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:
- The Mathematics of the Brain
- The Dynamics of Networks
- Capture and Harness Stochasticity in Nature
- 21st Century Fluids
- Biological Quantum Field Theory
- Computational Duality
- Occam’s Razor in Many Dimensions
- Beyond Convex Optimization
- What are the Physical Consequences of Perelman’s Proof of Thurston’s Geometrization Theorem?
- Algorithmic Origami and Biology
- Optimal Nanostructures
- The Mathematics of Quantum Computing, Algorithms, and Entanglement
- Creating a Game Theory that Scales
- An Information Theory for Virus Evolution
- The Geometry of Genome Space
- What are the Symmetries and Action Principles for Biology?
- Geometric Langlands and Quantum Physics
- Arithmetic Langlands, Topology, and Geometry
- Settle the Riemann Hypothesis
- Computation at Scale
- Settle the Hodge Conjecture
- Settle the Smooth Poincare Conjecture in Dimension 4
- 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!