UnsolvedNotable
Universality for Wigner Matrices: Optimal Moment Conditions
Probability TheoryMathematical StatisticsMathematical Physics
Unsolved Problems in the Mathematical Sciences
A repository of unsolved problems in the mathematical sciences, with special focus on machine-learning-adjacent areas such as statistics, learning theory, and optimization. Community contributed and sourced from leading journals and conferences. A live benchmark for AI mathematical reasoning.
Featured Problems
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Sharp minimax rate for central-space estimation in the low-signal SIR regime
unsolved·Dongming Huang, Songtao Tian, Qian Lin
Universality of exponential decay of the $d$-th SIR eigenvalue
unsolved·Dongming Huang, Songtao Tian, Qian Lin
Remove logarithmic gaps in minimax sample complexity for matrix normal covariance estimation
unsolved·Rafael Mendes de Oliveira, William Cole Franks, Akshay Ramachandran, Michael Walter
Full minimax characterization for tensor normal factor estimation beyond the largest factor
unsolved·Rafael Mendes de Oliveira, William Cole Franks, Akshay Ramachandran, Michael Walter
Optimal guarantees in the low-sample tensor regime (below constant-Frobenius threshold)
unsolved·Rafael Mendes de Oliveira, William Cole Franks, Akshay Ramachandran, Michael Walter
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All categories →Mathematical Statistics
Statistical estimation, hypothesis testing, asymptotic theory, nonparametric statistics, high-dimensional inference.
71 problemsInformation Theory
Shannon theory, coding theory, entropy, mutual information, channel capacity.
38 problemsProbability Theory
Probability theory, stochastic processes, random matrices, concentration inequalities, large deviations.
30 problemsLearning Theory
Computational learning theory, statistical learning, PAC learning, online learning, information-theoretic limits.
29 problemsOptimization & Variational Methods
Convex and non-convex optimization, combinatorial optimization, variational analysis, optimal control.
23 problemsCombinatorics & Graph Theory
Enumerative, algebraic, extremal, and probabilistic combinatorics; graph theory.
9 problemsA Live Benchmark for AI Mathematical Reasoning
Unsolved problems are the ultimate test of mathematical reasoning. Unlike textbook exercises, they have no known solutions. Can AI systems make progress on these challenges? Track attempts, partial results, and breakthroughs.