The 23 Toughest Math Questions 340
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.
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]
Different intent from Millennium Prize. (Score:1, Informative)
While there are some parallels, the Millenium Prize is a set of Problems. It's a set of specific theorems that are not proven. The challenge is to prove or disprove the theorem (P=NP, Poincare conjecture, Reimann Hypothesis, etc.) It starts with definite propositions that are believed to be true, and challenges proof of those propositions.
The DARPA Challenges is a set of questions that need answering. In a few cases (Reimann Hypothesis, Hodge Conjecture) they overlap. However, the DARPA questions are more typically like: "An Information Theory for Virus Evolution: Can Shannon's theory shed light on this fundamental area of biology?" In the DARPA case, they don't know whether their questions are answerable, or what the answers look like. The challenge is not one of proof, but one of developing new theory.
Those aren't questions (Score:5, Informative)
Re:no (Score:2, Informative)
Re:Here's a toughy (Score:3, Informative)
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
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.
Re:Bobby Heenan Said It Best... (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.
Re:Benefits the NSA (Score:3, Informative)
Maybe you misunderstood my tone when I used the phrase "abstract nonsense". It's not necessarily pejorative when used in the context of maths. It originally applied to category theory, but has been extended to refer to most types of pure maths
http://en.wikipedia.org/wiki/Abstract_nonsense [wikipedia.org]