Unsolved Problems
Showing 1-13 of 13 problems
Category
Problem Set
Status
The Dynamics of Networks
Develop high-dimensional mathematics to model and predict behavior in large-scale distributed networks....
Capture and Harness Stochasticity in Nature
Develop methods that capture persistence in stochastic environments, addressing Mumford's call for new mathematics....
21st Century Fluids
Extend classical fluid dynamics to handle complex substances like foams, suspensions, gels, and liquid crystals....
Beyond Convex Optimization
Determine whether algebraic geometry can systematically replace linear algebra in optimization....
Game Theory at Scale
Create scalable mathematics for differential games, replacing traditional PDE approaches....
Information Theory for Virus Evolution
Apply Shannon's information theory to biological evolution....
Computation at Scale
Develop asymptotics for systems with massive degrees of freedom....
Computational Duality
Use mathematical duality and geometry as foundations for developing novel computational algorithms....
Occam's Razor in Many Dimensions
Find lower bounds for sensing complexity as data collection grows, addressing entropy maximization....
Physical Consequences of Perelman's Proof
Apply Perelman's proof of the Poincaré conjecture to materials fabrication across scales....
Algorithmic Origami and Biology
Strengthen mathematical theory for isometric and rigid embedding relevant to protein folding....
Optimal Nanostructures
Develop mathematics for creating optimal symmetric structures through nanoscale self-assembly....
The Geometry of Genome Space
Establish appropriate distance metrics on genome space incorporating biological utility....