UnsolvedMajor
Optimal Mixing Time for Log-Concave Sampling
Mathematical StatisticsProbability TheoryOptimization & Variational Methods
Real research problems. No known solutions.
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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Online Conformal Prediction Beyond Symmetric Intervals and Toward Conditional Validity
unsolved·Liu, Dobriban, and Orabona
Decision-Optimal Prediction Sets with Group/Label-Conditional Guarantees
unsolved·Wang and Dobriban
Multiple Risk Control Beyond Sequential Order: Graph-Structured Dependencies
unsolved·Joshi, Sun, Hassani, and Dobriban
AdaBoost Always Cycles? (Global Dynamics Conjecture)
unsolved·Rudin, Daubechies, and Schapire
Fixed-Parameter Tractability of Zonotope Problems
unsolved·Vincent Froese et al.
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Browse by Category
All categories →Mathematical Statistics
Statistical estimation, hypothesis testing, asymptotic theory, nonparametric statistics, high-dimensional inference.
81 problemsLearning Theory
Computational learning theory, statistical learning, PAC learning, online learning, information-theoretic limits.
74 problemsOptimization & Variational Methods
Convex and non-convex optimization, combinatorial optimization, variational analysis, optimal control.
42 problemsInformation Theory
Shannon theory, coding theory, entropy, mutual information, channel capacity.
38 problemsProbability Theory
Probability theory, stochastic processes, random matrices, concentration inequalities, large deviations.
28 problemsTheoretical Computer Science
Computational complexity, algorithms, cryptography, quantum computing, formal languages.
18 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.