DARPA (The Defense Advanced Research Projects Agency) recently released the DARPA Mathematical Challenges (Word document)—23 challenging mathematical problems “with the goal of dramatically revolutionizing mathematics and thereby strengthening DoD’s scientific and technological capabilities.”

The titles of the challenges are:

1. The Mathematics of the Brain
2. The Dynamics of Networks
3. Capture and Harness Stochasticity in Nature
4. 21st Century Fluids
5. Biological Quantum Field Theory
6. Computational Duality
7. Occam’s Razor in Many Dimensions
8. Beyond Convex Optimization
9. What are the Physical Consequences of Perelman’s Proof of Thurston’s Geometrization Theorem?
10. Algorithmic Origami and Biology
11. Optimal Nanostructures
12. The Mathematics of Quantum Computing, Algorithms, and Entanglement
13. Creating a Game Theory that Scales
14. An Information Theory for Virus Evolution
15. The Geometry of Genome Space
16. What are the Symmetries and Action Principles for Biology?
17. Geometric Langlands and Quantum Physics
18. Arithmetic Langlands, Topology, and Geometry
19. Settle the Riemann Hypothesis
20. Computation at Scale
21. Settle the Hodge Conjecture
22. Settle the Smooth Poincare Conjecture in Dimension 4
23. What are the Fundamental Laws of Biology?

They are offering grants to those who want to tackle these problems (proposals due Sept. 29, 2009).

Give it a shot!

[via Wired]