It sounds like a math phobic's worst nightmare or perhaps Good Will Hunting for the ages.
Those wacky folks at he 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. 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.
DARPA perhaps obviously states research grants will be awarded individually but doesn't say how much they'd be worth. The agency does say you'd need to submit your research plan by Sept. 29, 2009.
So if you're game, take your pick of the following questions and have at it.
- The Mathematics of the Brain: Develop a mathematical theory to build a functional model of the brain 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 social sciences.
- Capture and Harness Stochasticity in Nature: Address Mumford's call for new mathematics for the 21st century. Develop methods that capture persistence in stochastic environments.
- 21st Century Fluids: Classical fluid dynamics 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 bacteria? Can these techniques be used to control pathogen evolution?
- 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 algorithms?
- Occam's Razor in Many Dimensions: As data collection increases can we "do more with less" by finding lower bounds for sensing complexity in systems? This is related to questions about entropy maximization algorithms.
- Beyond Convex Optimization: Can linear algebra be replaced by algebraic geometry in a systematic way?
- 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 novel materials?
- Algorithmic Origami and Biology: Build a stronger mathematical theory for isometric and rigid embedding that can give insight into protein folding.
- Optimal Nanostructures: Develop new mathematics for constructing optimal globally symmetric structures by following simple local rules via the process of nanoscale self-assembly.
- 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 control the quantum world.
- Creating a Game Theory that Scales: What new scalable mathematics is needed to replace the traditional Partial Differential Equations (PDE) approach to differential games?
- An Information Theory for Virus Evolution: Can Shannon's theory shed light on this fundamental area of biology?
- The Geometry of Genome Space: What notion of distance is needed to incorporate 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 variability.
- Geometric Langlands and Quantum Physics: How does the Langlands program, which originated in number theory and representation theory, explain the fundamental symmetries of physics? And vice versa?
- Arithmetic Langlands, Topology, and Geometry: What is the role of homotopy theory in the classical, geometric, and quantum Langlands programs?
- Settle the Riemann Hypothesis: The Holy Grail of number theory.
- Computation at Scale: How can we develop asymptotics for a world with massively many degrees of freedom?
- Settle the Hodge Conjecture: This conjecture in algebraic geometry is a metaphor for transforming transcendental computations into algebraic ones.
- Settle the Smooth Poincare Conjecture in Dimension 4: What are the implications for space-time and cosmology? And might the answer unlock the secret of "dark energy"?
- What are the Fundamental Laws of Biology?: This question will remain front and center for the next 100 years. DARPA places this challenge last as finding these laws will undoubtedly require the mathematics developed in answering several of the questions listed above.
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Mathematical Brain teasers
Tough problems indeed. Took me all day and most of the night. Now where do I send my answers?
I got em all covered before
I got em all covered before lunch. Who wants chicken?
Saucy McFoodlefist, Professional, was a grand old man from Pollokshields, with eyes of pale blue irradiated with dark blue—the loveliest eyes I've seen. In the time before becoming a professional, Saucy McFoodlefist led a wild, vagabond-like life spiced by absinthe and hashish. Saucy McFoodlefist, Professional, Libertine, was never married. His chief reasoning for never binding his destiny to another was that "a beautiful woman without a mind of her own leaves her lover with no resource after he had physically enjoyed her charms."
Later in life, Saucy McFoodlefist again returned to his pre-Professional ways. In Saucy McFoodlefist's view, “deceiving a fool is an exploit worthy of an intelligent man,” and most of his professional life was spent in this fashion.
In the view of the Earl of Rochester, "The only things about which Saucy McFoodlefist, Professional knows nothing are those which he believes himself to be expert: the rules of the dance, the French language, good taste, the way of the world, savoir vivre. It is only his comedies which are not funny, only his philosophical works which lack philosophy—all the rest are filled with it; there is always something weighty, new, piquant, profound. He is a well of knowledge"
u sponsor i take the challenge
but my knowledge about mathematics already rusting
All the answers
There is the posibility that if you solve any of the described queries though in a very elementary state you will have covered the basic structure of the mythical TOE.(Theory of everything.)
Stochasticity is a fact and has a pattern generated by the incidence described by a certain theorem that has already been discovered.Wanna guess which one?
I think I will get the Moola.Tahiti here we come.
Oh I forgot...research.
Psychohistory
Isn't question 2 a request for "psychohistory" as described by Isaac Asimov in his Foundation novels. It took the human race 12,000 years to get to that point in the novels, DARPA is more ambitious it seems...
Well, irreducibility... Good
Well, irreducibility...
Good point about the Psychohistory...
And in general, there is a strong argument against the "solvability" of many of the items on the list: computational irreducibility.
(Cf. Wolfram and Chaitin, for example.)
Some believe that this applies even to
the Riemann hypothesis.
It's also the reason why a lot's of mathematics is nowadays concerned with the problems of its
own making, not much concerned with the world "out there".
Navier-Stokes equations fail
Olga Ladazhinski published a paper over a 150 years ago questioning whether or not the full blown Navier-Stokes eqns model fluids. Basically, no one has even written an existance proof, so there is considerable doubt if they truely represent real fluids.
Math is hard. Let's go
Math is hard. Let's go shopping!
We Can Put an End to Word Attachments
Don't you just hate receiving Word documents in email messages? Word attachments are annoying, but worse than that, they impede people from switching to free software. Maybe we can stop this practice with a simple collective effort. All we have to do is ask each person who sends us a Word file to reconsider that way of doing things.
http://www.gnu.org/philosophy/no-word-attachments.html
hellooooooo
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