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Math Technology

The 23 Toughest Math Questions 340

Posted by kdawson
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 23 Toughest Math Questions

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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.

  • Benefits the NSA (Score:2, Insightful)

    by CRCulver (715279)
    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 [amazon.com] ). 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.
    • 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: (Score:3, Interesting)

          by Draek (916851)

          As a math student...

          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.

          True, but what the GP seems to be getting at is, if scientists in general and mathematicians in particular would think about the potential ethical ramifications of their work before doing it, perhaps the world would be a nicer place. A philosophy I'd tend to agree with, BTW, specially with regards to the US' NSA and DoD.

          I'm not doing this out of personal greed, I'm doing it because the mathematics involved is elegant and interesting.

          Best of lucks, then, and I hope I ever get the chance of looking at your work, the math involved *does* sound interesting from what little I've seen.

          Maybe you're happy working away on your abstract nonsense

          You just *had* to rui

  • 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?
      • by aero6dof (415422)

        Dude, this question is pretty irrelevant, I mean, when would a situation like that ever arise?

        Quit asking trick questions, everybody knows that the free market has this all taken care of!

    • Re: (Score:2, Offtopic)

      by kklein (900361)

      4. Will the entire economy go belly-up because some whiny voters who don't understand that this is a financially extinction-level event decide to get all moralistic instead of being pragmatic and fixing it, while making sure it can't happen again, like the liquidity trap of the Great Depression and the S&L fracas can't happen again?

      Answer: Yes.

      • Re: (Score:3, Insightful)

        by Sj0 (472011)

        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!

    • 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.

      Here's another one for your banker friend.

      Well you already charged the sub-prime borrowers a higher interest rate to offset them as a credit risk didn't you? or was the reasoning for the higher interest rate complete BS?

      Or in summary, were you lying to the people you were lending the money to, or are you lying now?

    • by houghi (78078)

      And for the first graders. How much would every citizen get if they gave all an equal share of that US$700b if there are 350m people in the USofA. (It also shows the money in a number that makes it understandable for people.)

    • 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

    • 1. No, 700B only covers the bad debt, not money it will cost to make the Financial Sector moving again. The Financial Sector has basically stopped moving.

      2. The Total Value is the Money you take, or give to the market. WHEN YOU SELL YOUR STOCK.

      3. What the contract says it is to be that I, and the Corporation that signed it says it will be.

      Bonus Question; YES!, But only when the Market Price of the house will be Greater than 125% of the Current Value.

      What did I win?

    • Answers:
      1. No. But read the fine print and you'll discover that you are giving more than 700 bilion.
      2. Nothing, it is being wiped out by stock invertors' ineptitude. (Or are you asking how much was lost by financing idiotic CEO's? That is a toughter question.)
      3. With a bailout, near US$800 bilion. Without it, they'll be out of the job by the year's end.

  • 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)

    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 wisty (1335733)
      I would say that most of these are so vague that they are 'research areas', rather than 'questions'. Sort of like 'develop a mathematically consistent model for the motions of heavenly bodies'. They do sound fun though.
    • by Zironic (1112127)

      Actually it is rather specific. They want you to build a working brain simulator with a math foundation rather then guesses at what the brain is doing biologically.

      AFAIK mathematically consistent means that it's all derived from the axioms without any hand waving.

      • "Actually it is rather specific. They want you to build a working brain simulator with a math foundation rather then guesses at what the brain is doing biologically."

        What they are asking for is a contradiction in terms, math is derived from thought, we do not think using abstract formal systems, we think using direct neurological computation, the "mathematics" we have invented is not the language of the brain, it is a derivitive language of some more basic unified language.

        Math is the problem, the brain doe

      • 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.
      • Actually it is rather specific. They want you to build a working brain simulator

        Define "working brain simulator". Include a complete and definitive set of criteria by which it can be determined whether something is a working brain simulator or not.

        Without that definition and those criteria, it's not specific at all.

        • You are Alan Turing and I claim my ten pounds.
          • by ajrs (186276)

            You are Alan Turing and I claim my ten pounds.

            If your a regular on slashdot, I'll bet you can claim a lot more pounds than 10.

    • by RockoTDF (1042780)
      What they mean is to nail down equations which can be used to govern and predict brain activity in a similar fashion to the ones we have in physics. Essentially they are saying that Neuroscience needs to be approached from a more quantitative perspective than biological due to its complexity. Ie we can't totally figure out the brain with MRI and microscopes. However, more of this work will be done on computers than chalkboards. Check this out: http://en.wikipedia.org/wiki/Computational_neuroscience [wikipedia.org]
    • by mangu (126918)

      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?

      The way I understood it is "develop a mathematical model of consciousness". Something that very [wikipedia.org] smart [wikipedia.org] people have been wondering about for some time.

    • This is DARPA research so the exact problem formulation is classified. ;-)

    • by tgv (254536)

      Well, the different opinions above already show there is not an easy interpretation, but it clearly says "functional". In neurospeak, that means: we're not interested in neural firing patterns or genetic expression of FOXP21 in a rat's hippocampus while learning to navigate a maze with electric shock plates during different phases of starvation. Instead, we're interested in language, vision, motor planning, memory, etc. The "mathematically consistent" bit is to me (IAACNCM: I Am A Computational Neuro-Cognit

    • Hilbert's original problems weren't all particularly well posed either- most of the ones that can be now considered "settled" were well-posed in 1900, as well as some of those outstanding (the conditions of the Riemann Hypothesis are clear, for example), but the original 23 contain a number of vague "discipline-extension" problems as well. Number 23 for example is "extend the methods of the calculus of variations," a task to which a large number of mathematicians can lay claim.
  • 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]

  • Hilbert's problems were stated fairly precisely. The Millenium Prize problems have detailed statements written by experts in the fields involved. Most of these DARPA questions could use some clarification as to what they're asking for. Hopefully that will be forthcoming.

  • DARPA Ethics (Score:2, Insightful)

    by Ralish (775196)

    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 live

    • 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.

    • While solutions to any of these mathematical conundrums would be grand

      It's not always the solutions but the math developed to try and find the solutions that get really interesting. Fermat's Last Theorem was solved not by a proof in a margin but by a combined effort over a century, and the math that resulted was greater than the sum of its parts.

      What is created as a result of this challenge may benefit millions of people in ways we never thought possible.

    • by Kagura (843695)

      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.

      Unfortunately, there will always be people who dislike other countries. In order to defend against those countries, one needs a suitable defense force or a steadfast ally who has a suitable defense force. For all the horrible things the US government has done for the past 200 years, I am much happier that it was the US who ended up on top, rather than a less open and less civilized country. I would prefer it stay this way, as the US still has a long way to go down the dark path to fall out of my favor entir

    • Re: (Score:3, Insightful)

      >>This can of course degenerate into a whole ethics and morality debate on the value of human life

      You call a debate on the value of human life a degeneration?

      Slashdot truly has become more cynical than I had imagined.

      -b

  • 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'.

  • If a train leaves Chicago at 8:30 headed for Denver traveling at 45 MPH...

    • by Jade E. 2 (313290) <slashdot AT perlstorm DOT net> on Tuesday September 30, 2008 @08:12AM (#25203605) Homepage

      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!

      • Re: (Score:3, Insightful)

        by Prien715 (251944)

        In cash, because they sue the track operators and get a huge class action lawsuit settled out of court for a bajillion dollars.

  • Not like the Millenium Prize problems, certainly. They're broad fields, some of which aren't even primarily mathematical and some of which already have some existing answers. That web page appears to be quoting the DARPA .doc precisely, but it reads as if it were a brief summary of a real RFP.

    Just looking at the first few examples:

    A predictive theory of the brain? That'll be a fantastic biological breakthrough, but I doubt it'll require any new mathematics.

    I'm happy to see that "persistence in stochastic

  • 1 Eat
    2 shit
    3 die

    Or, if you are an underpants gnome:

    1. Eat, shit, die
    2. ???
    3. Profit

    And to answer the question above it:

    Settle the Smooth Poincare Conjecture in Dimension 4. The Poincare Conjecture in Pantene's new Dimension 4 shampoo smooths out all stubborn theories in cosmology to unlock the secret of "dark energy" and give a depth to your space-time.

    • Hating to reply to myself but...

      What is the role of homotopy theory in the classical, geometric, and quantum Langlands programs?

      The role of homotopy theory in the classical, geometric and quantum Langlands programs is to teach fashion sense to the locals of the Langlands. Ensure their hair is styled in a manner that is both masculine and sensitive. Supply shirts with overly large collars, splashed with bright colours. Fragrant and condition the Langlanders skin to be soft to the touch. Therefore, the role o

  • Cool! (Score:4, Funny)

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

    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

  • That knowledge will be used against us... That's why I'm not telling them the answers...Please don't insist.

  • by clone53421 (1310749) on Tuesday September 30, 2008 @01:49PM (#25207795) Journal

    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.

The tree of research must from time to time be refreshed with the blood of bean counters. -- Alan Kay

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