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The 23 Toughest Math Questions
Posted by
kdawson
on Tue Sep 30, 2008 07:08 AM
from the innumerate-need-not-apply dept.
from the innumerate-need-not-apply dept.
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.
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The answer (Score:5, Funny)
42
Re: (Score:3, Funny)
I'm rather unhappy that I only got 11 of the 23 right.... guess my math skills are getting rusty.
Re:The answer (Score:5, Funny)
If you think you're unhappy.... I got 35 of the 23 questions right and I don't even know how I did that.
Parent
Re: (Score:3, Funny)
wrong (Score:5, Funny)
For any result greater than 3 the answer is 'A suffusion of yellow'
Parent
Re:no (Score:4, Funny)
Parent
Re:no (Score:5, Interesting)
Yep, google breaks! [google.com]
Parent
I have a challenge for the DoD: (Score:5, Insightful)
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.
Re: (Score:3, Funny)
What ads? Or are you some sort of IE user?
Like high school all over again. (Score:5, Funny)
Re:Like high school all over again. (Score:5, Funny)
Parent
Re:Like high school all over again. (Score:5, Funny)
Yes, except we won't get paid this time.
Don't you mean we won't get beat up if we don't?
Parent
Here's a toughy (Score:5, Insightful)
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.
Re:Here's a toughy (Score:5, Funny)
Parent
Re:Here's a toughy (Score:4, Insightful)
Well, you should probably get the facts straight.
First of all, this has nothing to do with 700B and a banker.
This also had nothing to do with lending people with bad debt.
I mean, the sub prime mortgages total about 61 billion total, of debt, for everyone who has a home in the USA.
The issue here, is that Commercial Banks, and Investment banks where combined together under the Federal Reserve (NOT a government institution, but a private entity) in the 90's to increase credit.
So, you had ludicrous deals in the 90's and later with leveraged buyouts of companies, propped up by investment bank CEO's through leverage of like 300 to 1, which is ridiculous.
This rampant abuse of credit by the Investment bank CEO's to fund these mergers and consolidations of billions of dollars of net worth, with almost no money down except the promise of higher stock values, was greedy and criminal.
I wish you people would stop swallowing what the press tells you, and do your own research online into these problems.
I mean, it is simple Math. Home mortgages cannot possibly bring the economy down to a 700B bailout. There simply isn't that many homes mortgaged.
This entire debacle was orchestrated by the Federal Reserve, condoned by Congress and greedily executed by the CEO's of these investment banks who funded these huge mergers that have happened over the past 10-15 years.
They used your savings, they used your 401K plans, they used your future earnings as credit.
Personally I do not care what happens. Either way, if we bail out the Investment CEO's, they get to walk away from all of this and we get to pay.
If we do not pay, the investment CEO's lose everything.
Either way, the USA is bankrupt.
So if we are going to go down, I would like to take the CEO's of these investment banks with me.
Put them in the bread line right next too me.
-Hackus
Parent
Re: (Score:3, Informative)
Encouraging? It's stronger than that.... (Score:5, Informative)
Congress didn't "encourage" subprime lending. They required [youtube.com] 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 [wikipedia.org]. 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.
Parent
Re: (Score:3, Insightful)
5. Will the economy go belly-up because the rate of increase of federal debt will cause the economy to become entirely dedicated to debt maintenance, requiring generations to pay high taxes and recieve few services to get the debt to managable levels?
Answer: Yes.
Don't worry, it's only 4 trillion dollars of new debt during Bush's presidency, more than the entire inflation adjusted federal debt after WWII!
How they formulate the requests? (Score:4, Interesting)
These are really hard problems and I wonder how does anyone formulate a research grant requests for them.
Following in Hilbert's footsteps huh (Score:3, Interesting)
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 [clarku.edu] in 1900. And well, the Riemann Hypothesis is there too. A hundred years later, and still no resolution.
Since you mentioned Good Will Hunting (Score:5, Insightful)
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.
the art of posing problems (Score:5, Insightful)
Re:the art of posing problems (Score:5, Insightful)
These are not mathematical problems (well, not all of them). Some are physics, most are algorithmic and a few are really mathematical questions. But things like "the brain" is not a mathematical object and thus has no place in the formulation of a mathematical question.
Parent
Yet another research grant... (Score:4, Informative)
..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 [vdash.org]
Those aren't questions (Score:5, Informative)
They're not asking for much. (Score:5, Insightful)
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'.
Cool! (Score:4, Funny)
Now I know what to do this evening.
No solve NP complete? (Score:3, Insightful)
I'd like to be the top travelling salesman in the world, damnit!
Re:No solve NP complete? (Score:5, Interesting)
So the DoD just leaked that they already know the solution to that one. Interesting.
Parent
Re:No solve NP complete? (Score:4, Insightful)
Parent
Requisite Warning (Score:5, Insightful)
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 [wikipedia.org] this is now a requisite warning whenever people talk about lists of difficult problems.
In case you missed it... (Score:3, Informative)
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
After looking at the problems... (Score:3, Insightful)
Strange. I don't see the one about the train leaving Chicago at 6:00...
-Loyal
Re:Here's a tough one. (Score:5, Funny)
How did the mathematician solve for constipation?
He worked it out with his pencil!
Parent
Re:Here's a tough one. (Score:5, Funny)
Why?
"Because calculators are a pain in the ass."
Parent
Re:Here's a tough one. (Score:4, Funny)
Not as much as using logs.
Parent
Re: (Score:3, Interesting)
Re:Come together right now (Score:4, Funny)
Or are we not as smart as we say we are?
Maybe you not smart. Me think good.
Parent
Re: (Score:3, Funny)
We need things that make us go!
Can you make us go?
Then we strong. And smart! *huhuhuhuhu*
Re:Come together right now (Score:5, Funny)
Parent
Re: (Score:3, Funny)
Re: (Score:3, Funny)
Re:Benefits the NSA (Score:4, Insightful)
(+5, the whole point). I'm a mathematician-in-training and I've just finished an MSc. It's so depressing to see that mathematics has been turned in the last 50 years from a way of expanding the mind and as a tool for scientific discovery to a channel for
(1) optimising wealth generation on the gambling paradise they call the stock market; and
(2) invading privacy to ensure those who have won the gamble get to keep their hardly-earnt gains.
This also means that half my fellow mathematicians are money/power-hungry bastards who remind me that there is no benevolent god (for no such god would reward nasty characters with so much talent). I am in an environment which through peer pressure discourages those who might pursue mathematical ars gratia artis, as it were.
Plato might despair, seeing mathematics today as precisely the toy of the world of change and decay he sought to distance it from. Hardy's ode to number theory could not have been more wrong.
Fuck DARPA and fuck the NSA. And before some idiot goes all "we'd have no Internet without...", (1) says who? the Internet was designed and implemented by a host of international contributors (2) so what? the end does not justify the means. I'm in the UK, and I've had the best of my peers prodded by our equivalent agencies to leave research and go work for them, and I'm so proud of them for having refused (fuck knows with my mouth they'd never ask me). These agencies all exist, ultimately, to oppress - whether abroad or at home.
Please, do not feed the hand that bites.
Parent
Re:Benefits the NSA (Score:5, Informative)
"I'm a mathematician-in-training and I've just finished an MSc. It's so depressing to see that mathematics has been turned in the last 50 years from a way of expanding the mind and as a tool for scientific discovery to a channel for
(1) optimising wealth generation on the gambling paradise they call the stock market; and
(2) invading privacy to ensure those who have won the gamble get to keep their hardly-earnt gains."
I'm also a mathematician in training, having finished an MSc. I'm about to start a PhD working on (1). I assume (2) is a reference to the study of cryptography. Studying wealth-generation techniques does not make me power-hungry or greedy, in the same way that the people working on the Manhattan project were not monsters who wanted to extinguish life.
I'm not doing this out of personal greed, I'm doing it because the mathematics involved is elegant and interesting.
Maybe you're happy working away on your abstract nonsense, but I think I'd prefer to work on something which might actually make a difference to people's lives. Just because an application has potential for abuse doesn't make it inherently evil, as you seem to suggest.
Parent
Re:Benefits the NSA (Score:5, Interesting)
Parent
Re:Benefits the NSA (Score:4, Interesting)
Speaking as a former airmen with a very similar past, aren't we not supposed to speak about that? EEFI?
Parent
Re:Benefits the NSA (Score:4, Funny)
Parent
Re:DARPA Ethics (Score:4, Interesting)
You also have the problem of whole fields of research popping up which depend on defense money, and then shrink once the DoD shifts its priorities. I specialize in a few minority languages of Russia. Back during the Cold War, the relevant linguistics department at Indiana University Bloomington got a tonne of funding from the Air Force because its work could be connected to Soviet areal studies. Once 1991 and the fall of the USSR came along, most of the funding dried up and most jobs were lost. They never saw a need to always keep up to date with other sources of funding, and now Uralic and Altaic studies in the US are a shadow of what they once were, with European universities outclassing them.
Parent
Re:They missed one (Score:5, Funny)
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!
Parent
Re: (Score:3, Funny)
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?