Algebra
16 recordsGroups, rings, representations, and algebraic structures, including their connections to geometry and topology.
Mathematics & theoretical computer science
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Algorithms and computation
19 recordsAlgorithms for graphs, strings, arithmetic, and matrix multiplication, together with computational complexity.
Analysis and probability
24 recordsFunctions, operators, differential equations, dynamics, and random systems, including analytic number theory and mathematical physics.
Combinatorics
15 recordsPatterns, colorings, and discrete constructions, including Ramsey theory, cap sets, and geometric combinatorics.
Geometry and topology
30 recordsShapes, distances, spaces, and their structure, including packings, metric embeddings, manifolds, and algebraic geometry.
Logic and formal proof
13 recordsMathematical foundations, decidability, proof systems, and AI-assisted formalization.
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Focused topics and problems 133
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AI-assisted formal proof
9 recordsFormal proof systems check deductions expressed in a precise language.
Algebra and representation theory
2 recordsAlgebra studies rings, modules, and categories.
Algebraic and complex geometry
5 recordsPolynomial equations define geometric spaces.
Cap sets
1 recordA cap set is a subset of vectors over the three-element field containing no three distinct vectors in an arithmetic progression.
Convex-body coverings
2 recordsCovering space with translates of convex shapes.
Differential geometry
2 recordsDifferential geometry studies smooth spaces and metrics.
Dynamical systems and ergodic theory
1 recordDynamical systems describe how states evolve.
Functional analysis
1 recordFunctional analysis studies spaces of functions and operators.
Claims, evidence & context
Browse archive Curated contributions
Latest reported contributions, newest first.
Morris–Claude reports: Snaky is a first-player win on 15×15
Trevor Morris reports that Maker, moving first on an empty 15×15 square board, can force a rotated or reflected Snaky hexomino against any blocking play in the weak maker-breaker game.
Read original source Morris–Claude: pinned statement, baseline and AI rolesgithub.com
OpenAI reports: Critical percolation on quasi-transitive graphs
OpenAI claims disappearance of infinite bond-percolation clusters at criticality on every infinite connected locally finite quasi-transitive graph whose critical threshold is below one.
Read original source Pinned primary manuscript · family 213github.com
OpenAI reports: a power saving for exact discrete Fourier transforms
The manuscript reports one deterministic algorithm computing the exact complex discrete Fourier transform at every length n in O(n(log n)^(1−10^−13)) operations, including scalar preparation, scheduling and indexing, in its specified arithmetic model.
Read original source Pinned manuscript, Theorem 1.1 and Corollary 1.2github.com