Slashdot Mirror
The 23 Toughest Math Questions
coondoggie sends in a Network World post that begins "It sounds like a math phobic's worst nightmare or perhaps Good Will Hunting for the ages. Those wacky folks at the Defense Advanced Research Projects Agency have put out a research request it calls Mathematical Challenges, that has the mighty goal of 'dramatically revolutionizing mathematics and thereby strengthening DoD's scientific and technological capabilities.' The challenges are in fact 23 questions that, if answered, would offer a high potential for major mathematical breakthroughs, DARPA said." Some of the questions overlap with the Millennium Prize Problems of the Clay Mathematics Institute, which each carry a $1M prize.
42
Don't use MS Word.
I also have a challenge for the slashdot janitors: Link to the original source instead of an ad-laden blog.
Do you even lift?
These aren't the 'roids you're looking for.
The portion of the DoD most interested in maths achievements is the NSA, which employs more mathematicians than any other institution in the world (see e.g. Bamford's Body of Secrets ). So when the authors of this list talk about increasing the abilities of the DoD, they really mean increasing violation of privacy and harrasment of anyone thinking too freely.
Does anyone else here feel like we're being asking us to do someone else's math homework for them?
I prefer rogues to imbeciles because they sometimes take a rest.
How did the mathematician solve for constipation?
He worked it out with his pencil!
Do you even lift?
These aren't the 'roids you're looking for.
Bonus question: Is lending a value that is worth 125% of the house it is secured against a good idea? State your reasons why and show your working out.
These are really hard problems and I wonder how does anyone formulate a research grant requests for them.
Or are we not as smart as we say we are?
Maybe you not smart. Me think good.
This comment is for entertainment purposes only. Any similarity to real insight or information is purely coincidental.
I wonder if it's just coincidence that the number of problems they list is the same as the number of problems David Hilbert listed in his famous address in 1900. And well, the Riemann Hypothesis is there too. A hundred years later, and still no resolution.
Qu'on me donne six lignes écrites de la main du plus honnête homme, j'y trouverai de quoi le faire pendre.
Say I'm working at N.S.A. Somebody puts a code on my desk, something nobody else can break. So I take a shot at it and maybe I break it. And I'm real happy with myself, 'cause I did my job well. But maybe that code was the location of some rebel army in North Africa or the Middle East. Once they have that location, they bomb the village where the rebels were hiding and fifteen hundred people I never had a problem with get killed.
Now the politicians are sayin' "send in the Marines to secure the area" 'cause they don't give a shit. It won't be their kid over there, gettin' shot. Just like it wasn't them when their number got called, 'cause they were pullin' a tour in the National Guard. It'll be some guy from Southie takin' shrapnel in the ass. And he comes home to find that the plant he used to work at got exported to the country he just got back from. And the guy who put the shrapnel in his ass got his old job, 'cause he'll work for fifteen cents a day and no bathroom breaks. Meanwhile my buddy from Southie realizes the only reason he was over there was so we could install a government that would sell us oil at a good price. And of course the oil companies used the skirmish to scare up oil prices so they could turn a quick buck. A cute, little ancillary benefit for them but it ain't helping my buddy at two-fifty a gallon. And naturally they're takin' their sweet time bringin' the oil back and maybe even took the liberty of hiring an alcoholic skipper who likes to drink seven and sevens and play slalom with the icebergs and it ain't too long 'til he hits one, spills the oil, and kills all the sea-life in the North Atlantic. So my buddy's out of work and he can't afford to drive so he's got to walk to the job interviews which sucks 'cause the shrapnel in his ass is givin' him chronic hemorrhoids. And meanwhile he's starvin' 'cause every time he tries to get a bite to eat the only blue-plate special they're servin' is North Atlantic scrod with Quaker State.
So what'd I think? I'm holdin' out for somethin' better. I figure I'll eliminate the middle man. Why not just shoot my buddy, take his job and give it to his sworn enemy, hike up gas prices, bomb a village, club a baby seal, hit the hash pipe and join the National Guard? Christ, I could be elected President.
How we know is more important than what we know.
There is an art in finding good questions. Hilbert did it in 1900 with his 23 problems or the millenia problems in 2000. Some of the 23 problems stated are too vague. The first example: "Develop the mathematics of the brain". This covers large parts of computer science, artificial intelligence and psychology. What does "mathematically consistent" mean? A mathematical problem can be taken seriously if there is a clear goal and if there is a possibility to determine, when the problem is solved. This is not the case for many of the problems listed on this website.
..and most of the challenges have little to do with math. Meanwhile, here's something which could lead to real progress in mathematics (From the Slashdot Firehose):
An anonymous reader writes:
link
Why?
"Because calculators are a pain in the ass."
While solutions to any of these mathematical conundrums would be grand, I'm not sure I'd want to do so in the name of DARPA, or even have any association of my discoveries with DARPA.
At the end of the day, DARPA specialises in technology that is designed to benefit the military, and as a result, is frequently designed for either either killing people, or making it easier to do so. Yes, there's the whole "defence" argument; that the technology will be used for saving lives. But this is a half-truth, the lives being saved are almost always select (only lives belonging to a certain state(s) (the US and potentially its allies in this case)), and often at the cost of other lives.
This can of course degenerate into a whole ethics and morality debate on the value of human life, but ideally, I'd rather such findings published through an academic institute, e.g. a university, that doesn't have any ties to military technology, but rather, a persuasion to applying scientific breakthroughs in the advancement of the common good for humanity as a whole.
I know there have been advancements that DARPA has made that have benefited humanity as a whole, such as the Internet, but keep in mind this was not the primary intent. The Internet turned out to have enormous potential outside the military, but it was military benefits that were the primary focus of the project, and they no doubt got them; the military portion of the Internet split from the public domain and is now a highly classified network, possibly with numerous innovations that are not available to the public.
They are asking the reader to create entire fields! how lazy of them.
Unsure...
:(){
Not as much as using logs.
They only want a mathematical model of the brain, a mathematical model of society as a whole, and fundamental laws of biology so they can answer 'why we are here'.
Huh... I just figured out a neat, elegant solution to #17, but there's not quite enough space in this margin to fit it in...
Dude, I think I can see my house from here.
Surely there are enough nerds on slashdot to figure these out. Or are we not as smart as we say we are?
You must be new here.
My blog
69 FTW!
Am I eval()? - http://www.monst3r.com.br
77 is better. You get 8 more.
Oooh, I remember that one. If a train leaves Chicago at 8:30 headed for Denver traveling at 45 MPH, and at 8:45 it's parent company declares bankruptcy because Congress refused to bail out the bank that owned a controlling stake in them, and it's going the wrong direction due to a glitch in one of the two data centers that handle the entire nations routing, and the train derails in Pennsylvania at 9:00 due to track damage that was never repaired from the last hurricane, killing most of the people on board, where do they bury the survivors?
I can't believe they left that off the list!
Now I know what to do this evening.
Apparently, according to Google this is a pretty dang hard question to answer:
Yep, google breaks!
The best I've heard is:
If Carol has 5 oranges, and
Ted has 7 apples, and
Sue has 3 bananas, then
(wait for it)....
How many nuts does Bill have?
Don't be apathetic. Procrastinate!
I'd like to be the top travelling salesman in the world, damnit!
Personally, I think a more useful and trickier math question is 'You have $2.17 and the 6-pack of beer costs $7.99, how do you buy the beer?' That answer has to be worth a 1 million dollars, or at least $5.82.
A positive attitude may not solve all your problems, but it will annoy enough people to make it worth the effort.
For any result greater than 3 the answer is 'A suffusion of yellow'
A learning experience is one of those things that say, 'You know that thing you just did? Don't do that.' - D. Adams
Just in case anyone is late to this discussion, let's be very clear about one thing: "These are not homework problems!"*
*Thanks to George Dantzig this is now a requisite warning whenever people talk about lists of difficult problems.
EvilCON - Made Famous by
Here's the list:
* The Mathematics of the Brain: Develop a mathematical theory to build a functional model of the Terminator that is mathematically consistent and predictive rather than merely biologically inspired.
* The Dynamics of Networks: Develop the high-dimensional mathematics needed to accurately model and predict behavior in large-scale distributed networks that evolve over time occurring in communication, biology and the Matrix.
* Capture and Harness Stochasticity in Nature: Address Mumford's call for new mathematics for the 21st century. Develop methods that apply extrodinary rendition to persistence in stochastic environments.
* 21st Century Fluids: Classical chemical warfare and the Navier-Stokes Equation were extraordinarily successful in obtaining quantitative understanding of shock waves, turbulence and solitons, but new methods are needed to tackle complex fluids such as foams, suspensions, gels and liquid crystals.
* Biological Quantum Field Theory: Quantum and statistical methods have had great success modeling virus evolution. Can such techniques be used to model more complex systems such as biological warfare agents? Can these techniques be used to control the battlefield?
* Computational Duality: Duality in mathematics has been a profound tool for theoretical understanding. Can it be extended to develop principled computational techniques where duality and geometry are the basis for novel weapon systems?
* Occam's Razor in Many Dimensions: As data collection increases can we "do more with less" by finding lower bounds for surveiling each and every citizen on the planet? This is related to questions about entropy maximization algorithms.
* Beyond Convex Optimization: Can linear algebra be replaced by algebraic geometry in a systematic weapon guidance system?
* What are the Physical Consequences of Perelman's Proof of Thurston's Geometrization Theorem?: Can profound theoretical advances in understanding three dimensions be applied to construct and manipulate structures across scales to fabricate giant robots?
* Algorithmic Origami and Biology: Build a stronger mathematical theory for isometric and rigid embedding that can give insight into protein destruction.
* Optimal Nanostructures: Develop new mathematics for constructing optimal globally symmetric structures by following simple local rules via the process of nanoscale self-assembling armor plates.
* The Mathematics of Quantum Computing, Algorithms, and Entanglement: In the last century we learned how quantum phenomena shape our world. In the coming century we need to develop the mathematics required to blast the quantum world into little tiny pieces.
* Creating a Game Theory that Scales: What new scalable mathematics is needed to replace the traditional Partial Differential Equations (PDE) approach to android targeting systems?
* An Information Theory for Virus Evolution: Can Shannon's theory shed light on this fundamental area of biological warfare?
* The Geometry of Genome Space: What notion of distance is needed to disintegrate biological utility?
* What are the Symmetries and Action Principles for Biology?: Extend our understanding of symmetries and action principles in biology along the lines of classical thermodynamics, to include important biological concepts such as robustness, modularity, evolvability and head mounted laser beams.
* Geometric Langlands and Quantum Explosives: How does the Langlands program, which originated in number theory and repres
We need things that make us go!
Can you make us go?
Then we strong. And smart! *huhuhuhuhu*
Any sufficiently advanced intelligence is indistinguishable from stupidity.
Strange. I don't see the one about the train leaving Chicago at 6:00...
-Loyal
I aim to misbehave.
Ok, first you invest that money in the stock market...nevermind.
When I have a kid, I want to put him in one of those strollers for twins and then run around the mall looking frantic.
Yeah. And if you define 2 as being 2=17, then 2+2 is 34. Sofuckingwhat?
How about we use the correct term and call it what it is: legislation.
...and yes, I expect to get modded down just because the video is clearly pro-McCain.
Congress didn't "encourage" subprime lending. They required it. (please excuse the McCain propaganda in this video...not meant to be political but it has some very relevant facts to the question at hand)
Doesn't anyone remember "redlining" mortgages from the 80's and 90's? Here is some background info. Read the part about mortgages.
Congress reacted to this by legislating subprime lending and requiring banks to provide X% of their loans to people who probably should not have gotten them.
Yeah right, Pierre. You have no idea how much confusion your little joke is going to cause, do you?
Find environmentally and socially responsible products on http://buy-right.net
So if you have ever wanted to settle the Riemann Hypothesis, which I won't begin to describe but it is one of the great unanswered questions in math history, experts say. Or perhaps you've always had a theory about Dark Energy, which in a nutshell holds that the universe is ever-expanding, this may be your calling.
I can't really call it a sentence, because somehow it turned into two of them... and it doesn't really work like that.
Alexander Peter Kristopeit bought his basement from his mommy for one dollar.
It matters because of rounding. It's a typical computer science mathematics problem, because it's quite common to calculate a bunch of percentages that don't add up to 100%, and they'll still be accurate. Well, mostly.
Just because you're too stupid to understand it doesn't mean you have to use foul language to put an exclamation point on your ignorance.
My blog. Good stuff (when I remember to update it). Read it.
It's over 9000!
In cash, because they sue the track operators and get a huge class action lawsuit settled out of court for a bajillion dollars.
-- Political fascism requires a Fuhrer.