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Pure Math, Pure Joy
e271828 writes "The New York Times is carrying a nice little piece entitled Pure Math, Pure Joy about the beauty and applicability of pure math as carried out at the Mathematical Sciences Research Institute. There is an accompanying slideshow of pictures of mathematicians in action; I particularly loved the picture titled Waging Mental Battle with a Proof."
The joy of pure math. Second only to the joy of pure self-mutilation.
Very cool article! I liked the statement: "Nobody knows when some abstruse bit of math will float off a blackboard at a place like this and become a..." It reminded me of the radiant primes observation
I imagine it will be a method similar to this that helps us discover the first billion digit prime number, not some brute-force method. Speaking of prime numbers & slightly off-topic, on 5/31/2003 there was an eclipse (solar) over Norway from 4:43AM to 6:41AM. 5, 31, 2003, 443 & 641 are all prime...
What this picture doesn't show is the analogue clock just above the blackboard.. they aren't thinking.. just clock-watching !
"I am not bound to please thee with my answers" [William Shakespeare]
But the "unreasonable effectiveness" of mathematics in explaining the world, as the physicist Eugene Wigner once put it, is a minor motivation at best for those immersed in the field. Most mathematicians say they are in it for the math itself, for the delirious quest for patterns, the thrill of the detective chase and the lure of beautiful answers.
I sure hope this isn't really true. If mathematicans aren't really interested in helping understand the world, why should society fund them? I certainly know that a major motivation for my career in science is that understanding the world through science will help people, cure diseases, etc.
I like the picture where someone is drawing a fish on the blackboard while others are doing math.
Who knew that I had a future in advance mathematics when I was doodling in my math notebook during class? : )
They took the pic just as he was about to draw the eye...
You can't take the sky from me...
could someone please explain the point of this article ? like most nytimes science article it seems to have zero content. it would be nice if for a change they explained something about mathematics
OK, not in it's entirety, and not it is a serious problem, but it would be nice if the editors could make sure that each Sunday, we don't see so many postings from a single news source. Maybe some sort of summary each Sunday on interesting stories in the NYT Sunday Edition.
Pure Math, Pure Joy
Does Google = God?
Harry Potter and the Entertainment Industry
I'd never studied linear algebra until recently when I had to learn just enough to work through the inverse kinematics of a robot arm. Actually, I never really got along with Mathematics very well anyway. But looking at how matrices can solve all kinds of problems just by drawing zig-zags through rows and columns of numbers made me wonder whether the problems they model or the problems themselves came first. As I was learning the little bit of this math that I did, it started to seem to me that the Math has an independent existence, and a somewhat mysterious set of relationships of correlations and causalities connected to but not dependant on physical nature.
"Being interested in helping the world" is not the same thing as "helping the world". An ox is not interested in helping plow the farmer's field, but the farmer still feeds it.
It's rare that you're presented with a knob whose only two positions are Make History and Flee Your Glorious Destiny.
This article also reminded me of a good book (story wise, not much math) that a lot of you have probably read. It's called Fermat's Enigma. If you haven't read it you should. It's a really good book and an easy read. I might even make you want to read a real math book again ;)
Honk if you're horny.
What are prime numbers useful for in daily life?
Searching 1976 to present...
Results of Search in 1976 to present db for:
"prime number": 1238 patents.
SCO employee? Check out the bounty
Very large prime numbers are the basis of the RSA asymmetric encryption algorithms which you trust your credit card numbers and other private information to.
Anyway, I'm almost thinking you're trolling because the rest of your post demonstrates some sort of keen-ness for over-simplification. Maybe you're just not out of secondary school yet, but for your information, trig, calculus and the rest are useful for a lot more stuff than what you mention. All the different areas of maths often intermingle in any physical subject.
For the interesting tidbit of information, there has yet to be a mathematical discovery which has not found practical applications. Even group theory, which at first was thought to have nothing to do with physics or any engineering sciences, was found to be very applicable to some extremely interesting problems of fundamental physics (describing the symmetries of fundamental particles).
Daniel
Carpe Diem
Erdos himself was a device for converting speed into theorems. Ironically he lived to be 83 years old, prolifically creating new math until the very end.
My guess is that more mathematicians use amphetamines than is commonly acknowledged. This is how some older mathematicians try to keep their "edge".
BTW have you computed your Erdos Number?
How arbitrary is that?
How is e) (prime) less valid than the solution?
How about g) (The only number greater than 29)?
How about a) because its the "bad luck" number in Chinese culture (Too bad you missed out on that one, "white devil")?
How about j) (Because today is Sunday and I feel like its the correct answer)?
The surprise isn't how often we make bad choices; the surprise is how seldom they defeat us.
Results of Search in 1976 to present db for:
"prime number": 1238 patents. [uspto.gov]
Ah! So prime numbers are useful for getting patents.
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- - You can't take something off the Internet! That's like trying to take pee out of a swimming pool.
Why else would a major newspaper have a piece that describes maths in a positive light?
You ever hear of an evil or mad Mathematician? Nope, only evil or mad scientists.While they may not be philanthropists, they are not super weapon packing misanthropes. Oh well, back to the lab...
My (insert close relative here) does minimal surfaces and hangs out with some of these guys. They look far too neatly dressed in the pictures. Anyway, for a good time, you might want to take a look at some of the galleries of images that these crazy minimal surfaces guys do. I remember about ten years ago, one of my (insert close relative)'s colleagues sold a few images to the Grateful Dead for their concerts.
http://www.msri.org/publications/sgp/jim/images/
http://www.gang.umass.edu/
There is another site out at Minnesota but I'm too lazy to look for it today.
Can you point us to the authoritative "hierarchy of simplicity?
No. I think the best way is to imagine that you have to explain both alternatives to somebody who is completely clueless, and see which is quicker and easier to explain.
Of course this method does not always work, but I think that in this case most would agree that the symmetry alternative is simpler.
"See if, you turn the paper, the 8 still looks the same. It is the same if you look at it from either direction. If you put a mirror in the middle it does not change. If you look at the other numbers, this does not happen; look!"
"See, the 5 is a prime number. That means that it can only be divided evenly by itself, and one. Division means that...[lengthy explanation]. Even division means that [lengthier explanation]. The reason that one is not included in the definition is that [....]. Now we can look at all the other numbers in turn and see that they are not prime numbers [lengthy calculations, or even lengthier explanations on how they can be indentifed quickly]. Etc. Etc."
Tor
I'm a second year college student of pure math. I just wanted to tell all you non-believers taht its true. There is something amazingly beautiful in pure math. And in the way it is almost "above" reality. Math is applied philosophy. And if you've ever tried tackling a hard philosophical problem you know what it's like trying to understand a prinicipal in math...
God made the natural numbers; all else is the work of man - Kronecker
Yep and ofcourse everybody knows that mathematicians do it smoothly and continuously or discretely in groups and in fields. Interesting lifestyle :P
If they are deliberately creating questions that have a "correct but not the answer we were looking for" solution, then they are knowingly creating poor tests of intelligence. What they are really looking for then is "people who think like we do" not "very intelligent people".
It's sort of like the old biased college aptitude tests and the cup/saucer question where kids from well off white families would know that cup and saucer go together, but poor minority kids had probably never encountered a saucer in their life.
Education is a better safeguard of liberty than a standing army.
Edward Everett (1794 - 1865)
Obviously there are many solutions. Extra points for the largest possible number (with a decent explanation)
0 -> 0 = 0
1 -> 1 ! = 1
2 -> 2 ! ! = 2
3 -> 3 ! ! ! = 6 ! ! = 720 ! approx. 2.6 E+1746
Any higher ??
In Murphy We Turst
But the whole point with this question type is that the answer you get depend very much on what assumptions you make.
The question should be unambiguous, otherwise you are testing to see if people "think like you". If you call it an intelligence test then you must be the definition of intelligence. The question should have opened by stating that these symbols should not be interpretted as representing mathematical numbers.
The Mensa/ Ockham's razor based approach is to find the solution which makes the fewest possible assumptions.
I think you are misusing Ockham's razor. Ockham said entitites should not contain any uneccesary multiplications. Theorizing that one number is unique because it is prime and the others are not does not contain any unecessary assumptions as primality is a basic feature of certain numbers that is true of them regardless of the system used to express them.
Education is a better safeguard of liberty than a standing army.
Edward Everett (1794 - 1865)
Euclid alone has looked on Beauty bare.
Let all who prate of Beauty hold their peace,
And lay them prone upon the earth and cease
To ponder on themselves, the while they stare
At nothing, intricately drawn nowhere
In shapes of shifting lineage; let geese
Gabble and hiss, but heroes seek release
From dusty bondage into luminous air.
O blinding hour, O holy, terrible day,
When first the shaft into his vision shone
Of light anatomized! Euclid alone
Has looked on Beauty bare. Fortunate they
Who, though once only and then but far away,
Have heard her massive sandal set on stone.
--Edna St. Vincent Millay
"How to Do Nothing," kids activities, back in print!
Pain is merely failure leaving the body
The title of the article is "Pure Math, Pure Joy" and it's about MSRI. While it is a phenomenal place, it is no picnic for young mathematicians for sure and is often referred to as "misery", as in "yeah, I spent a year in misery (MSRI)".
For the love of $DEITY, loose != not win!!!!!
It is clearly the only answer written in binary.
Bitter and proud of it.
Pure math has been described by one friend of mine as "mathturbation", while another observed that the entire field of computer science has a severe case of "Math Envy". I'm more down with the later opinion.
-cbare