

[us7892]

I did not know that the two problems described were unsolved. I thought that "how to calculate exactly the path of a projectile under gravity and subject to air resistance" was already figured out. I guess "exact path" is the trick here. An the other about an "object striking a wall"...

Should make for even better gaming physics...

Re:I thought these were pretty much known already

[Anonymous Coward]

There is no problem solving the equations numerically. This kid found analytical solutions to the equation of motion (or at least, that's how I read TFA). Punching in the exact solution is faster and more accurate than taking a zillion small but discrete steps, which is what you're stuck doing right now. Well, that depends on the complexity of the solution, but as a general rule...

Re:I thought these were pretty much known already

[Lord_Jeremy]

I'm slightly confused as well. In my high school AP calculus-based physics class we did projectile motion with air resistance and gravity at the beginning of the year. In fact, my teacher used that particular topic to "weed out" the students that probably wouldn't be able to handle the remainder of the course. He taught the material way above the actual AP requirement and make the topic exam so hard that a few kids switched into the lower-level physics course afterward.

Re:I thought these were pretty much known already

[Lord_Naikon]

Finding out where a projectile lands given a certain initial angle and velocity is a lot easier than finding out at what angle to shoot given a certain destination and velocity. I guess he found out how to do that because I was unable to solve it myself (when the total force on the projectile is dependent on its velocity).

Re:I thought these were pretty much known already

[Anonymous Coward]

You forgot a lot of things:
-gravity is not a constant vector force downward. It is a radial force inward toward the center of the Earth, and its intensity varies with altitude.
-air resistance is not constant either. It depends on air pressure which varies with altitude as well.
-air resistance is not perfectly proportional to v^2, especially at transonic and supersonic speeds.
-if the projectile is spinning, it may cause a net aerodymamic force in a direction other than -v. Like a curveball.
-the earth is a spinning frame of reference, which results in various annoying effects.
-the air is not necessarily stationary. Wind exists.
and so on.

But we don't know whether this dude accounted for any of this stuff or not, because the goddamn article doesn't tell us.

Re:I thought these were pretty much known already

[Sique]

You forgot that not only the length but also the direction of the resistance vector is changing, depending on the velocity.

Re:I thought these were pretty much known already

[maxwell demon]

Yeah, since when weren't there already precise analytical solutions to this? Gravity is a constant vector force downward, air resistance is proportional to the square of the velocity and opposite to that direction, plug it all into f=ma and you get

mg{0,0,-1} + -k((d/dt)x)^2 = m(d^2/dt^2)x

where x is position vector. Express x as a function of t, set initial conditions from starting velocity, integrate and yer done. Have I forgotten something? (It has been a while...)

You've forgotten to actually give the analytical solution to this differential equation.

Re:I thought these were pretty much known already

[Lumpy]

"-gravity is not a constant vector force downward. It is a radial force inward toward the center of the Earth, and its intensity varies with altitude."

for any calculations on a scale less than 10 miles, assuming a constant will give you the same answer within a margin of error that is outside the ability of any store bought calculator.

Re:I thought these were pretty much known already

[Brett Buck]

All of which is very well known and (nearly) trivial to simulate. I presume what he did was come up with a *closed form* solution.

     

Re:I thought these were pretty much known already

[Impy the Impiuos Imp]

Because it's freakin' cannon balls. I don't know about you, but I'm concerned on a scale less than ten miles.

Re:I thought these were pretty much known already

[WillHirsch]

You appear to be unaware what the word analytical means.

It's a problem where you plug in the initial numbers and out pops the answer. You don't need to do integration. a+b=c.

A differential equation finds an approximation which may be very very close, but it is not an analytical solution.

You appear to be unaware what the word solution means (hint: it's not a problem).

Re:I thought these were pretty much known already

[Exoman]

Interesting timing. I was just talking with my wife about how amazing it is that a 10 or 11 year old kid in the outfield can solve this problem in the outfield in the moments after a ball is hit, and then run to that position to catch the ball. There is a lot of correction happening until the catch, but the main calculation is pretty quick. Also note that most kids step IN as their first reaction, even when it's going to be over their heads, but the good ones do not, and they track the ball amazingly well.

This includes top & bottom spin, lateral spin (slice & hook) on the ball, and other interesting complexity. While the visual pickup and transfer to the computer are very difficult for a computer, it is bordering on trivial for a competent ball player.

Re:I thought these were pretty much known already

[Lumpy]

Funny, I find anything on a Macro Scale to be boring and predictable.

Re:I thought these were pretty much known already

[fahrbot-bot]

for any calculations on a scale less than 10 miles

Of course, many, many uses for extremely accurate ballistic equations are on a scale exceeding 10 miles... For example, the 16 inch guns on WWII battleships had a range of 26 miles.

Re:I thought these were pretty much known already

[copsi]

Solving that differential equation analytically (as opposed to numerically) will yield an analytic solution to this problem. Also, accounting for the initial conditions is part of solving an equation. A differential equation itself does not give an answer (neither exact or approximate) - you have to solve it using some method (which can be exact, approximate or numerical).

The right hand side of the closed form solution might also include integration (eg if there are some integrals which cannot be represented using elementary functions), infinite series etc and it would still count as an analytic solution (although I suppose it depends on the exact definition of "analytic solution"), even though evaluating it for some particular point in time (in this particular case) can not be done exactly (you would have to numerically evaluate the integrals etc).

Granted, as has been pointed out, GP has not provided us with an analytic solution to that equation.

Re:I thought these were pretty much known already

[JeffAtl]

The OP was referring to the altitude of the shell, not its range.

Re:I thought these were pretty much known already

[JeffAtl]

Many of those cannot be accounted for though.

Atmospheric conditions such as gusts of wind and air pressure are not exactly knowable at the moment the projectile will encounter them. Any solution would have to assume some level of uniformity.

Specifics?

[Rie Beam]

Can anyone actually find the problems in question somewhere? I've been scouring Google and the whole thing is very vague -- no story really goes into depth about the actual problem he solved and how.

Re:Specifics?

[Neil_Brown]

I've been scouring Google and the whole thing is very vague - no story really goes into depth about the actual problem he solved and how.

Looks like he's just invented the recursive puzzle!

Re:Specifics?

[Slippery_Hank]

The problem he solved is determining the exact path of a projectile, when accounting for air resistance. The drag coefficient for air resistance depends nonlinearly on velocity, so when it is included in the model the equations become difficult to solve (previously impossible, but apparently now done. Though I haven't found any links to his actual work). Here is an example of setting up the problem, and then solving it numerically.

Re:Specifics?

[HeLLFiRe1151]

This is an article from 1983. I believe it explains the problem.

http://www.annualreviews.org/doi/pdf/10.1146/annurev.fl.15.010183.000245

Re:Specifics?

[St.Creed]

Yes, a link hidden by a redirector posted by an anonymous account... what could possibly go wrong if I clicked it?

Re:Specifics?

[maxwell demon]

If you have the right extensions installed, nothing — by clicking on it you'd see that it redirects to Slashdot, and can decide to follow the link ...

Re:Specifics?

[black3d]

Is it wrong that I found page 15 arousing?

Re:Specifics?

[loom_weaver]

Here's a post where someone determined what the original equations were and verified Ray's answer (in the picture of him holding a solution) in Maple:

http://www.reddit.com/r/worldnews/comments/u7551/teen_solves_newtons_300yearold_riddle_an/c4szejb

Re:Specifics?

[FrootLoops]

Is it wrong that I found page 15 arousing?

Only if you're gay. (Seriously, the pictures look like boobs and such.)

Re:Specifics?

[Sqr(twg)]

Thank you for this! So to summarize (assuming this is his solution. I'd still like a link to something written by him that includes the equations.)

He considered the 2-dimensional problem of a projectile under influence of gravity and a frictional force that is proportional to the square of its speed.

He "solved" it in the velocity (u,v) plane. To get the (x,y) trajectory you'd have to integrate in time (which would be tricky because you don't have u and v as functions of time, see below).

The "solution" is a function f(u,v) that is constant on the trajectory. It does not tell you u(t) or v(t). In fact, t is not in f. Nor does it give you an expression for u(v) or v(u), because f can't be inverted analytically. For any of that, you still have to do numeric calculations.

Difference between Germany and the US

[Anonymous Coward]

German media praise math geniuses, while american media praise hollywood actors/actresses (read: human rubbish) and reality show weirdos. In the US a "genius" is someone who makes millions, especially with lower education and without being able to do anything. That's "free market economy", and "supply and demand", right?

"The land of the free and of the brave" (with some fat on the belly).

Re:Difference between Germany and the US

[wealthychef]

"In fact, neuroscience and psychology points the opposite direction: happiness leads to success. If we could grasp that one fact we'd all be better off."

That's philosophy. Let's stick to the facts: what can a math or physics genius become in the US? Maybe a university professor, making 100-150 K$ a year. Or maybe the R&D leader of a major company, but the salary would be nearly the same, the only way to get "rich" would be with stock options, which depend on factors that have nothing to do with R&D (marketing makes a company more profitable than R&D). An hollywood weirdo makes 10 millions per movie instead.

That's the obvious consequence of the mighty law of "supply and demand" that nobody wants to oppose: people are retarded and spend lots of money to go to the movies rather than financing scientific research. That's the "demand", so the "supply" will act accordingly. And who doesn't agree with this system is considered a "communist".

Now, who's more useful to mankind, a physicist or an actress? If answering "a phycicist" makes me a communist, well I'm proud to be one.

No, that's not philosophy. That's science. The facts are on my side, not yours. Read "The Happiness Advantage" for details. I'm not denying supply and demand, arguing that a physicist makes more than Tom Cruise (although in general physicists make more than actors), or anything else you might think I'm saying. I'm saying as a matter of fact, based on good science, that the human brain is generally more productive and powerful when it's happy, which leads to increased success, but having success does not reliably trigger happy brain states.

Re:Difference between Germany and the US

[ultranova]

Superstition is what keeps humans backward. It plays to their most degenerate desires for controlling others on a mental level. It is based on falsehood, and should be constantly scorned and ridiculed in order to reduce the number of new converts.

So, your grand strategy for fighting religion is to simultaneously give the adherents something harmless to feel martyrs over and make the whole thing seem like a cool, dangerous counterculture to potential young recruits?

Re:Difference between Germany and the US

[steelyeyedmissileman]

If any adherents can PROVE their imaginary friend is real, I'll recant

Proofs exist, and many people could provide the proofs. It wouldn't do any good, however, because you'd just wave it off.

The problem isn't with the proof, the problem is with the AXIOMS. Very good and convincing proofs of the existence of God are there, if you take a particular set of axioms as the basis for your outlook. That's the faith part.

It's a real problem in our world today that people take math and science as gospel. Everyone seems to forget that all of math and science are based on axioms, things that we assume must be correct because there's no way to prove it. We have to make those assumptions, though, to do anything at all. You might say "well, so far nothing has shown those assumptions to be wrong, so we must be right!", but that's only good to a point. Newton's law of gravity is correct, but only if you assume a Euclidean geometry. Is that correct? Well... not exactly... but that doesn't make Newton's laws worthless; many models we run on today rely on those principles which aren't, technically, true.

So I'm sorry, but I decline to offer my proofs. If you'd like to talk axioms, on the other hand, that might be a more interesting (and fruitful) conversation.

Re:Difference between Germany and the US

[eulernet]

In fact, neuroscience and psychology points the opposite direction: happiness leads to success.

I don't know where you read that, but psychology and neurosciences (there are several) will never be able to show that, because happiness and success are totally unrelated !

Firstly, because you need to define what success is. If success is living a life doing a lot of things, you'll get a rich life, but probably not a wealthy one.
If success is making a lot of money, it just means that you tend to take risks, it's like betting your life on your choices.
The risk of getting unsuccessful is greater than the risk of getting successful.
In any case, I don't see how this can lead to happiness.
Happiness is not related to comfort, money or other external results.
A poor guy is probably happier than a rich guy, because his happiness will not depend on money, while the rich guy will focus his life on work and money, and it's impossible to succeed your life personally and at work.

Secondly, because if your happiness is related to success, it means that if you fail, you are unhappy.
When you fail, it means that you need to understand the lessons of your failure, and try to correct this.
Perhaps should you not take risks in the future ?

Please, stop reading/listening gurus who try to sell their method to become rich and happy. They are just marketeers, who sell themselves.
The happy guys never brag about being happy.

Re:Difference between Germany and the US

[Asic Eng]

Well similar articles appear in US media whenever some kid has early success in science or technology. As evidenced by the fact that this piece of news has even made it to Fox.

I would agree in general that Germany doesn't suffer quite as much from anti-intellectualism as the US, but it's not a black and white scenario, either.

Re:Difference between Germany and the US

[wealthychef]

In fact, neuroscience and psychology points the opposite direction: happiness leads to success.

I don't know where you read that, but psychology and neurosciences (there are several) will never be able to show that, because happiness and success are totally unrelated !

I'll just quote myself from another post here which you probably missed. I'm saying as a matter of fact, based on good science, that the human brain is generally more productive and powerful when it's happy, which leads to increased success, but having success does not reliably trigger happy brain states. Clear enough? For just one study, see Lyubomirsky, S., King, L. & Diener, E. (2005) The benefits of frequent positive affect: Does happiness lead to success? Psychological Bulletin, 131, 803-855.

Firstly, because you need to define what success is. If success is living a life doing a lot of things, you'll get a rich life, but probably not a wealthy one. If success is making a lot of money, it just means that you tend to take risks, it's like betting your life on your choices. The risk of getting unsuccessful is greater than the risk of getting successful.

It's a good thing to think about. I define success in the dictionary definition: the favorable or prosperous termination of attempts or endeavors.

In any case, I don't see how this can lead to happiness.... blah blah more stuff to show you missed my point entirely.... The happy guys never brag about being happy.

Read my post again. I did not say that success leads to happiness. You are arguing against a straw man.

Re:Difference between Germany and the US

[eulernet]

No, I didn't miss your point, your message was not very clear.

Thanks for the article, it contains a lot of information, but mostly statistical.

The goal of our life is to live a happy life, but a lot of people focus on getting wealthy instead.

Frankly, success or failure are not very important, as long as you can be happy.

Re:Difference between Germany and the US

[wealthychef]

OK, I can buy that my post was not clear. If you are more interested in the subject and wish to explore more causal and interesting studies, please look at "The Happiness Advantage." I cannot find my copy at the moment, or I'd cite some of its studies. It's on Amazon and it's cheap and a good read. I would quibble with your argument that success and failure are not very important. They are sometimes important and sometimes not. What's skewed in our present culture is our insistence than every success and failure is a measure of the worth of the people seeking their results. That itself works against happiness. I also would say as a footnote that happiness is measurable, definable and achievable. And to attain it might be called a type of success, no? Thus showing that some successes are important. :-)

Re:Difference between Germany and the US

[eulernet]

Here is a good read, and it's free:
http://isites.harvard.edu/icb/icb.do?keyword=k29669&pageid=icb.page135336

About measure, I disagree, I know EQ, but I don't like too much the principle.
I'm for the zen approach, which is to let your thoughts pass, we are unhappy because of our thoughts.
As long as we are in the instant present, we live fully.
I like the zen quote: "When I eat, I eat, and when I sleep, I sleep".
Whatever (positive or negative) happens at me is a lesson, what can I learn from it ?
Can I unlearn my bad thoughts' habits, that took so much time to acquire ?
This is the secret of happiness.

Re:Difference between Germany and the US

[wealthychef]

Thanks for the interesting link. I will see if I can find time to read it. A casual perusal shows me nothing there about happiness, though. I have not spoken of E.Q. and am not a fan either -- it's an interesting but outdated idea, I think, modeled on another inadequate idea: I.Q. That is not the measure of which I speak. I'm talking about observing the human brain and human behavior that precedes and apparently causes people to report themselves as happy. These things can be measured and reported. Also, we can observe the human brain with increasing fidelity and see what this thing "happiness" is in other terms to see what more can be understood about it.

Re:Difference between Germany and the US

[daemonenwind]

You need to read more German media.

For example:
http://www.bild.de/lifestyle/startseite/lifestyle/lifestyle-15478526.bild.html

For counter example, I would note that ESPN will be covering the Scripps National Spelling Bee this year.

Perhaps your perspective on this has more to do with you than with Germany or the United States.

Re:Difference between Germany and the US

[eulernet]

The link is about Positive Psychology, and it's Ben-Shahar's course (mentioned in the book you mentioned, I'll read it when I'll have more time).

EQ is interesting in order to measure what kind of coping we are able in our relationships.
Epstein's book about "Constructive Thinking" seems a lot more interesting than EQ.

I have my own personal approach, because I started with a psychoanalysis while practicing some caycedian sophrology, I experienced the different levels of consciousness.
I stopped doing psychoanalysis because I realized that it reinforced the mental process of thoughts.
I had my peak performance moment (winning a national championship), then had to take familial responsibilities (my wife is in a wheelchair).
All these events changed me deeply, but I still don't believe in brain.

I have a large IQ (>140), and I realized that obsessing about IQ is useless.

My deep belief (thanks to sophrology and zazen) is that my "reality" is a small point in my body located around my belly button.
The brain is just a sense, like vision, audition or smell. This sense is working with thoughts.
So what we are studying with brain is not what we truly are, but how this sense works.
A lot of our brain illnesses originate from our belly bacteria (like multiple sclerosis). They may attack the brain when our brain has problems coping with reality.

IMHO, observing the brain behaviour is less important than discovering our "true" nature.

Re:Difference between Germany and the US

[wealthychef]

Thank you for your thoughts and the leads on other thinkers. Yes, I've read some Ben-Shahar, but not Epstein, and the Happiness Advantage is by one of his students as I recall. I understand what you mean by not believing in brain, and I agree, as well as taking your point about MS and, perhaps, implicitly epigenetics and mind-body. I personally identify more with an idea of mind-body that itself is an illusion formed from dualist thinking. I have not seen anything that makes me believe that we truly are anything in particular in the sense you seem to mean. "There is no dance and no dancer, there is only you dancing." Your measured IQ is larger than mine and your achievements are as well, congratulations. :-) I am sorry for your wife's trouble and can see you love her. Speaking of M.S., if your wife by chance has that ailment, then have you seen or heard of Dr. Wahls' diet?

Re:Difference between Germany and the US

[eulernet]

Luckily, my wife doesn't suffer from MS, but she has to lose weight in order to be operated (hips replacement).
One of my old friends suffers from MS (he introduced me to sophrology and meditation, because he wanted to lessens his disease), but I guess he's dead now :-(

About my achievements, there are none, except perhaps a boost in self-confidence.
I didn't get wealthy because of my work, but I did a massive burn-out during 8 years of my life (while working in the videogame industry), but I'm now pretty happy, even though life is always tough, but so full of lessons and meaningless at the same time.

About the duality concept, I agree with you, but I believe that I'm still "something". Trying to find its location may solve this duality.
I also think that the cycle of reincarnations stops when you removed all your beliefs, even the belief of reincarnation, it's quite recursive ;-)

Recently, I've stopped trying to understand myself and the others. Trying to understand reduces yourself, instead of trying to push your own limits.
I realized that I was limitless, but I'm also very lazy, so I doubt I'll ever get rich, except internally.

Re:Difference between Germany and the US

[Guy Harris]

The problem isn't with the proof, the problem is with the AXIOMS. Very good and convincing proofs of the existence of God are there, if you take a particular set of axioms as the basis for your outlook. That's the faith part.

So does that, ultimately, amount to "you will be convinced of the existence of God if you make assumptions about the world that require the existence of God"? Unless there's a non-faith-based reason to make those assumptions, the proof isn't going to be convincing to people who don't make those assumptions, making it just an entertaining exercise for those who happen to make those assumptions, not something to take seriously as a reason to believe.

It's a real problem in our world today that people take math and science as gospel. Everyone seems to forget that all of math and science are based on axioms, things that we assume must be correct because there's no way to prove it. We have to make those assumptions, though, to do anything at all. You might say "well, so far nothing has shown those assumptions to be wrong, so we must be right!", but that's only good to a point.

Yes, math is a subject where you start with a set of axioms and derive theorems from it, and all that matters is whether the axioms are consistent (i.e., one axiom doesn't contradict another) and, for any theorem, whether derivation is correct.

Science, however, is not such a subject. One might think of a particular scientific theory as having axiom-like assumptions from which one derives theorem-like predictions (although they're not necessarily stated in a mathematical form). However, the theorem-like predictions aren't just proven; they have to be tested against the real world. This means you don't get to choose your axioms arbitrarily and still have your theory taken seriously; if its predictions don't match the real world, you're not likely to be taken seriously unless you can show that there's something wrong with the experiments done to test the predictions.

Newton's law of gravity is correct, but only if you assume a Euclidean geometry.

Well, more accurately, Newton's laws of motion, as laid out by Newton, involve motion in a Euclidean space, and Newton's law of gravity, as laid out by Newton, involves a gravitational force in that space, whereas Einstein's general relativity involves special relativity-style laws of motion in a space-time that might be curved by the presence of matter, so that, the paths of matter not affected by (non-gravitational) forces being "straight lines" (geodesics) in that space-time, those paths might be affected by the presence of matter. However, Newtonian gravity can be formulated in a fashion similar to Einsteinian gravity, curved space and all.

Re:Difference between Germany and the US

[couchslug]

"So I'm sorry, but I decline to offer my proofs."

Then you have no evidence you dare produce for debate.

Re:Difference between Germany and the US

[wealthychef]

I agree we are something. :-) The duality occurs because of the looking but is not there in reality, I think. All dualities are simply a function of a distinction drawn by an observer. Evolution has taught us to value patterns and we classify them to communicate, but the classification is an artifact of mind. Or so it all seems to me. :-) Reincarnation seems to be another attempt to see beyond the grave, which is futile from what I can tell. Beyond death all is just confusion -- I suspect this is because there is no "beyond death." We cannot comprehend our own annihilation. And that's the big mystery to me. That I comprehend at all, and cannot comprehend not comprehending anything. :-)

Re:Difference between Germany and the US

[fr!th]

I read /. at least twice a week, for the last ten years or so. And congratulations, you + parent are the first one I can remember who has summed up the 'science vs. religion' subject in a relatively objective fashion. At least, that is how you started. I have long thought this was true:

"The problem isn't with the proof, the problem is with the AXIOMS. Very good and convincing proofs of the existence of God are there, if you take a particular set of axioms as the basis for your outlook. That's the faith part.

So does that, ultimately, amount to "you will be convinced of the existence of God if you make assumptions about the world that require the existence of God"? Unless there's a non-faith-based reason to make those assumptions, the proof isn't going to be convincing to people who don't make those assumptions, making it just an entertaining exercise for those who happen to make those assumptions, not something to take seriously as a reason to believe."

But few consider the implications of this. IMHO, faith by *definition* is axiomatic. One doesn't prove the existence of God/Supreme Being, one *assumes* it. But the converse is also true. One does not 'disprove' or 'disbelieve', rather one assumes 'lack of existence'. The two statements are mutually exclusive, and both based on faith.

I think the thing that ends up tripping both sides is that, starting with *either* axiom (does exist/doesn't exist) you can produce our world. That is, there is nothing that requires a 'Supreme Being', but also nothing that precludes it. This is why some scientists believe and others don't - because it doesn't affect the outcomes of your experiment or how you reason about it. Its a philosophical axiom, and therefore unprovable in any sense.

Just had to add my $0.02 - you guys made my day!

When in Doubt...

[Rie Beam]

...go to the source! The German articles I've scoured seem to have a little more information about the problem itself and what he actually accomplished. The oldest one only records that he "claims" to have solved them (earlier this month), but so far no actual data. Close.

http://www.enso-blog.de/jugend-forscht-drei-arbeiten-aus-ostsachsen-beim-bundeswettbewerb
http://www.morgenpost.de/vermischtes/article106358144/16-jaehriger-Schueler-loest-uraltes-Mathe-Problem.html

Re:Shouryya Ray, a 16-year-old Kolkata boy ...

[Anonymous Coward]

So basic grammar is used to emphasize his origin? Really?

skeptic

[Anonymous Coward]

Due to the lack of specifics, just seems to be an article where a dad is bragging about his son, I'll reserve belief that Mr. Ra has solved anything until I see a published solution in a mathematics journal. Given the sheer number of ballistic weapons used by the US and other armies since the initial World War, I kinda doubt that there is a new solution to this problem of predicting where a shell would fall.

Wolfram Alpha

[Anonymous Coward]

Man, he just went home and popped up Wolfram Alpha, what's with all the fuss?

Gotcha!

[Rie Beam]

http://jugend-forscht-sachsen.de/2012/teilnehmer/fachgebiet/id/5

Text is in German. It all stems from a Youth Research competition he entered into back in March of this year. This is, so far, the best summary I've found -- there is a paper, apparently, but no link just yet.

'Two problems in classical mechanics have withstood several centuries of mathematical endeavor. The first problem is therefore to calculate the trajectory of a body thrown at an angle in the Earth's gravitational field and Newtonian flow resistance. The underlying power law was discovered by Newton (17th century). The second problem is the objective description of a particle-wall collision under Hertzian collision force and linear damping. The collision energy was derived in 1858 by Hertz, a linear damping force has Stokes (1850) is known. This paper has so far only the analytical solution of this approximate or numerical targets for the problems solved. First, the two problems are solved fully analytically. For the first problem will be investigated further using the analytical solution, the physical behavior of the system and set up outline solutions for generalized models. For the second problem is carried out in order to increase efficiency and convergence control a semi-analytical optimization. Finally, the analytical results are compared with numerical solutions so as to validate accuracy and convergence to numerically."

Re:Gotcha!

[Rie Beam]

On a sad note, he only placed 2nd in the overall competition :(

Re:Gotcha!

[imbusy]

It seems like no one simply bothered doing it before him because everything is done much easier numerically. And you can do a lot more with numerical integration (account better for the environment) than this one specific case of the problem could ever handle.

Re:Gotcha!

[St.Creed]

Number one cured cancer AND solved the world's energy problem. That's hard to top. :)

Re:Gotcha!

[WillHirsch]

It's hardly worth even doing numerically. Within the 85km thick shell where the atmosphere behaves anything like a Newtonian fluid, Earth's gravitational field strength only varies by about ±1.5%. The difference between any application of the analytical solution and the equivalent constant-g solution will be dwarfed in real life by chaotic atmospheric conditions. I suspect that as a differential equation with an unusual combination of second-order polynomials, there isn't much else you can transfer the solution to either.

Re:Gotcha!

[bcrowell]

That helps a little, but still doesn't really clarify completely what he did. I'll explain a little about what I know about the projectile problem and what I can figure out about what he might have accomplished here.

In the Principia, Newton poses three closely related problems. One is projectile motion under the influence of a frictional force that's proportional to velocity (book II, section I). Next he considers the case where the friction is proportional to the square of the velocity (book II, section II), and finally the case where it's of the form av+bv^2, where a and b are constants (book II, section III). Let's call these cases 1, 2, and 3.

Case 1 is pretty straightforward. The x and y motions are decoupled, and each of the motions is governed by a first-order, linear, inhomogeneous equation.

Case 2 is actually of more physical interest than case 1 for most real-world projectiles. For example, when you toss a baseball in air, its Reynolds number is about 10^4 or 10^5, and in that regime, a force proportional to v^2 is a pretty decent approximation. There is a well known closed-form solution for the one-dimensional subcase (I actually had a student a few years back who figured it out for herself, which was impressive), which is y=A ln[cosh(t sqrt(g/A))].

A hint is that this page has a photo of him holding up a large sheet of paper with his closed-form solution on it. The equation is clearly visible, and reads g^2/(2u^2)+(alpha g/2)[v sqrt(u^2+v^2) / u^2 + arsinh |v/u|] = const. The notation isn't explained, but clearly u and v are the components of some vector, probably the velocity vector. If so, then the constant alpha has to have units of inverse meters.

This makes me think that what he's solved is the full two-dimensional version of case 2. It can't be case 3, because besides g there is only the one constant alpha appearing in his equation. If you write down the equation of motion, a=F/m=(mg-bv^2)/m=g-(b/m)v^2, the constant that naturally occurs is b/m, which has units of inverse meters. It also makes sense that his solution has a hyperbolic trig function in it, since the y(t) for the one-dimensional version of case 2 has a hyperbolic trig function in it.

If my interpretation is right, then you should get a correct one-dimensional result from his equation when u=0. Unfortunately his equation blows up to infinity in that case, so I'm not sure how to extract any sane interpretation from it. By setting alpha=0, you should also get the case with zero friction. That does sort of make sense, since it says u is a constant, which it should be in that case.

It would be interesting to see if my interpretation is right by doing a numerical simulation and seeing if his expression really does seem to be a constant of the motion.

One thing to point out is that he may not have actually solved the full problem as set by Newton. He hasn't found the equation of the trajectory in closed form (which I think was what Newton was most interested in), and he also hasn't found the position in closed form as a function of time. (This is all assuming my interpretation is right.)

Re:Gotcha!

[Anonymous Coward]

You're right, he's demonstrated a constant of motion (i.e. a first integral) in the 2D version of Newton's Case 2. The constant alpha in his equation is what you called b. Gravity points in the -v direction.

You can easily check this by differentiating his equation with respect to time, and then eliminating the derivatives of u and v using the expressions

du/dt = -b u sqrt(u^2 + v^2)
dv/dt = -b v sqrt(u^2 + v^2) - g

His solution can probably be extended to Case 3 quite easily, if anyone feels like a challenge :)

Re:Gotcha!

[bcrowell]

Doing a reply-to-self because I checked my interpretation using a numerical simulation. I wrote some python 3 code, which does a reasonably realistic simulation of a baseball being hit for a home run. Slashdot's lameness filter wouldn't let me post it, so I put it here: http://ideone.com/yeP4y

The results:

u= 36.86184199300463 v= 25.810939635797073 Ray= 0.07075915491208162 KE+PE+heat= 147.825
u= 30.646253624059415 v= 12.467830176777555 Ray= 0.07075939744839914 KE+PE+heat= 147.82340481003814
u= 26.608846983666997 v= 1.6625489055858707 Ray= 0.07075957710355621 KE+PE+heat= 147.8224303518585
u= 23.559420165753 v= -7.761841618975968 Ray= 0.08597247439794412 KE+PE+heat= 147.82171310054588
u= 20.86163826256129 v= -16.094802395195508 Ray= 0.10413207421166563 KE+PE+heat= 147.82115230900214
range= 120.88936569485678 , vs 194.17117929504738 from theory without air resistance
u= 18.25141606403427 v= -23.242506129076933 Ray= 0.12066666645699123 KE+PE+heat= 147.8207286473949
u= 15.70673363979356 v= -29.088976584679852 Ray= 0.1353850869274781 KE+PE+heat= 147.8204307883206
u= 13.30143766684643 v= -33.65200048062784 Ray= 0.14867603720136566 KE+PE+heat= 147.8202356199746
u= 11.11267911406159 v= -37.07517115834146 Ray= 0.16096016949002218 KE+PE+heat= 147.8201144079141
u= 9.186200956690504 v= -39.564763699985484 Ray= 0.17255826567110216 KE+PE+heat= 147.82004160975018

The notation is that u and v are the x and y components of the velocity vector, "Ray" is the expression that Ray seems to be claiming is a constant of the motion, and the final column is the total energy, which should be conserved.

I tested my code two ways: (1) Energy is very nearly conserved. (2) If I turn off air friction, the range is very nearly as calculated by theory.

Let R be the expression that Ray says is a constant, under my interpretation of his variables. Then dR/dt appears to be very nearly zero early on in the simulation. However, later on it starts to drift upward. So I suspect that one of the following is true: (1) Ray is wrong; (2) my interpretation of his notation is wrong; or (3) my simulation doesn't use good enough numerical techniques to demonstrate with good precision that Ray is right.

Anyone who's got Runge-Kutta, etc., on the tip of their tongue want to try a better simulation of this?

Re:Gotcha!

[c0lo]

In fact, if you multiply his equation through by u^2, then set u=0 you are left with g+alpha v^2=0. Similarly, setting v=0 you have g=const u^2 which is equivalent if const=-alpha and v=u. So it appears to not blow up.

I'm not sure what it's really telling us though! v^2 is proportional to g? I think we need to know more about his notation.

Tells you that the KE and PE go hand in hand?

Re:Gotcha!

[bcrowell]

In fact, if you multiply his equation through by u^2, then set u=0 you are left with g+alpha v^2=0

Not quite, because v sqrt(v) isn't v^2, it's v^2 sign(v). As the projectile approaches terminal velocity, your approximations hold, but with the sign flipped relative to yours, and the expression you've found equals (with a sign flip) the acceleration, which is zero. When the projectile has small u but isn't close to terminal velocity, your approximations fail (u isn't small enough compared to v).

Similarly, setting v=0 you have g=const u^2

Setting v=0 isn't physically interesting in the same way that setting u=0 is. There are physical solutions of the equations of motion in which u is constant and zero -- vertical free fall. There aren't physical solutions of the equations of motion in which v is constant and zero.

Re:Gotcha!

[bcrowell]

You can easily check this by differentiating his equation with respect to time, and then eliminating the derivatives of u and v using the expressions

du/dt = -b u sqrt(u^2 + v^2)
dv/dt = -b v sqrt(u^2 + v^2) - g

Awesome! I didn't want to grind out the calculus by hand, so I did it with maxima:

load (f90)$
 
r(u,v) := 1/(u**2)+v*sqrt(u*u+v*v) / (u*u) + asinh(abs(v/u)) ;
/* Ray's expression, multiplied by 2, with alpha=g=1 */
 
foo : diff(r(u,v),u)*u*sqrt(u*u+v*v) + diff(r(u,v),v)*(1+v*sqrt(u*u+v*v));
/* total derivative with respect to time */
 
f90('foo = foo);

Unfortunately maxima wasn't smart enough to simplify it show that it vanished identically, so I had it output it as fortran code, and then tested numerically that it vanished with random numbers as inputs:

double precision u,v,foo
u = 0.3776
v = 0.1209
foo = u*sqrt(v**2+u**2)*(-abs(v)/(u*abs(u)*sqrt(v**2/u**2+1))-2*v&
*sqrt(v**2+u**2)/u**3+v/(u*sqrt(v**2+u**2))-2/u**3)+(v*sqrt(v**2+&
u**2)+1)*(v/(abs(u)*sqrt(v**2/u**2+1)*abs(v))+sqrt(v**2+u**2)/u**&
2+v**2/(u**2*sqrt(v**2+u**2)))
write (*,*) foo
end

Re:Gotcha!

[bcrowell]

Hmm...actually it only works for v>0, which is the reason for the goofy behavior I was seeing in this post. Notice how the numerical simulation shows Ray's expression as a perfect constant of the motion up until v becomes negative, and then it starts changing.

This is because if you simplify the total derivative from this post, you don't actually obtain zero, you get (v/|v|-1)/sqrt(u^2+v^2), which only vanishes for positive v.

So it looks like the expression shown on the big piece of paper in the photo is only for v>0. I don't know if there's some trivial modification that would generate a valid expression for the negative v case.

Re:Gotcha!

[Xtifr]

Which, since we've been unable to track down the actual results, may simply indicate that what he did is much less impressive than some news reporters are making it sound.

Re:Gotcha!

[martin-boundary]

He's being a good slashdot commenter who's offering stuff that matters to the small contingent of us who have advanced maths degrees?

Re:Gotcha!

[semi-extrinsic]

Cloned your code and added a classical fourth-order Runge Kutta. Here. There isn't really any difference, presumably because you used 100 000 time steps. The difference between Euler and RK4 is tiny for non-stiff problems and small time steps.

So I guess either your interpretation is wrong, or he is wrong.

Re:Gotcha!

[bcrowell]

You missed the other factor of u. The expression u sqrt(u^2 + v^2) gives the x component of a vector with squared magnitude u^2 + v^2 that points in the direction of (u,v).

Re:Gotcha!

[bcrowell]

Cool, thanks for checking that! As explained here, what's going on is that the expression is only a constant of the motion for v>0.

Re:are those problems NP?

[geoskd]

The problems he solved are not NP. They are essentially calculus, but they are both very nasty calc problems, and the traditional way to solve calc problems is using newton approximations until the answer is close enough to what you want. An analytical / precise way to solve these problems is extremely useful to the physics folks, as the solution will probably also lead to better models of particle motion.

-=Geoskd

Re:are those problems NP?

[ceoyoyo]

This is not a decision problem so the P-NP complexity classes do not apply.

Re:Exceptional intelligence in ethnic sub-group?

[Rie Beam]

Good job there, providing zero evidence outside of hearsay and stereotyping. Because if there's one thing that will provide evidence for eugenics, it's the opinions of other people who want to provide evidence for eugenics.

Fermat & Poincaré

[Bananatree3]

Andrew Wiles solved Fermat's Last Theorm with paper only, as he despised the use of computers in writing mathematical Proofs. Another famous example is Grigori Perelman who solved the Poincaré Conjecture - with hundreds and hundreds of pages of mind-numbingly dense mathematics vs computer search.

Re:Fermat & Poincaré

[Machtyn]

It does seem pointless to me to use a computer to create a proof, except when using it to quickly calculate the known and already proven equations.

Of course, that's coming from a guy who continually messes up a number or sequence here or there.

Re:Fermat & Poincaré

[Chase Husky]

Another famous example is Grigori Perelman who solved the Poincaré conjecture - with hundreds and hundreds of pages of mind-numbingly dense mathematics vs computer search.

Perelman's three primary papers ("The entropy formula for the Ricci flow and its geometric applications" http://arxiv.org/abs/math.DG/0211159, "Ricci flow with surgery on three-manifolds" http://arxiv.org/abs/math.DG/0303109, and "Finite extinction time for the solutions to the Ricci flow on certain three-manifolds" http://arxiv.org/abs/math.DG/0307245) on modifying Hamilton's Ricci flow program to deal with singularities and proving Thurston's geometrization conjecture only span 68 pages, with the actual proofs/meaningful remarks comprising about 45 pages of that.

Re:Fermat & Poincaré

[2.7182]

Well, that is true but then after those papers appeared there was a several year effort by 3 groups to fill in the details and make it more digestible. Each of the resulting books/documents are several hundred pages long.

Some problems just require longer proofs.

Re:Fermat & Poincaré

[Anonymous Coward]

It seems pointless to you because you are totally ignorant of math. A lot of these "hundreds of pages of mind-numbingly dense mathematics" proofs are long but tedious derivations which a computer can grind through in seconds.

If you're doing a half page proof that square root of 2 is irrational, then a computer would be pointless, but clearly you don't know that math is more complicated than that.

And to head off potential flames, I completely respect people who want to and are able to work through those derivations by hand, but to think doing it with a computer is pointless just shows your ignorance.

Re:Fermat & Poincaré

[Anonymous Coward]

Actually, it should be the other way around. The 45-odd pages comprise the actual proofs/meaningful remarks.

Re:Fermat & Poincaré

[Dodgy G33za]

This is why I read /.

Re:Fermat & Poincaré

[nuckfuts]

Number of pages is not a very meaningful measure. It is dependent on formatting. As anyone with an e-book reader knows, one can increase the number of pages of any document by simply choosing a larger font.

Re:Fermat & Poincaré

[djjockey]

As anyone who had to turn in a paper with a page limit also knows... that and the spacing between characters, words and lines all helps!

Re:Fermat & Poincaré

[ais523]

Half a page? If (x/y)^2 = 2, then x^2 = 2y^2, so x is even. Let z = x/2, now we have 2z^2 = y^2, so y is also even. Thus, any fraction that's equal to the square root of 2 cannot be expressed in lowest terms, so cannot exist. That's, what, three lines at most?

I agree with the main point, though; quite a few of the proofs I do are just boring churning through tens of possible cases. Up to 100 or so it's plausible to do it by hand, although tedious and it's easy to make mistakes; significantly beyond that, though, you're going to want to automate it.

Re:Fermat & Poincaré

[brillow]

To me it seems pointless do work in any inefficient way to the ends of pride.

Re:Fermat & Poincaré

[arglebargle_xiv]

Andrew Wiles solved Fermat's Last Theorm with paper only, as he despised the use of computers in writing mathematical Proofs. Another famous example is Grigori Perelman who solved the Poincaré Conjecture - with hundreds and hundreds of pages of mind-numbingly dense mathematics vs computer search.

The fact that two guys with somewhat abnormal personalities (and I mean that as a general observation rather than any criticism, more normal people wouldn't have taken this approach) obsessively worked on pencil-and-paper proofs isn't really an indication that this is a good way to do things. If you can do the same thing with less effort on a computer (and a prime example of this is the four-colour theorem) then do it on a computer. Use the right tool for the job, not pencil-and-paper because you don't trust computers.

(Oh gawd, please don't let this degenerate into a long thread about OCD and the like, I'm trying to point out that you need to use the right tool for the job, and if the right tool is a computer then go ahead and use it).

Re:Fermat & Poincaré

[Darby]

It does seem pointless to me to use a computer to create a proof,

I believe the poster you're responding to meant something different.

Say you have some complicated ("chaotic", maybe) formula which determines the behavior of a system. Say just to make it easy the system is a single particle moving under various influences. Now say you know where it is now (it's a big particle like a planet or something, so ignore Heisenberg and such) and you want to know where it will be 500 seconds later. Many systems currently require iterating through all 500 steps or other time intensive tasks in order to find that answer due to only having approximate methods with which to solve the system. An analytic solution as the OP was using it would be more like a function where you plug in 500 and get your answer. If you plugged in 500 Billion, you'd find that answer in more or less the same amount of time as for 500.

So computers can potentially make taking the wetware time to find an analytic solution to an equation (system of differential equations, optimization problem etc.) less valuable in some of the meanings of the word, if in practical applications you can get say 10 decimal places closer to the answer than you need in microseconds.

Computers proving theorems is a different thing. The Four Color Problem is the most common example of that I'm aware of. I think it's cool that people managed to do that, but it's unsatisfying in that it doesn't really add much in the way of understanding. Some theorems people have come up with are similarly unsatisfying.
Existence theorems which demonstrate that a certain thing must exist in some given circumstances yet provide no clue whatsoever as to how to actually find it would fit. Also, brute force methods in general (which is what the four color proof is, only done via computer to save time) tend to leave mathematicians satisfied that the given fact is true yet still looking for a more elegant solution that provides greater understanding.
Andrew Wiles's proof of Fermat's Last Theorem is fundamentally different in that it did (eventually) provide a huge degree of insight showing unsuspected ties between disparate branches of mathematics. Technically, Wiles didn't prove Fermat's Last Theorem, he proved the Taniyama Shimura conjecture (demonstrating a deep relationship between elliptic curves and modular forms) which someone else had proven would imply FLT if true.

Re:Fermat & Poincaré

[Anonymous Coward]

Half a page? If (x/y)^2 = 2, then x^2 = 2y^2, so x is even. Let z = x/2, now we have 2z^2 = y^2, so y is also even. Thus, any fraction that's equal to the square root of 2 cannot be expressed in lowest terms, so cannot exist. That's, what, three lines at most?

It's also not a mathematical proof.

Re:Fermat & Poincaré

[sco08y]

It seems pointless to you because you are totally ignorant of math. A lot of these "hundreds of pages of mind-numbingly dense mathematics" proofs are long but tedious derivations which a computer can grind through in seconds.

If you're doing a half page proof that square root of 2 is irrational, then a computer would be pointless, but clearly you don't know that math is more complicated than that.

And to head off potential flames, I completely respect people who want to and are able to work through those derivations by hand, but to think doing it with a computer is pointless just shows your ignorance.

Most importantly, if there are hundreds of pages of dense computation to prove X, if I'm writing a function and I have some invariant, I can just write a comment,

"And invariant Y remains satisfied because of X, see the fun proof at..."

I don't really give a damn about the details, It Just Works.

Re:Fermat & Poincaré

[doccus]

Not much use with a word limit though..

Re:Fermat & Poincaré

[ais523]

Yes it is; it's bad practice to pad a proof out just so it looks more proofy when it genuinely is that simple.

So what is Newtons Puzzle?

[rossdee]

Its not that desktop ornament with the steel balls on strings is it?

I thought the puzzle about Newton was why did Apple abandon it.

Flash journalism

[yoctology]

These stories about overwhelming acts of personal genius, especially stories that lack the details of the alleged act, are, without memorable exception, false. But we all like a good story about an under-caste upsetting gray hairs and the established order of things.

Think about that for a moment. A story supposedly lionizing science lacking the most basic facts that would permit substantial verification, or falsification, of that science. This is just flash journalism at work.

Re:Flash journalism

[Anonymous Coward]

Agreed. I wish we could go back to the good old days of HTML + JavaScript journalism.

Re:Flash journalism

[thePig]

Not in this case though.
People re-engineered the solution and found the way he solved it - and it checks out -
http://www.reddit.com/r/worldnews/comments/u7551/teen_solves_newtons_300yearold_riddle_an/c4t03fl

So, this is real.

Re:Flash journalism

[FrangoAssado]

Since we're linking to comments from Reddit: people also found out that this solution was known since at least 1860, and was published in a modern journal in as recently as 1977.

It's great that a 16 year old discovered this, and it could have been a cute (but not as flashy) story. But the reporter didn't even bother to talk to someone familiar with the field.

George Dantzig

[tepples]

We all had that moment in school when a teacher would pose an "impossible" problem, thought to ourselves "Well, they've never faced ME before!", spent a few minutes toying with it and finally giving up. This kid...did not.

Nor did George Dantzig at UC Berkeley in 1939. Without him, Good Will Hunting would be a movie about buying a suit at a thrift store.

Re:Mispelled name in TFS

[Anonymous Coward]

His name is Shouryya Ray.

You can call him Ray, or you can call him Jay. . .

Shouryya Ra = German?

[Gothmolly]

I don't think so.... Aryan maybe, but not German.

Re:Europe

[Noughmad]

So the crazy old guy in that movie with the long title was right all along?

Gave Up

[Frankie70]

And the submitter gave up right while copying the name of the kid from the article to slashdot.
"Shouryya Ray" became "Shouryya Ra" and samzenpus also let it through without any corrections.

Re:Gave Up

[PNutts]

Sugar Ray does not approve.

Re:are those problems NP?

[EMN13]

While P/NP is indeed pretty way offtopic here, P vs. NP doesn't necessarily apply solely to decision problems. Furthermore, many problems can be rephrased as decision problems; e.g. Does the cannonball need more than 10 second to complete its flight?

For a traditional P/NP example: the traveling salesman problem is about finding the shortest path, which is also not a decision problem.

This bright Dude comes across as down to earth

[quax]

This longer piece (German) quotes him pointing out that he is very weak in Graph theory and Combinatorics. Nevertheless he skipped two classed in school and will be able to start university this fall.

Won't be the last time we heard form this guy.

Re:This bright Dude comes across as down to earth

[Georules]

Oh no, he's weak in graph theory and combinatorics? Only about 1% of college graduates even know what those things are anymore. He's clearly doomed.

Is his last name Ray or Ra?

[damn_registrars]

In the summary he is first named Ra, and then later referred to as "Mr. Ray". Which one is correct?

Re:Is his last name Ray or Ra?

[bef]

If his name is Raj the Germans will pronounce it Ray.

Kudos to the kid but...

[PhilistineGuillotine]

I think it's great that this guy found an analytic solution to an old problem, but it is of no practical significance. Most of the complication in ballistics arises from the complicated effects of air resistance which are not limited to simple drag. Numerical solutions will still be required for anything as simple as a golf ball if you want any accuracy at all.

Military

[glorybe]

I am sort of surprised that there is any news on this as the ability to predict a projectile's path would be of great interest to military units possessing large guns. You know, when you are throwing 3,000 lbs. of wicked, fierce explosive 75 miles down range it is sort of nice to hit your target rather than the convent or kindergarten a few yards away.

Journal pages or manuscript pages?

[Latent Heat]

Journal pages or manuscript pages? Single-column publication form used in many math journals or the scrunched two-column format used by many engineering and science journals?

20 digits of precision ?

[perpenso]

"-gravity is not a constant vector force downward. It is a radial force inward toward the center of the Earth, and its intensity varies with altitude."

for any calculations on a scale less than 10 miles, assuming a constant will give you the same answer within a margin of error that is outside the ability of any store bought calculator.

Brick and mortar only or app stores too? Can a calculator that offer 20 digits of precision get inside that margin? Many store bought, and many apps based upon the FPU - a bad idea for many reasons, only seem to offer around 14 give or take.

FWIW, the actual motivation for 20 digits of precision was to be able to handle calculations compatible with 64-bit results. Not the sort of exercise above.

artillery can go 26 miles

[Chirs]

Unassisted shells have pretty decent range (26 miles or so), and specialty weapons can go even further.

Artillery is going self guided ...

[perpenso]

Artillery shells are in the process of becoming self guided. They are no longer limited to ballistic trajectories.

Besides, the ballistic models that the modern militaries use incorporate an incredible number of variables. This research would probably offer no practical improvement, it most likely uses a simplified model of air resistance.

That said I am no expert, I merely did a ballistics project as part of a differential equations class.

Shoulda Woulda Coulda Example

[retroworks]

I have a couple of these "don't listen to parents" examples. I had the idea in 6th grade to have a car run on perpetual motion, just put a generator in front to capture the energy and feed it back. My parents and grandparents told me, correctly, that' won't work because of the laws of theromdynamics, which they explained and I understood. I thought about it, then said "But what if I wanted the car to stop? Could it be used as a brake, to capture the energy?"

No, they said. And I dropped it.

"naivety" that's exactly it

[Snaller]

Too man sciences too quickly KNOW that something IS NOT POSSIBLE. They forget that absolute certain belongs in the realm of religion.

Re:Military

[wdsci]

For one thing, the military doesn't automatically classify anything that is relevant to them. But also, the problem of projectile motion with air resistance was already solvable by computer simulation, and it will continue to be solved by computer simulation. This result doesn't change that, it's just some interesting physics.

The problem he solved?:

[Jookey]

Take the case of throwing a baseball. This is case 2 from parent

Assume that the magnitude of the drag on the ball is proportional to the square of its velocity. Also, assume that the magnitude of the gravitational force is constant. You get the following set of differential equations:

x''(t)*m=A * (x'(t)^2+y'(t)^2) * cos(theta)
y''(t)*m=A * (x'(t)^2+y'(t)^2) * sin(theta) + g * m
theta=arctan(y'(t)/x'(t))

Where:
x(t) is the horizontal position of the ball at time t
x'(t) is the horizontal velocity of the ball
x''(t) is the acceleration
y(t) is the vertical position of the ball
(x'(t)^2+y'(t)^2) is the square of the velocity
theta is the angle of travel above the horizontal
m, A and g are constant over time*

*
A=-1/2*drag coefficient*cross sectional area of ball*air density
m is the mass of the ball
g is acceleration due to gravity

Shenanigans

[darthlurker]

Article from 2009 http://www.news.com.au/technology/german-teen-shouryya-ray-solves-300-year-old-mathematical-riddle-posed-by-sir-isaac-newton/story-e6frfro0-1226368490157#ixzz1w3LI5N1w' Bernoulli numbers solved by a 16 year-old. In this case an immigrant from Iraq living in Sweden. Bernoulli instead of Newton. But essential the same story.

I don't think it's by design

[turing_m]

I'm honestly not sure that the system is actually designed to discourage this (though it certainly feels like it). It's just an unintended consequence of the relatively low IQ levels of the teachers and administrators who design such systems, and the teachers who are actually doing the teaching. IQ, intelligence, call it what you will - is distributed in something approximated by a bell curve. If you had the brains to be doing advanced geometry and algebra at age 8, you are very, very likely to be smarter than virtually everyone involved in designing, administering and implementing education at any given primary or secondary school. You have an IQ that is high enough to be very rare.

There are lots of sad corollaries to this fact. Firstly, there are no resources to design an education system around a student that is 1/500, 1/1000, let alone 1/10000 in terms of rarity in the population. As soon as we approach the inverse of school population, there may not even be any student in the school who is that smart.

Secondly, it takes a smart person to understand statistics, the concept of distributions and the like. Even understanding my first two paragraphs is above the head of the average person. Due to influence of PC, its component blank slatism and the like, the number of people who both can and would even want to understand IQ, bell curves and the implications of the distribution of intelligence is even less. The ramification of this is that the vast majority of people automatically assume that anything they can't understand is either wrong or crazy, and impossible for anyone else to understand. It is insulting for many people to realize that there are problems that are too difficult for them to ever solve, but that others can solve with varying amounts of difficulty (or ease). They have an in-built chip on their shoulder towards these concepts. Most people also assume that they are smart enough to figure out who is smarter than they are, despite not realizing that there is a class of problems for which they will never, ever solve or perhaps even understand the solution, and so are incapable of judging those who will solve such things.

Then you have the problem of recruiting teachers who are capable of teaching a very bright child, if that is what you want your school system to do. There aren't any. The vast majority of the very small relative number of bright people in a given country are taking advantage of the exploitation of IQ by companies. Those who aren't duped by graduate schools into pursuing graduate education with no monetary payoff are busy earning lots of money, with job security and great working conditions. Why would they want to teach a bunch of relative dullards, when the pay is not there and the working conditions are crap? They are off doing medicine, engineering, law, business and the like.

So what do you get when your average teacher does not (want to) realize that any kid in class is smarter than they are, and can do mental gymnastics that they will never, ever achieve? And does not have the resources to allocate to it? And do not have teachers capable of teaching them? You get the current education system.

If you want to give a smart kid the opportunities to learn, you must do as the parents of the boy in this article did. You must school him yourself until he hits the point where he can autodidactically learn anything he wants to, and then give him the resources to pursue that. There is no substitute for a smart, motivated parent, involved in his child's education.

Re:I don't think it's by design

[turing_m]

One additional comment - at the younger levels, you do not need a genius to teach a genius, provided that the teacher is smart enough to recognize a smart child and teach to his level. At higher levels this is certainly true though, whether that genius is present in person or as an author of a work (book, web page, video, game), the child learning autodidactically. Also, being able to break a given problem or skill down into all the component skills necessary to solve that problem, and teaching them in order - that in itself requires above average intelligence. Much more than is probably thought.

Re:I don't think it's by design

[tehcyder]

You can't expect a school system to educate everyone equally effectively when you have thirty kids to one teacher. Particularly slow or quick pupils require additional help, and this basically needs to come from their parents.

If you're that much of a genius, you will always be outside the norms that schools cater for, and you should be able to find your own way forwards anyway.

Re:are those problems NP?

[doshell]

You're entirely correct, but I would add the following. You can rephrase non-decision problems as decision problems, but the computational complexity of the two versions may not be the same. As an example, even if you had a polynomial-time algorithm for the decision problem version of TSP, it would not be obvious at all whether you could use it to solve the shortest-path version in polynomial time, since the number of distinct path lengths in a graph is exponential in the general case.

Re:are those problems NP?

[doshell]

I've just realized that my example is wrong, because it seems to me that for the shortest-path version of TSP you can get away with a binary search over all the possible lengths (since the length of a path is upper bounded in a finite graph), which is just a (polynomial-time) iteration over the decision problem. I'm fairly certain that my comment on the differing complexities is true in general, but I'd rather someone else chime in with a correct example :)

Re:Europe

[redneckmother]

So the crazy old guy in that movie with the long title was right all along?

POE = Purity Of Essence = Peace On Earth.

Grain alcohol and rain water!

Funny, but when I was youger, there were times when we were warned not to make snow cones out of the snow, because of the atmospheric atom bomb tests.

Oh yeah, and GET OFF MY LAWN!

Re:are those problems NP?

[ceoyoyo]

P, NP etc. DOES apply solely to decision problems: http://en.wikipedia.org/wiki/NP_(complexity). The definition requires it.

Many problems, such as the travelling salesman problem, can be posed as decision problems, and when people talk about those being in NP, they are talking about the decision problem formulation.

I can only say I'm so jealous

[lulipa]

I'm good at math but my teacher tried to teach me calculus at age 16 and I couldn't understand shit.

What, exactly, is the problem?

[rgbatduke]

He worked out how to calculate exactly the path of a projectile under gravity and subject to air resistance.

What does this even mean? Linear (Stokes) drag forces (idealized)? Turbulent drag forces? Something in between? For a bluff body? A streamlined body? A tumbling body? In still air of uniform density? In a wind? In actual air that might well vary significantly in density and temperature along the (highly ballistic) trajectory?

I'm assuming that it isn't just Stokes drag, as that never struck me as being unsolvable (it certainly isn't vertically) or quadratic drag (also directly integrable vertically) so it must be one of the "interesting" cases, but TFA doesn't say. Not to take anything away from the young man in question, either -- I'm sure he's very bright and that his solutions are peachy-keen.

I am, however, having a hard time seeing how this will improve ballistics solutions in any case whatsoever compared to numerical solutions; ultimately one has to deal with real nonlinear fluid dynamics to solve almost any sort of less-idealized ballistics problem, the sort involving Navier-Stokes and solution spaces that haven't even been formally proven to exist yet. The idealized problems are good for understanding qualitative behavior, but not so good for quantitative prediction in all but very special cases. Computers really are going to win hands down in almost all problems one can pose in this general arena.

rgb

Re:This article is crap. The problem has been solv

[rgbatduke]

As I posted further down, I think I agree. Although I still don't know which problem it is that can't be solved that he solved -- I'm assuming linear drag forces, which should indeed be analytically solvable. It certainly is in one dimension.

But this does not (as I also note) really help, since almost nothing falls according to Stokes drag.

rgb

Skeptical

[jk80D8]

From the article, a quote from the boy's father (an engineer who personally taught his son calculus):
"He never discussed his project with me before it was finished and the mathematics he used are far beyond my reach,"

Far beyond his reach? Anyone who has taken a basic calculus course should have the background to follow the nicely reverse-engineered proof featured here on reddit: http://www.reddit.com/r/worldnews/comments/u7551/teen_solves_newtons_300yearold_riddle_an/c4t03fl

Seriously, go ahead and try it. Use an integral table for the last step if you have to. The math background of an engineer (multiple courses in calculus and differential equations) should be adequate. I know we don't have the original proof yet, but, given the simple elegance of the above solution, I'll bet it's very similar. Just saying.

The German School System ...

[twms2h]

... is far from perfect. Depending on which measure us use, Germany ranks somewhere in the top middle of the statistics. And it is definitely bad for both extremes of students: Those that are really bright and those that are - em - "intellectually challenged".

Re:This article is crap. The problem has been solv

[HuguesT]

Ray's solution is an invariant during the trajectory. It doesn't really help with the integration, which is still to be done numerically.

overhyped; not new, not a solution

[bcrowell]

As often seems to be the case with these news articles about teenage prodigies, this has been overhyped. It turns out that what he did is not new and is not a complete solution to the problem.
Parker, Am J Phys 45 (1977) 606 has a summary of the preexisting results. The expression immediately after equation 23 is the constant of the motion that Ray rediscovered.

A reddit user has a nice simple derivation: http://redd.it/u74no (Note that there is an error because he claims to have proved it in general, but it's only valid when v (the vertical velocity) is positive.)

For more on the history of the problem:

Synge and Griffith, Principles of Mechanics, p.~154 http://archive.org/details/principlesofmech031468mbp

Whittaker, A treatise on the analytical dynamics of particles and rigid bodies, p.~229 http://archive.org/details/treatisanalytdyn00whitrich

According to Whittaker this was first done by D'Alembert in 1744.

Newton, 350 years?

[dscheink]

Perhaps next year Mr. Ra will solve one of Einstein's 120 year old problems.

Over Hyped by Media?

[nukenerd]

Without seeing his solution (no links given in TFA) and peer review I cannot get excited yet.

I had not realised this is an unsolved problem. How then does artillery calculate elevation, and how did those WW2 battleships, with only electro-mechanical 'calculators', and AA gun 'Predictors' work it out? Just from empirical tables? I do have vague memories of doing this in Applied Maths at school, even taking air resistance into account. Just asking, like I'm just being naive and curious.

But is this media hype? I have known people who have gained an achievement and were then "picked up" by the media, even national media, out of all proportion to the achievement. The media always want stories.

And this : http://www.vip.it/wp-content/uploads/2012/05/Shouryya-Ray-256x300.jpg is a German 16 year-old?

If this happened in America

[davydagger]

The achievement would be downplayed. Then some "well respected"(read con-artist) 40-something would claim he found it first and will sue. about a month or two later the kid will be reprimanded in school, and we'll see him washed up at 19 struggling to fit in with the Marine Corps.

Typeface, not font!

[Benfea]

If you choose larger-sized text, you still have the same typeface, but a different font. Sorry for the derail, but the constant misuse of "font" really bugs me.

Just to reiterate, Helvetica is a typeface. Twelve point Helvetica bold is a font.