23 Mathematical Challenges [DARPA]
From the webpage:
Discovering novel mathematics will enable the development of new tools to change the way the DoD approaches analysis, modeling and prediction, new materials and physical and biological sciences. The 23 Mathematical Challenges program involves individual researchers and small teams who are addressing one or more of the following 23 mathematical challenges, which if successfully met, could provide revolutionary new techniques to meet the long-term needs of the DoD:
- Mathematical Challenge 1: The Mathematics of the Brain
- Mathematical Challenge 2: The Dynamics of Networks
- Mathematical Challenge 3: Capture and Harness Stochasticity in Nature
- Mathematical Challenge 4: 21st Century Fluids
- Mathematical Challenge 5: Biological Quantum Field Theory
- Mathematical Challenge 6: Computational Duality
- Mathematical Challenge 7: Occam’s Razor in Many Dimensions
- Mathematical Challenge 8: Beyond Convex Optimization
- Mathematical Challenge 9: What are the Physical Consequences of Perelman’s Proof of Thurston’s Geometrization Theorem?
- Mathematical Challenge 10: Algorithmic Origami and Biology
- Mathematical Challenge 11: Optimal Nanostructures
- Mathematical Challenge 12: The Mathematics of Quantum Computing, Algorithms, and Entanglement
- Mathematical Challenge 13: Creating a Game Theory that Scales
- Mathematical Challenge 14: An Information Theory for Virus Evolution
- Mathematical Challenge 15: The Geometry of Genome Space
- Mathematical Challenge 16: What are the Symmetries and Action Principles for Biology?
- Mathematical Challenge 17: Geometric Langlands and Quantum Physics
- Mathematical Challenge 18: Arithmetic Langlands, Topology and Geometry
- Mathematical Challenge 19: Settle the Riemann Hypothesis
- Mathematical Challenge 20: Computation at Scale
- Mathematical Challenge 21: Settle the Hodge Conjecture
- Mathematical Challenge 22: Settle the Smooth Poincare Conjecture in Dimension 4
- Mathematical Challenge 23: What are the Fundamental Laws of Biology?
(Details of each challenge omitted. See the webpage for descriptions.)
Worthy mathematical challenges all but what about a more modest challenge? One that may help solve a larger one?
Such as cutting across the terminology barriers of approaches and fields of mathematics to collate the prior, present and ongoing research on each of these challenges?
Not only would the curated artifact be useful to researchers, but the act of curation, the reading and mapping of what is known on a particular problem, could spark new approaches to the main problem as well.
DARPA should consider a history curation project on one or more of these challenges.
Could produce a useful information artifact for researchers, train math graduate students in searching across approaches/fields, and might trigger a creative insight into a possible challenge solution.
I first saw this at Beyond Search: DARPA May Be Hilbert