All 372 results
OpenAI’s math release has 719 papers, grouped into 372 results and numbered as in OpenAI’s catalog. A result is one main claim plus any companion papers, such as alternative proofs, supporting results or consequences. Each episode explains one whole result, all of its papers included.
372 results have an episode so far. Every other result has a page with OpenAI’s summary, its papers, and where the claim stands.
372 results, by number.
How to read a row
The three boxes are, in order: posted as a preprint, peer reviewed, checked in Lean.
- Done.
- Not yet.
- OpenAI published a Lean proof of part of the claim, not the main theorem.
- 6:09 An episode is out, with its length.
- 3 papers The result groups several papers; single-paper results show no note.
Lean status is taken from OpenAI’s own scope notes. Nothing here has been peer reviewed yet.
- 001 Milne’s rationality conjecture and algebraic specialization Number theory Episode, 6:09
- 002 The full BSD formula from low Selmer corank Number theory 3 papers Episode, 8:10
- 003 The quasi-Riemann hypothesis Number theory 3 papers Episode, 8:45
- 004 Hilbert’s tenth problem over ℚ Number theory 2 papers Episode, 6:50
- 005 Irrationality of Catalan’s constant Number theory Episode, 7:02
- 006 Goldfeld’s conjecture: densities and mean analytic rank Number theory 2 papers Episode, 6:38
- 007 Ordinary two-point correlations and the corrected Elliott conjecture Number theory Episode, 7:51
- 008 The Deligne–Drinfeld conjecture Number theory Episode, 6:27
- 009 Function-field reconstruction from Milnor K-theory and Galois data Number theory 3 papers Episode, 6:03
- 010 Unrestricted pro-modularity at the prime two Number theory 3 papers Episode, 5:19
- 011 Prime-factor statistics of Number theory 3 papers Episode, 6:11
- 012 Independent largest prime factors of consecutive integers Number theory Episode, 5:15
- 013 Ostmann’s inverse Goldbach conjecture Number theory Episode, 4:23
- 014 Restricted geometric Langlands, global Arthur enhancements, and generic Ramanujan Number theory 8 papers Episode, 5:29
- 015 Torus-packet equidistribution in prime, quartic, and sextic degrees Number theory 3 papers Episode, 5:27
- 016 Zilber–Pink in abelian varieties and the Siegel threefold Number theory 4 papers Episode, 5:08
- 017 The irrationality exponent of π is 2 Number theory Episode, 4:37
- 018 The Margulis–Platonov conjecture over global fields Number theory 2 papers Episode, 6:57
- 019 The local p-adic section conjecture and global consequences Number theory 2 papers Episode, 5:51
- 020 Squarefree quartics and power-free polynomial values Number theory Episode, 4:54
- 021 A quadratic bound for Jacobsthal’s function Number theory Episode, 4:36
- 022 The weak inhomogeneous Duffin–Schaeffer conjecture Number theory Episode, 4:33
- 023 Patterson's first moment for cubic Gauss sums Number theory Episode, 5:14
- 024 An asymptotic formula for the number of totients Number theory Episode, 4:20
- 025 Short Egyptian fractions Number theory Episode, 4:22
- 026 Positive lower density of large prime gaps Number theory Episode, 3:47
- 027 Potential integral density on curve character varieties Number theory Episode, 6:18
- 028 Uniformly bounded components of Gaussian-prime graphs Number theory Episode, 4:31
- 029 Primitive roots for every admissible integer base Number theory 2 papers Episode, 5:11
- 030 Modularity of elliptic curves over imaginary quadratic fields Number theory Episode, 4:53
- 031 Uchida’s conjecture for open homomorphisms of Galois groups Number theory Episode, 4:17
- 032 The rational Hodge conjecture for CM abelian varieties Algebraic and complex geometry 5 papers Episode, 7:53
- 033 Iitaka subadditivity, variation, and logarithmic additivity Algebraic and complex geometry 5 papers Episode, 5:43
- 034 Log abundance for compact Kähler spaces under logarithmic Iitaka subadditivity Algebraic and complex geometry 14 papers Episode, 6:22
- 035 Log-canonical threefold abundance in numerical dimension one Algebraic and complex geometry 2 papers Episode, 4:32
- 036 Numerical semiampleness and generalized minimal models Algebraic and complex geometry 4 papers Episode, 5:09
- 037 The ordinary-double-point volume gap Algebraic and complex geometry 2 papers Episode, 4:37
- 038 Fujita’s freeness conjecture Algebraic and complex geometry Episode, 5:08
- 039 Nagata’s conjecture and maximal Seshadri constants Algebraic and complex geometry 4 papers Episode, 4:45
- 040 Bloch’s conjecture for complex surfaces Algebraic and complex geometry Episode, 4:44
- 041 Hyperkähler SYZ and projective-space bases Algebraic and complex geometry 2 papers Episode, 4:36
- 042 Oka classification for minimal compact complex surfaces: Kodaira dimension zero and class VII Algebraic and complex geometry Episode, 4:34
- 043 P = W for fixed-determinant SLn moduli spaces Algebraic and complex geometry Episode, 4:02
- 044 The equivariant cohomological Hikita conjecture Algebraic and complex geometry Episode, 5:14
- 046 Shafarevich counterexamples in dimension two and with large fundamental group Algebraic and complex geometry 2 papers Episode, 5:25
- 047 Zariski cancellation and affine fibrations over the complex numbers Algebraic and complex geometry Episode, 4:53
- 048 A characteristic-zero counterexample to Lipman–Zariski Algebraic and complex geometry Episode, 4:20
- 049 A stable-coordinate counterexample in four variables Algebraic and complex geometry 2 papers Episode, 4:41
- 050 A counterexample to Griffiths’ positivity conjecture Algebraic and complex geometry Episode, 4:44
- 051 Kobayashi’s canonical-ampleness conjecture Algebraic and complex geometry Episode, 5:55
- 052 Tangent splittings and product decompositions Algebraic and complex geometry 2 papers Episode, 6:11
- 053 A counterexample to Pixton completeness in Chow Algebraic and complex geometry Episode, 4:55
- 054 Irrational cubic fourfolds with Hodge-theoretic and categorical K3 associations Algebraic and complex geometry Episode, 5:28
- 055 Gepner symmetry and large-volume stability on threefolds Algebraic and complex geometry 2 papers Episode, 5:00
- 056 Termination of projective and Kähler fourfold minimal model programs Algebraic and complex geometry 5 papers Episode, 7:35
- 057 Fundamental groups of special complex varieties and root orbifolds Algebraic and complex geometry 3 papers Episode, 7:03
- 058 Semialgebraic universal covers and bounded domains Algebraic and complex geometry 2 papers Episode, 6:50
- 059 Counterexamples to Zariski’s multiplicity conjecture Algebraic and complex geometry 2 papers Episode, 6:06
- 060 The Global Spherical Shell conjecture Algebraic and complex geometry Episode, 5:12
- 062 Projective contact classification and the LeBrun–Salamon conjecture Algebraic and complex geometry Episode, 6:04
- 063 The generalized Mukai conjecture Algebraic and complex geometry Episode, 5:36
- 064 Topological triviality of μ-constant surface singularities Algebraic and complex geometry Episode, 5:55
- 065 Virasoro constraints for complete intersections and projective-bundle towers Algebraic and complex geometry 2 papers Episode, 5:47
- 066 Bounded klt complements for Fano contractions Algebraic and complex geometry 2 papers Episode, 5:40
- 067 The Campana–Peternell conjecture in dimension six Algebraic and complex geometry Episode, 5:09
- 068 Anticanonical nonvanishing in every dimension Algebraic and complex geometry 7 papers Episode, 6:06
- 069 Global quantum geometric Langlands at irrational level Algebraic and complex geometry Episode, 5:59
- 071 Koebe’s circle-domain conjecture Real and complex analysis 2 papers Episode, 6:22
- 072 Brennan's conjecture and the integral-means spectrum Real and complex analysis 2 papers Episode, 5:31
- 073 The Falconer distance conjecture Real and complex analysis Episode, 5:43
- 074 Kakeya in three and four dimensions Real and complex analysis 2 papers Episode, 7:34
- 075 The Fourier-convergence conjecture Real and complex analysis Episode, 6:00
- 076 Real ultraflat Littlewood polynomials and unbounded binary merit factors Real and complex analysis 3 papers Episode, 6:11
- 077 Fourier restriction for positively curved surfaces Real and complex analysis 2 papers Episode, 5:49
- 078 The three-dimensional Bochner–Riesz conjecture Real and complex analysis Episode, 4:58
- 079 Local smoothing in three dimensions Real and complex analysis Episode, 6:32
- 080 The exact Sobolev endpoint for Schrödinger convergence Real and complex analysis 2 papers Episode, 6:02
- 081 Riesz transforms and rectifiability in higher codimension Real and complex analysis Episode, 5:30
- 082 Annular variation and dyadic absolute bounds for the triangular Hilbert transform Real and complex analysis 3 papers Episode, 5:35
- 083 Hilbert transforms along Lipschitz directions Real and complex analysis Episode, 5:48
- 084 The geometric case of the Erdős similarity conjecture Real and complex analysis 2 papers Episode, 5:27
- 085 Endpoint Sobolev regularity of centered disk averages Real and complex analysis Episode, 6:40
- 086 An L3 bound for the trilinear Hilbert transform Real and complex analysis Episode, 6:05
- 087 The Mahler conjectures, functional inequalities and polar-product symplectic width Convex and metric geometry 3 papers Episode, 7:52
- 088 Sharp projection-body inequalities and a counterexample to simplex maximization Convex and metric geometry 2 papers Episode, 6:18
- 089 Bounded-distortion L1 embeddings of planar and bounded-treewidth graphs Convex and metric geometry 2 papers Episode, 6:40
- 090 Triangular-lattice optimality, long-range Riesz and Coulomb energies, and spherical logarithmic energy Convex and metric geometry 4 papers Episode, 8:18
- 091 Logarithmic and Lp Brunn–Minkowski inequalities and the B-conjecture Convex and metric geometry Episode, 7:17
- 092 The optimal order of convex-body covering density Convex and metric geometry 2 papers Episode, 7:10
- 093 Dimension-free logarithmic Sobolev inequality for subgaussian log-concave measures Convex and metric geometry Episode, 6:21
- 094 Subpolynomial dimension reduction in Lp Convex and metric geometry Episode, 6:22
- 095 Hyperbolicity cones without semidefinite lifts Convex and metric geometry 3 papers Episode, 8:19
- 096 The Gaussian propeller conjecture in every dimension Convex and metric geometry Episode, 6:23
- 097 The Euclidean Steinitz–Bergström bound Convex and metric geometry Episode, 6:20
- 098 Compact counterexamples to bi-Lipschitz dimension reduction Convex and metric geometry Episode, 6:41
- 099 The sharp exponential scale of edit-distance distortion Convex and metric geometry 3 papers Episode, 6:09
- 100 Cylinder coverings below the half-area bound Convex and metric geometry 4 papers Episode, 6:33
- 101 The sharp simplex conjecture for isotropic constants Convex and metric geometry Episode, 6:08
- 102 The Unique Games Conjecture and optimal approximation thresholds Theoretical computer science 5 papers Episode, 7:15
- 103 Exact derandomization of logarithmic space: Theoretical computer science Episode, 6:12
- 104 Quasipolynomial algorithms for mean-payoff, stochastic and parity games Theoretical computer science 4 papers Episode, 7:10
- 105 Perfect completeness for 2-to-1 games Theoretical computer science Episode, 6:15
- 106 Hardness of coloring three-colorable graphs Theoretical computer science Episode, 5:58
- 107 Matrix multiplication with exponent at most 9/4 Theoretical computer science 3 papers Episode, 5:36
- 108 A cubic permanent–determinant lower bound Theoretical computer science Episode, 6:00
- 109 Integer multiplication below Theoretical computer science Episode, 5:53
- 110 Optimal-order randomized k-server on arbitrary metrics Theoretical computer science 2 papers Episode, 6:02
- 111 One-sample matroid prophet inequalities against an almighty adversary Theoretical computer science Episode, 5:55
- 112 Beyond the square-root exponent for depth-three circuits Theoretical computer science Episode, 5:27
- 113 Approximate counting and entropy of perfect matchings Theoretical computer science 2 papers Episode, 5:53
- 114 Approximate counting of common integer polymatroid bases Theoretical computer science 2 papers Episode, 5:52
- 115 Sampling and counting contingency tables with arbitrary margins Theoretical computer science 2 papers Episode, 6:46
- 116 Uniform black-box noncommutative identity testing across characteristics Theoretical computer science 3 papers Episode, 6:43
- 117 Uniform sparsest cut: hardness and semidefinite gaps Theoretical computer science 2 papers Episode, 6:21
- 118 Bin packing and unbounded configuration-LP gaps Theoretical computer science Episode, 5:54
- 119 The Courtade–Kumar and Hellinger conjectures Theoretical computer science 2 papers Episode, 5:50
- 120 Almost-linear-time exact matching and prescribed-degree factors in general graphs Theoretical computer science Episode, 5:23
- 121 Almost-linear approximation of edit distance Theoretical computer science Episode, 7:32
- 122 Quantitative trace-reconstruction bounds with a uniform decoder Theoretical computer science 3 papers Episode, 7:06
- 124 Polynomial-time scheduling on three identical machines Theoretical computer science Episode, 6:59
- 125 The metric k-median approximation threshold and recovery Theoretical computer science 2 papers Episode, 7:23
- 126 Exponential semidefinite complexity of perfect matching Theoretical computer science Episode, 7:12
- 127 Average sensitivity of polynomial threshold functions Theoretical computer science Episode, 7:10
- 128 A factor-two approximation for shortest common superstring Theoretical computer science Episode, 7:19
- 129 Exponential state costs for two-way automata Theoretical computer science 2 papers Episode, 7:41
- 130 Exact Fourier transforms below Theoretical computer science 2 papers Episode, 7:20
- 131 Rapid mixing of graph switches for every degree sequence Theoretical computer science Episode, 6:23
- 132 A superquadratic separation of sensitivity and block sensitivity Theoretical computer science Episode, 6:26
- 133 The computational complexity of Weisfeiler–Leman refinement Theoretical computer science 4 papers Episode, 8:05
- 134 Generalized star height at most three Theoretical computer science 3 papers Episode, 6:15
- 135 Homogeneous depth-five lower bounds for iterated matrix multiplication Theoretical computer science Episode, 7:12
- 136 A quasilinear PCP theorem for PPAD Theoretical computer science Episode, 6:28
- 137 One-tape time simulation in two-fifths-power space Theoretical computer science Episode, 6:27
- 138 Subset Sum in time Theoretical computer science 2 papers Episode, 6:33
- 139 Subpolynomial query complexity for log-concave sampling Theoretical computer science Episode, 6:25
- 140 Memory–sample lower bounds for noiseless Gaussian regression Theoretical computer science 6 papers Episode, 6:13
- 141 Existential–universal real sentences in the counting hierarchy Theoretical computer science Episode, 5:56
- 142 Deterministic polynomial factorization over prime fields Theoretical computer science Episode, 7:33
- 143 Hilbert's sixteenth problem: uniform bounds for limit cycles Dynamical systems and ergodic theory 2 papers Episode, 7:05
- 144 Banach’s simple Lebesgue-spectrum problem Dynamical systems and ergodic theory Episode, 6:19
- 145 Rokhlin’s multiple-mixing problem Dynamical systems and ergodic theory Episode, 6:28
- 146 Positive metric entropy for the standard map Dynamical systems and ergodic theory Episode, 6:16
- 147 The near-boundary Birkhoff conjecture Dynamical systems and ergodic theory 2 papers Episode, 6:32
- 148 The entropy-rate dimension formula for self-similar measures Dynamical systems and ergodic theory Episode, 6:23
- 149 Classwise permanence for weakly reversible mass-action systems Dynamical systems and ergodic theory 2 papers Episode, 6:38
- 150 Weak mixing of triangular billiards with an irrational angle Dynamical systems and ergodic theory 2 papers Episode, 6:50
- 151 A C1 counterexample to the entropy conjecture Dynamical systems and ergodic theory Episode, 7:24
- 152 Zero entropy does not guarantee a smooth positive-volume model Dynamical systems and ergodic theory Episode, 7:19
- 153 Arithmetic classification and non-Pisot singularity for Bernoulli convolutions Dynamical systems and ergodic theory Episode, 6:44
- 154 Pointwise multiple ergodic averages for mixing transformations Dynamical systems and ergodic theory 4 papers Episode, 7:02
- 155 A counterexample to periodic tiling in dimension three Combinatorics Episode, 6:54
- 156 Borsuk's conjecture fails in dimension nine Combinatorics Episode, 6:00
- 157 Graph coloring, clique minors, and Colin de Verdière invariants Combinatorics 3 papers Episode, 6:47
- 158 The Euclidean plane cannot be colored with five colors Combinatorics Episode, 6:33
- 159 Erdős’s reciprocal-sum conjecture and quasipolynomial Szemerédi bounds Combinatorics Episode, 6:10
- 160 Superexponential van der Waerden numbers Combinatorics Episode, 6:28
- 161 Counterexamples to Sidorenko’s conjecture and the forcing conjecture Combinatorics Episode, 6:29
- 162 Counterexamples to Ryser’s covering conjecture Combinatorics 2 papers Episode, 6:31
- 164 Hindman’s finite sums and products conjecture Combinatorics Episode, 5:42
- 165 The Harary–Hill and Zarankiewicz crossing-number formulas Combinatorics 2 papers Episode, 5:53
- 166 The higher-dimensional Erdős distinct-distances conjecture Combinatorics Episode, 5:48
- 167 Planar distinct distances and unit-distance bounds Combinatorics 2 papers Episode, 6:52
- 168 Combinatorial invariance of Kazhdan–Lusztig polynomials Combinatorics Episode, 5:47
- 169 Shareshian–Wachs elementary positivity Combinatorics Episode, 5:44
- 170 Sharp logarithmic exponents for off-diagonal Ramsey numbers Combinatorics 2 papers Episode, 5:36
- 171 The hypercube Ramsey conjecture Combinatorics Episode, 5:49
- 172 Classification of finite Euclidean Ramsey configurations Combinatorics Episode, 6:22
- 173 Seymour’s second-neighborhood conjecture Combinatorics Episode, 5:24
- 174 Deterministic construction of strong thin spanning trees Combinatorics 2 papers Episode, 6:55
- 175 Talagrand’s expectation thresholds, discrete convexity, and graph decompositions Combinatorics 3 papers Episode, 7:13
- 176 The second Kahn–Kalai conjecture with an edge-count bound Combinatorics Episode, 5:37
- 177 Bounded-degree coboundary expanders Combinatorics Episode, 6:52
- 178 Deterministic nonbipartite Ramanujan graphs in every fixed degree Combinatorics Episode, 7:05
- 179 The circulant Hadamard and Barker-sequence conjectures Combinatorics Episode, 6:00
- 180 Barnette’s Hamiltonian-cycle conjecture Combinatorics Episode, 5:48
- 181 The Erdős–Gallai cycle-decomposition conjecture Combinatorics Episode, 7:04
- 182 Power savings for intersective polynomial differences and prime arguments Combinatorics 3 papers Episode, 7:01
- 183 Power savings for planar halving lines and k-sets Combinatorics Episode, 5:59
- 184 Correspondence coloring with a fixed forbidden subgraph Combinatorics 2 papers Episode, 8:18
- 185 Counterexamples to infinite matroid intersection and packing/covering Combinatorics Episode, 7:36
- 186 Uniform influence and sharp thresholds for graph and hypergraph properties Combinatorics 2 papers Episode, 8:42
- 187 Snaky in 21 Maker moves Combinatorics Episode, 6:46
- 188 The sharp terminal leave in random triangle removal Combinatorics Episode, 6:30
- 189 Cycle–clique Ramsey numbers Combinatorics Episode, 6:46
- 190 Polynomial removal fails for ordered binary matrices Combinatorics Episode, 7:29
- 191 A power improvement in the Heilbronn triangle lower bound Combinatorics Episode, 7:02
- 192 Boolean functions violate the square-root degree bound by arbitrary factors Combinatorics Episode, 5:59
- 193 Serre’s intersection-multiplicity conjecture Algebra Episode, 5:50
- 194 Lech’s multiplicity conjecture Algebra Episode, 6:09
- 195 A counterexample to the small Cohen–Macaulay module conjecture Algebra Episode, 6:12
- 196 A counterexample to Kaplansky’s zero-divisor conjecture Algebra Episode, 5:48
- 197 A torsion-free group algebra that is not directly finite Algebra 4 papers Episode, 7:36
- 198 A counterexample to finitistic-dimension finiteness Algebra Episode, 6:10
- 199 Counterexamples to Auslander–Reiten, Tachikawa and related homological conjectures Algebra 2 papers Episode, 6:24
- 200 Eisenbud–Green–Harris and lex-plus-powers Algebra 2 papers Episode, 5:52
- 201 A counterexample to Kurosh’s division-ring problem Algebra Episode, 5:13
- 202 The blockwise Alperin weight conjecture Algebra Episode, 5:06
- 203 Donovan's conjecture over fields and complete mixed-characteristic DVRs Algebra 2 papers Episode, 4:38
- 204 Tensor saturation for even spin groups Algebra Episode, 4:21
- 205 Saxl’s conjecture and universal tensor squares Algebra 2 papers Episode, 3:57
- 206 Finite lattice representation and undecidability Algebra 2 papers Episode, 3:56
- 207 The ℓ¹-Bass conjecture for all discrete groups Algebra 2 papers Episode, 3:59
- 208 Finite symmetric tensor categories and the Verlinde tower Algebra Episode, 4:09
- 209 Integral counterexamples to Gersten’s conjecture Algebra 2 papers Episode, 4:17
- 210 Foulkes' conjecture for sixth powers and quadratic stabilization Algebra 2 papers Episode, 3:52
- 211 The geometric phase diagram, diffusion, and spectra of random planar maps Probability and statistical mechanics 7 papers Episode, 4:25
- 212 Planar first-passage geometry and the absence of bigeodesics Probability and statistical mechanics 2 papers Episode, 4:53
- 213 Critical percolation on every quasi-transitive graph Probability and statistical mechanics 2 papers Episode, 4:43
- 214 The Benjamini–Schramm nonuniqueness conjecture Probability and statistical mechanics Episode, 4:11
- 215 Canonical continuum limit and exact mass asymptotics Probability and statistical mechanics 5 papers Episode, 4:48
- 216 Critical and near-critical XY scaling and BKT universality Probability and statistical mechanics 6 papers Episode, 4:36
- 217 The low-temperature Sherrington–Kirkpatrick fluctuation law Probability and statistical mechanics 2 papers Episode, 4:13
- 218 Conformal universality for weakly interacting and random-bond Ising models Probability and statistical mechanics 6 papers Episode, 4:18
- 219 GOE bulk universality for regular graphs with weak Anderson disorder Probability and statistical mechanics 2 papers Episode, 3:49
- 220 Directional zero–one laws beyond iid environments and iid ballisticity Probability and statistical mechanics 3 papers Episode, 4:15
- 221 The Mézard–Parisi formula for diluted spin glasses Probability and statistical mechanics Episode, 5:08
- 222 Perceptron free energies and microscopic jamming exponents Probability and statistical mechanics 4 papers Episode, 5:45
- 223 Random-cluster interfaces: critical, disordered, thermal, and natural-time scaling Probability and statistical mechanics 6 papers Episode, 5:15
- 224 Critical and quenched near-critical universality for Poisson–Voronoi percolation Probability and statistical mechanics 3 papers Episode, 4:54
- 225 Gaussian free field limits throughout the balanced six-vertex regime Probability and statistical mechanics Episode, 4:26
- 226 The double-dimer loop ensemble converges to CLE4 Probability and statistical mechanics Episode, 4:22
- 227 Critical SK autocorrelation processes and dynamics across the temperature transition Probability and statistical mechanics 8 papers Episode, 5:07
- 228 Continuum phase transitions for radial pair potentials Probability and statistical mechanics 2 papers Episode, 4:26
- 229 Exact three- and four-state reconstruction thresholds and four-state tree capacity Probability and statistical mechanics 3 papers Episode, 4:47
- 230 Exact Hausdorff gauges for SLE Probability and statistical mechanics 2 papers Episode, 4:35
- 231 The free uniform spanning forest is a factor of IID Probability and statistical mechanics Episode, 4:33
- 232 Gaussian fields and interfaces for triangular-lattice Lipschitz heights Probability and statistical mechanics 3 papers Episode, 4:40
- 233 The joint critical Ashkin–Teller current limit Probability and statistical mechanics Episode, 4:32
- 234 All-temperature pressure of orthogonally invariant Ising spin glasses Probability and statistical mechanics Episode, 4:34
- 235 Limiting random SAT thresholds, sharp variance and computability Probability and statistical mechanics 4 papers Episode, 4:33
- 236 The exact factor-of-IID threshold for free Ising spins on trees Probability and statistical mechanics Episode, 4:45
- 237 The three-quarter exponent for honeycomb self-avoiding walk Probability and statistical mechanics 13 papers Episode, 4:34
- 238 Optimal logarithmic mixing of the Thorp shuffle Probability and statistical mechanics 12 papers Episode, 4:33
- 239 Sharp singularity rates for symmetric random sign matrices Probability and statistical mechanics 2 papers Episode, 4:14
- 240 Shelah's eventual categoricity and the prescribed-threshold obstruction Mathematical logic 2 papers Episode, 5:05
- 241 Rigidity of the Turing degrees Mathematical logic Episode, 4:35
- 242 Single-fold Diophantine representations and undecidability under an at-most-one-solution promise Mathematical logic Episode, 4:12
- 243 Separating choiceless counting from polynomial time and witnessed choice Mathematical logic 2 papers Episode, 4:32
- 244 The Partition Principle does not imply Choice Mathematical logic Episode, 4:16
- 245 Weak normalization implies strong normalization in pure type systems Mathematical logic Episode, 4:22
- 246 Cannon's conjecture Group theory Episode, 4:42
- 247 An infinite finitely presented residually finite 2-group and a finitely presented nil algebra Group theory 2 papers Episode, 4:48
- 248 Thompson's group F is nonamenable Group theory Episode, 4:46
- 249 A finitely generated Eilenberg–Ganea counterexample Group theory Episode, 4:34
- 250 Boone–Higman embeddings with higher finiteness Group theory 3 papers Episode, 4:46
- 251 Amenability, unitarizability, and strong Ulam stability Group theory 2 papers Episode, 4:36
- 252 A torsion-free hyperbolic group that is neither residually finite nor linear over any field Group theory Episode, 5:08
- 253 An infinite finitely presented simple amenable group Group theory Episode, 4:13
- 254 Classifying spaces and geometric obstructions for Artin groups Group theory 3 papers Episode, 5:00
- 255 Quasi-isometric recognition of virtually polycyclic groups Group theory Episode, 5:02
- 256 Nonsingular systems of equations over arbitrary groups Group theory 2 papers Episode, 5:16
- 257 A hyperbolic group without a geometric CAT(0) action Group theory Episode, 4:25
- 258 Gersten’s conjecture and virtual compact specialness of one-relator groups Group theory 2 papers Episode, 4:05
- 259 A group without fixed price Group theory Episode, 3:42
- 260 Spacetime Penrose inequalities: enclosing area, charge, rotation, and anti-de Sitter extensions Mathematical physics 13 papers Episode, 4:54
- 261 Localization and delocalization in the Anderson model Mathematical physics 2 papers Episode, 4:16
- 262 Sharp finite-matrix Lieb–Thirring inequalities and all equality cases Mathematical physics 3 papers Episode, 3:47
- 263 The ionization and generalized ionization conjectures Mathematical physics 3 papers Episode, 3:50
- 264 Strong cosmic censorship near two-ended Kerr data Mathematical physics 3 papers Episode, 4:03
- 265 Area laws and tensor networks for two-dimensional gapped systems Mathematical physics 2 papers Episode, 3:46
- 266 Exactly three mutually unbiased bases in dimension six Mathematical physics 2 papers Episode, 4:17
- 267 Positive-temperature Bose–Einstein condensation and exact quantum depletion Mathematical physics 5 papers Episode, 4:22
- 268 The spin-one Haldane gap Mathematical physics 2 papers Episode, 3:54
- 269 Uniform Laughlin gap and stability under bounded scalar disorder Mathematical physics 2 papers Episode, 4:31
- 270 Threshold and positive-energy bound states of the BFSS matrix model Mathematical physics 2 papers Episode, 3:41
- 271 Bloch's law, its lattice correction, and the spherical magnetization law Mathematical physics 4 papers Episode, 4:09
- 272 Entanglement without distillable secret key Mathematical physics Episode, 4:08
- 273 The entropy photon-number inequality Mathematical physics Episode, 3:28
- 274 Parity is not in QAC0 Mathematical physics 2 papers Episode, 3:32
- 275 QMA-hardness of continuum Coulomb energy Mathematical physics 2 papers Episode, 3:42
- 276 Classical capacity of generalized amplitude damping Mathematical physics Episode, 3:21
- 277 Threshold repetition for entangled games Mathematical physics Episode, 3:25
- 278 Failure of Kohn–Sham ensemble representation Mathematical physics Episode, 3:34
- 279 Exact quantum factoring over a fixed finite gate set Mathematical physics Episode, 3:16
- 280 Unitary vertex operator algebras and conformal nets Mathematical physics Episode, 3:57
- 281 QAOA attains the SK optimum in the thermodynamic-first limit Mathematical physics 2 papers Episode, 3:39
- 282 From scale symmetry to local conformal symmetry in four-dimensional QFT Mathematical physics Episode, 4:12
- 283 Polynomial-time unitary synthesis from a Boolean oracle Mathematical physics Episode, 3:23
- 284 The optimal quartic separation between randomized and quantum queries Mathematical physics Episode, 3:27
- 285 Counterexamples to Baum–Connes and Kadison–Kaplansky Operator algebras 3 papers Episode, 4:07
- 286 Rigidity and arithmetic of lattice von Neumann algebras Operator algebras 2 papers Episode, 3:31
- 287 Isomorphism of the free group factors Operator algebras Episode, 3:56
- 288 Kadison's similarity conjecture Operator algebras Episode, 3:51
- 289 Strong Kadison–Kastler stability and its spatial boundaries Operator algebras 3 papers Episode, 3:37
- 290 Relative bicentralizers and modular spectral recovery Operator algebras 2 papers Episode, 3:45
- 291 Cuntz comparison, nuclear dimension, and equivariant Jiang–Su stability Operator algebras 4 papers Episode, 3:59
- 292 Kirchberg's norm-ultrapower embedding problem Operator algebras Episode, 4:26
- 293 Invariant projections, hyperinvariant subspaces, and transitive algebras Operator algebras 2 papers Episode, 4:45
- 294 Kaplansky's quasitrace conjecture and failure of tensor-product stable finiteness Operator algebras Episode, 4:11
- 295 The Kadison–Ringrose cohomology conjecture Operator algebras Episode, 4:30
- 296 The generator problem for finite factors Operator algebras Episode, 4:19
- 297 A ZFC counterexample to Naimark's problem Operator algebras Episode, 4:12
- 298 Two notions of free entropy differ even when both are finite Operator algebras Episode, 4:06
- 299 The Kirchberg–Rørdam character criterion and infinite tensor-power Jiang–Su stability Operator algebras Episode, 3:42
- 300 Approximation and quadratic strong-operator paving Operator algebras 2 papers Episode, 4:04
- 301 Trace cones and Razak–Jacelon stabilization Operator algebras Episode, 3:50
- 302 Radius of comparison equals half the mean dimension Operator algebras 2 papers Episode, 3:57
- 303 Weak pure infiniteness and Cuntz-algebra absorption Operator algebras Episode, 4:09
- 304 The Hilbert–Smith conjecture in every dimension Topology Episode, 4:38
- 305 Four-dimensional disk embedding and Wall's conjecture Topology 3 papers Episode, 4:54
- 306 The purely cosmetic surgery conjecture Topology Episode, 4:36
- 307 Failure of rational injectivity for maximal coarse assembly Topology 2 papers Episode, 4:47
- 308 Finite Smith–Toda complexes at every height Topology 2 papers Episode, 4:26
- 309 The Kervaire invariant problem at the prime three Topology Episode, 4:34
- 310 Quillen's conjecture in rational homology Topology Episode, 4:16
- 311 The Hovey–Strickland and Chai conjectures Topology Episode, 4:07
- 312 The Grothendieck homotopy hypothesis Topology Episode, 4:31
- 313 Finite generation for the -local sphere Topology Episode, 4:20
- 314 Cyclic length and chromatic fixed-point loss Topology Episode, 5:06
- 315 The four-dimensional Singer conjecture Topology Episode, 4:48
- 316 Curtis’s conjecture Topology Episode, 4:20
- 317 Thomason model structures in all strict higher dimensions Topology Episode, 4:18
- 318 Chromatic splitting: filtrations and counterexamples Topology 5 papers Episode, 4:18
- 319 Counterexamples to finite generation at chromatic height two Topology Episode, 3:41
- 320 Nonhomeomorphic closed aspherical four-manifolds Topology Episode, 3:43
- 321 A counterexample to Wall's finite D(2) problem Topology Episode, 3:18
- 322 Tingley’s sphere-isometry problem Functional analysis Episode, 3:42
- 323 Independence of the separable quotient problem Functional analysis Episode, 4:11
- 324 Lipschitz equivalent Banach spaces need not be linearly isomorphic Functional analysis 2 papers Episode, 3:51
- 325 The complete Crouzeix conjecture Functional analysis 2 papers Episode, 3:51
- 326 The cotype–cotype conjecture under the approximation property Functional analysis Episode, 3:57
- 327 Markov type characterizes superreflexivity Functional analysis Episode, 3:33
- 328 Nonexpansive fixed points in reflexive Banach spaces Functional analysis Episode, 3:50
- 329 A counterexample to metric-entropy duality Functional analysis Episode, 3:45
- 330 A uniformly discrete counterexample to bounded approximation in Lipschitz-free spaces Functional analysis Episode, 3:49
- 331 Reflexive midpoint convexity and diamond distortion Functional analysis 7 papers Episode, 3:58
- 332 Metric Markov cotype of ℓ1 and Hilbert-space Lipschitz extension Functional analysis Episode, 3:51
- 333 Smooth isometric immersions of surfaces into ℝ4 Differential geometry Episode, 3:30
- 334 A smooth surface metric with no local isometric immersion in ℝ3 Differential geometry Episode, 4:18
- 335 Gromov’s integral scalar-curvature bound for simplicial volume Differential geometry 2 papers Episode, 4:18
- 336 Spectral scalar curvature, Urysohn width, and macroscopic dimension Differential geometry 3 papers Episode, 5:01
- 337 Sharp Cartan–Hadamard isoperimetry and rigidity Differential geometry 2 papers Episode, 4:28
- 338 Yau's uniformization conjecture Differential geometry Episode, 4:26
- 339 Katok's entropy rigidity conjecture Differential geometry Episode, 3:55
- 340 A counterexample to the nearby Lagrangian conjecture Differential geometry Episode, 3:59
- 341 Donaldson's hypersymplectic deformation conjecture Differential geometry Episode, 4:00
- 342 Donaldson's tamed-to-compatible conjecture Differential geometry Episode, 3:51
- 343 Symplectic ball packing in higher dimensions Differential geometry Episode, 3:27
- 344 The metric Blaschke conjecture Differential geometry Episode, 4:02
- 345 Infinitely many closed geodesics on Riemannian spheres and closed three-manifolds Differential geometry Episode, 4:26
- 346 Sharp singular-set bounds for stationary integral varifolds Differential geometry 2 papers Episode, 4:37
- 347 Counterexamples to stable-Morse and strong Arnold fixed-point bounds Differential geometry 5 papers Episode, 4:57
- 348 Nonnegative-curvature Einstein classification and an L2 topological gap Differential geometry 3 papers Episode, 4:42
- 349 The Solomon–Yau least-volume conjecture Differential geometry Episode, 4:28
- 350 Yau’s nodal bounds: surfaces and higher dimensions Differential geometry 3 papers Episode, 4:09
- 351 Scalar curvature and finite-time Ricci-flow singularities Differential geometry 3 papers Episode, 4:11
- 352 A finite-time singularity of Calabi flow Differential geometry Episode, 4:04
- 353 Affine Bernstein rigidity through dimension nine and a smooth dimension-ten counterexample Differential geometry 2 papers Episode, 4:15
- 354 The isoperimetric profile of the cubic three-torus Differential geometry Episode, 3:51
- 355 Unique tangent flows at the first surface singularity Differential geometry Episode, 4:18
- 356 Gigli’s characterization of Alexandrov curvature Differential geometry 2 papers Episode, 4:15
- 357 Bi-Lipschitz coordinates at every regular RCD point Differential geometry Episode, 4:10
- 358 A three-manifold without conjugate points or nonpositive curvature Differential geometry Episode, 3:50
- 359 Negative Kähler curvature without bounded holomorphic coordinates Differential geometry 2 papers Episode, 4:29
- 360 Weak MTW curvature gives convexity and regular optimal transport Differential geometry 2 papers Episode, 4:08
- 361 Failure of integer-degree harmonic dimension comparison Differential geometry 2 papers Episode, 3:52
- 362 Global smoothness for relativistic Vlasov–Maxwell Partial differential equations Episode, 3:48
- 363 Nonuniqueness with local conservation for the hard-sphere Boltzmann equation Partial differential equations 2 papers Episode, 3:49
- 364 Kinetic limits and fluctuations over the Boltzmann lifespan Partial differential equations 2 papers Episode, 3:44
- 365 Joint metric and connection recovery from one boundary patch Partial differential equations 3 papers Episode, 4:04
- 366 The planar Mumford–Shah regularity conjecture and local weak-L4 gradient bounds Partial differential equations Episode, 3:59
- 367 The critical dimension for the one-phase Bernoulli problem Partial differential equations Episode, 3:56
- 368 The three-dimensional Ball–Evans approximation problem Partial differential equations 2 papers Episode, 4:01
- 369 The hot spots conjecture for simply connected planar domains Partial differential equations Episode, 4:02
- 370 The Lane–Emden and Hénon–Lane–Emden conjectures Partial differential equations Episode, 4:18
- 371 Stable blowup for the defocusing Schrödinger equation Partial differential equations Episode, 4:29
- 372 Global uniqueness in smooth isotropic elasticity Partial differential equations Episode, 3:56
- 373 Nonattainment of the three-marginal Coulomb Monge problem Partial differential equations Episode, 3:55
- 374 Sharp one-third stability of Brenier maps Partial differential equations Episode, 3:40
- 375 De Giorgi's conjecture in dimension eight Partial differential equations Episode, 4:12
- 376 Universal computation in forced Navier–Stokes flows Partial differential equations 9 papers Episode, 4:26
- 377 Interior regularity for infinity-harmonic functions Partial differential equations Episode, 3:52
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Titles from OpenAI’s catalog, used under the Apache License 2.0. Last checked October 19, 2026. The same data is available as JSON.