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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.
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)

    by Anonymous Coward on Tuesday September 30 2008, @07:09AM (#25203101)

    42

  • by larry bagina (561269) on Tuesday September 30 2008, @07:13AM (#25203123) Journal

    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.

  • by NotBornYesterday (1093817) * on Tuesday September 30 2008, @07:17AM (#25203147) Journal
    Does anyone else here feel like we're being asking us to do someone else's math homework for them?
  • Here's a toughy (Score:5, Insightful)

    by Anonymous Coward on Tuesday September 30 2008, @07:24AM (#25203207)
    You are a banker who has US$700b in bad loans mostly provided to people who had a history of bad debt and whom have defaulted on their repayments. The Government is offering you somebody elses money to cover your poor judgement and prop up your terrible lending practices. Answer the following questions (1 point each):
    1. Is US$700b enough?
    2. What will be the total value wiped of the global stock markets by your ineptitude?
    3. How big will your bonus be this year

    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.

    • by IceCreamGuy (904648) on Tuesday September 30 2008, @07:37AM (#25203313) Homepage
      Dude, this question is pretty irrelevant, I mean, when would a situation like that ever arise?
    • Re:Here's a toughy (Score:4, Insightful)

      by hackus (159037) on Tuesday September 30 2008, @09:08AM (#25204153) Homepage

      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

      • Re: (Score:3, Informative)

        Encouraging someone to do something stupid doesn't actually change the fact that it's stupid though :)
        • by tacokill (531275) on Tuesday September 30 2008, @10:37AM (#25205205)
          How about we use the correct term and call it what it is: legislation.

          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.

          ...and yes, I expect to get modded down just because the video is clearly pro-McCain.
      • 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!

  • by azgard (461476) on Tuesday September 30 2008, @07:25AM (#25203223)

    These are really hard problems and I wonder how does anyone formulate a research grant requests for them.

  • by dido (9125) <dido.imperium@ph> on Tuesday September 30 2008, @07:29AM (#25203247) Homepage

    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.

  • by QuantumG (50515) * <qg@biodome.org> on Tuesday September 30 2008, @07:30AM (#25203255) Homepage Journal

    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.

  • by e**(i pi)-1 (462311) on Tuesday September 30 2008, @07:31AM (#25203263) Homepage Journal
    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.
      • by Yvanhoe (564877) on Tuesday September 30 2008, @08:07AM (#25203563) Journal
        A mathematically consistent formulation would have prevented me from submitting "cat /dev/null" as a proposition, with the annotation that this is a program simulating the output of a dead brain.

        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.
  • by Anonymous Coward on Tuesday September 30 2008, @07:31AM (#25203269)

    ..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:

    "Cameron Freer [mit.edu], an instructor in pure mathematics at MIT, is working on an intriguing project called vdash.org [vdash.org] (video from O'Reilly Ignite Boston 4 [youtube.com]): a math wiki which only allows true theorems to be added! Based on Isabelle [in.tum.de], a free-software theorem prover, the wiki will state all of known mathematics in a machine-readable language and verify all theorems for correctness, thus providing a knowledge base for interactive proof assistants [wikipedia.org]. In addition to its benefits for education and research, such a project could reveal undiscovered connections between fields of mathematics, thus advancing some fields with no further work being necessary."

    link [vdash.org]

  • by ghostunit (868434) on Tuesday September 30 2008, @07:44AM (#25203371)
    They are asking the reader to create entire fields! how lazy of them.
  • by jdc180 (125863) on Tuesday September 30 2008, @07:52AM (#25203421)

    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)

    by Kj0n (245572) on Tuesday September 30 2008, @08:29AM (#25203767) Homepage

    Now I know what to do this evening.

  • by Sobrique (543255) on Tuesday September 30 2008, @08:32AM (#25203815) Homepage
    I'm quite disappointed that they didn't include the general solution to an NP complete problem in their list.

    I'd like to be the top travelling salesman in the world, damnit!

    • by Anonymous Coward on Tuesday September 30 2008, @09:04AM (#25204131)

      So the DoD just leaked that they already know the solution to that one. Interesting.

      • by CodeBuster (516420) on Tuesday September 30 2008, @01:07PM (#25207295)
        Everyone knows or at least strongly suspects that P not equal NP, it's just that nobody has been able to prove that yet. It is exceedingly unlikely that DoD or even NSA (which would certainly be interested in a proof and practical demonstration of P = NP) has proven the conjecture and even less likely that they have proven it in the affirmative ( P = NP). Decades of research by some of the best minds in theoretical computer science have barely scratched the surface of this problem (mostly closing off leads that were once thought to be promising and further reinforcing the reputation of the difficulty of the proof). The solution to this problem and a practical demonstration would be worth billions, possibly even trillions, of dollars and name placement among the great mathematicians of history. If someone had a proof it would be very unlikely that they could keep it secret for very long with those sorts of incentives for being the first to announce the discovery.
  • Requisite Warning (Score:5, Insightful)

    by Comatose51 (687974) on Tuesday September 30 2008, @09:01AM (#25204105) Homepage

    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.

  • by Nazlfrag (1035012) on Tuesday September 30 2008, @09:07AM (#25204141) Journal

    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

  • by LoyalOpposition (168041) on Tuesday September 30 2008, @09:39AM (#25204481)

    Strange. I don't see the one about the train leaving Chicago at 6:00...

    -Loyal

    • by Anonymous Coward on Tuesday September 30 2008, @07:33AM (#25203289)

      (+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.

      • Re:Benefits the NSA (Score:5, Informative)

        by SoVeryTired (967875) on Tuesday September 30 2008, @09:36AM (#25204435)

        "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.

    • Re:DARPA Ethics (Score:4, Interesting)

      by CRCulver (715279) <crculver@christopherculver.com> on Tuesday September 30 2008, @07:59AM (#25203473) Homepage

      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.

    • 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!

    • 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?