Named problems, A to Z
The 520 named conjectures, problems, and hypotheses that the release's results claim to prove, disprove, or make progress on. This index is Emergent Mind's: an LLM read each result's summary and abstracts, and every name it gave was checked against that text. Outcomes are as the manuscripts claim them; none has been peer reviewed.
A
Abelian Zilber–Pink conjecture
Proved in result 016
Abhyankar–Sathaye conjecture
Partial progress in result 049
Abhyankar–Sathaye conjecture in ambient dimension four
Disproved in result 049
Abundance in numerical dimension one for terminal threefolds in positive characteristic
Proved in result 035
Affine Bernstein conjecture
Partial progress in result 353
All-temperature exponential spin-decay conjecture for these models
Proved in result 215
All-temperature lattice mass-generation conjecture for this periodic state
Proved in result 215
Almost-everywhere regularity conjecture of Brena, Decio, and De Lellis
Proved in result 346
Alon–Krivelevich–Sudakov coloring conjecture
Proved in result 184
Amenability problem for F
Proved in result 248
Anti-de Sitter Penrose Inequality
Proved in result 260
Approximation-paving conjecture of Popa and Vaes
Proved in result 300
Ara–Maltsiniotis conjecture
Proved in result 317
Arnold's corank problem
Disproved in result 059
Artin conjecture
Proved in result 254
Artin's primitive root conjecture
Proved in result 029
Ascoli–He–Park–Talagrand graph-decomposition conjecture
Proved in result 175
Asymptotic Gotsman–Linial conjecture
Proved in result 127
Auslander–Gorenstein conjecture
Disproved in result 199
Auslander–Reiten conjecture
Disproved in result 199
B
B-semiampleness for compact log-smooth Kähler fibrations
Proved in result 033
Ball's extension problem for this target
Proved in result 332
Ballisticity conjecture
Proved in result 220
Banach's simple Lebesgue-spectrum problem
Proved in result 144
Bang's half-area cylinder-covering bound
Disproved in result 100
Barker-sequence conjecture
Proved in result 179
Barnette's conjecture
Proved in result 180
Bass trace conjecture for every discrete group
Proved in result 207
Beauville's compatible splitting conjecture
Proved in result 052
Benjamini–Schramm criticality conjecture for bond percolation
Proved in result 213
Benjamini–Schramm nonuniqueness conjecture
Proved in result 214
Benson–Etingof–Ostrik conjecture
Partial progress in result 208
Berezinskii–Kosterlitz–Thouless essential singularity
Proved in result 216
Berezinskii–Kosterlitz–Thouless prediction that the critical spin-correlation exponent is 1/4
Proved in result 216
Binary corrected Elliott conjecture
Proved in result 007
Birch–Swinnerton-Dyer leading-term formula for elliptic curves over ℚ whose full q-power Selmer group has corank zero or one
Proved in result 002
Birkar's Stein-degree conjecture for ordinary ℚ-pairs
Proved in result 034
Blass–Gurevich–Shelah noncapture conjecture
Proved in result 243
Bloch's conjecture for smooth connected projective complex surfaces with
Proved in result 040
Bloch's T3/2 law
Proved in result 271
Bogoliubov leading quantum-depletion law
Proved in result 267
Bogomolov–Pop reconstruction conjecture
Proved in result 009
Bondi Penrose inequality
Proved in result 260
Boone–Higman conjecture
Proved in result 250
Borel conjecture in dimension four
Disproved in result 320
Borsuk's conjecture
Partial progress in result 156
Borsuk's conjecture in dimension nine
Disproved in result 156
Bounded-data Fourier restriction conjecture for the sphere in three dimensions
Proved in result 077
Bounded-domain question of Kollár and Pardon
Proved in result 058
Boundedness conjecture for finite weakly reversible mass-action systems
Proved in result 149
Brannen's proposed simplex maximum
Disproved in result 088
Brennan's conjecture
Proved in result 072
Burdzy's simply connected hot spots conjecture
Proved in result 369
Burr–Erdős hypercube Ramsey conjecture
Proved in result 171
C
Campana's abelianity conjecture
Proved in result 057
Campana's orbifold Iitaka subadditivity conjecture
Proved in result 033
Campana–Peternell conjecture in dimension six
Proved in result 067
Campana–Peternell inequality
Proved in result 034
Cannon's conjecture
Proved in result 246
Canonical nonvanishing for smooth projective varieties
Proved in result 034
Cardy's formula for critical Poisson–Voronoi percolation
Proved in result 224
Cardy's formula for square-lattice bond percolation with free boundary edges
Proved in result 223
Carleson's Schrödinger convergence problem
Partial progress in result 080
Carleson's Schrödinger convergence problem at the Sobolev endpoint
Proved in result 080
Cartier-divisor conjecture of Birkar and Shokurov for rational boundaries in characteristic zero
Proved in result 066
Cartier-divisor conjecture of Birkar and Shokurov for real boundaries over ℂ
Proved in result 066
CAT(0) conjecture for Artin groups
Disproved in result 254
Chai's invariant-ideal conjecture
Proved in result 311
Charged spacetime Penrose inequality
Proved in result 260
Chen's smooth long-time existence conjecture for Calabi flow
Disproved in result 352
Christandl's PPT-square conjecture
Disproved in result 272
Circulant Hadamard conjecture
Proved in result 179
Classical Nakayama conjecture
Disproved in result 199
Classification conjecture for connected smooth closed Einstein four-manifolds with strictly positive sectional curvature
Proved in result 348
Closed-geodesic infinitude problem
Proved in result 345
Closed-surface form of the four-dimensional isometric-immersion problem
Proved in result 333
Coarse Novikov conjecture
Disproved in result 307
Coefficient-free reduced Baum–Connes conjecture
Disproved in result 285
Colin de Verdière chromatic conjecture
Disproved in result 157
Combinatorial invariance conjecture
Proved in result 168
Complete Crouzeix conjecture
Proved in result 325
Conformal-invariance conjecture for this model
Proved in result 224
Conjecture of Nam, Sly and Zhang
Proved in result 236
Conjectured cubic relation
Disproved in result 284
Conjectures 3.4.5 and 3.4.6 of Gaitsgory–Lafforgue–Raskin
Proved in result 014
Connes' bicentralizer conjecture for every type III1 factor with separable predual and every faithful normal state
Proved in result 290
Constant-error Aaronson–Kuperberg unitary synthesis problem
Proved in result 283
Contact-Fano homogeneity conjecture
Proved in result 062
Cotype–cotype conjecture under the approximation property
Proved in result 326
Courtade–Kumar conjecture
Proved in result 119
Curtis's conjecture
Proved in result 316
Cycle–clique conjecture of Erdős, Faudree, Rousseau and Schelp
Proved in result 189
D
Dadarlat–Toms question
Proved in result 299
David–Semmes Riesz-transform question
Partial progress in result 081
David–Semmes Riesz-transform question in its remaining higher-codimension range
Proved in result 081
De Giorgi's conjecture in dimension eight
Proved in result 375
Degreewise finiteness question of Hovey and Hovey–Strickland
Proved in result 313
Deligne–Drinfeld conjecture
Proved in result 008
Derandomization for bounded-error logarithmic-space computation
Proved in result 103
Diagonal Fourier extension conjecture for positively curved surfaces in three dimensions
Proved in result 077
Dimension-free logarithmic Sobolev conjecture for subgaussian log-concave measures
Proved in result 093
Directional zero–one conjecture
Proved in result 220
Directionwise normalized 1-Codimensional Cylinder Covering Conjecture
Disproved in result 100
Directionwise normalized half-bound conjecture
Disproved in result 100
Dixmier's unitarizability problem
Proved in result 251
Dolgachev–Weisfeiler affine-fibration conjecture over 𝔸1 and 𝔸2
Disproved in result 047
Domain form of the small Cohen–Macaulay module conjecture
Disproved in result 195
Donaldson's hypersymplectic deformation conjecture
Proved in result 341
Donaldson's tamed-to-compatible conjecture
Proved in result 342
Donovan's conjecture over algebraically closed fields
Proved in result 203
Dyadic case of the Erdős similarity conjecture
Proved in result 084
E
Eccles's conjecture
Proved in result 316
Effective Iitaka fibration conjecture
Proved in result 034
Effective log Iitaka conjecture in dimension four
Proved in result 034
Eilenberg–Ganea conjecture
Disproved in result 249
Eisenbud–Green–Harris conjecture
Proved in result 200
Embedded Zariski multiplicity conjecture
Disproved in result 059
Endpoint question of Hajłasz and Onninen in the planar centered-disk case
Proved in result 085
Entire-graph affine Bernstein assertion in dimension ten
Disproved in result 353
Entropy photon-number conjecture
Proved in result 273
Entropy-rate dimension conjecture
Proved in result 148
Equivariant cohomological Hikita conjecture
Proved in result 044
Erdős and Hall’s scaling question
Proved in result 024
Erdős and Prachar question
Proved in result 026
Erdős’s conjecture on short Egyptian fractions
Proved in result 025
Erdős's conjecture on the largest fibers of Euler's totient function
Proved in result 011
Erdős–Faudree–Rousseau–Schelp conjecture
Proved in result 189
Erdős's fixed relative-gap conjecture
Disproved in result 076
Erdős–Gallai cycle-decomposition conjecture
Proved in result 181
Erdős–Pomerance joint Dickman conjecture
Proved in result 012
Erdős's reciprocal-sum conjecture
Proved in result 159
Erdős similarity conjecture
Partial progress in result 084
Erdős's superexponential-growth question for van der Waerden numbers
Proved in result 160
Eskin–Fisher–Whyte lattice-recognition conjecture
Proved in result 255
Euclidean Cartan–Hadamard isoperimetric conjecture in dimensions at least three
Proved in result 337
Euclidean-complete affine Bernstein conjecture in dimensions three through nine
Proved in result 353
Euclidean singular-set conjecture recorded by Brena, Decio, and De Lellis
Proved in result 346
Euclidean Steinitz–Bergström conjecture
Proved in result 097
Eventual Parisi-optimality conjecture of Basso, Farhi, Marwaha, Villalonga, and Zhou
Proved in result 281
Exclusion of additional bound states at N = 2
Disproved in result 270
F
F∞ form of the higher-dimensional Higman embedding question
Proved in result 250
Falconer distance conjecture
Proved in result 073
Fermionic Laughlin spectral-gap conjecture for the full V1 interaction
Proved in result 269
Finite case of the Benson–Etingof–Ostrik conjecture
Proved in result 208
Finite-fold conjecture
Proved in result 242
Finite lattice representation problem
Disproved in result 206
Finite-presentation existence question for simple amenable groups
Proved in result 253
Finite-presentation version of Kurosh's algebraic finiteness question
Disproved in result 247
Finite-rational-coefficient semi-log-canonical index conjecture
Proved in result 034
Finite-volume continuum-random-tree prediction for critical Fortuin–Kasteleyn planar maps at every fixed q > 4
Proved in result 211
Finitely presented Burnside problem
Disproved in result 247
Finitely presented nil- and radical-algebra nilpotence questions
Disproved in result 247
Fixed-clique-size independence conjecture of Ajtai, Erdős, Komlós and Szemerédi
Proved in result 184
Fixed-degree bulk-universality conjecture for random regular graphs
Proved in result 219
Fixed-determinant P = W conjecture in every coprime rank
Proved in result 043
Fixed-power question posed by Green and Sawhney
Proved in result 182
Forcing conjecture of Skokan and Thoma
Disproved in result 161
Ford–Konyagin–Luca conjecture
Proved in result 011
Foulkes' conjecture
Partial progress in result 210
Foulkes' conjecture for the sixth symmetric power
Proved in result 210
Four-dimensional disk-embedding conjecture
Disproved in result 305
Four-dimensional Hausdorff-dimension Kakeya conjecture
Proved in result 074
Four-dimensional Singer conjecture
Proved in result 315
Fractional-coloring weakening discussed by Reed and Seymour
Disproved in result 157
Free group factor isomorphism problem
Proved in result 287
Friedgut–Kalai hypergraph threshold-width conjecture
Proved in result 186
Friedgut–Kalai sharp-threshold conjecture
Proved in result 186
Friedgut–Kalai threshold-width conjectures for graphs and fixed-uniformity hypergraphs
Proved in result 186
Fujita's freeness conjecture
Proved in result 038
Full ordinary descendant Virasoro conjecture
Partial progress in result 065
G
Gaboriau's general fixed-price problem
Disproved in result 259
Gaitsgory–Raskin's full-support conjecture
Proved in result 014
Gaussian moat conjecture
Proved in result 028
Gaussian propeller conjecture
Proved in result 096
General factor question for unimodular random graphs
Proved in result 231
General-graph perfect-matching approximation problem
Proved in result 113
Generalised Abundance Conjecture for projective klt ℚ-pairs
Proved in result 036
Generalized Cartan–Hadamard isoperimetric conjecture
Proved in result 337
Generalized Hodge conjecture
Partial progress in result 032
Generalized Hodge conjecture for CM abelian varieties
Proved in result 032
Generalized Hodge conjecture for self-powers of a projective complex K3 surface on the K3 quadratic locus
Proved in result 032
Generalized ionization conjecture
Proved in result 263
Generalized Lax conjecture
Disproved in result 095
Generalized Mukai conjecture
Proved in result 063
Generalized Nakayama conjecture
Disproved in result 199
Generalized Ramanujan conjecture
Partial progress in result 014
Generalized Ramanujan conjecture for cuspidal automorphic representations of split connected adjoint absolutely simple groups with a generic unramified component at every unramified place
Proved in result 014
Generalized Ramanujan conjecture for globally generic cuspidal automorphic representations of split connected adjoint exceptional groups
Proved in result 014
Generator problem
Proved in result 296
Geoghegan's conjecture
Proved in result 248
Geometric Generalized Lax conjecture
Disproved in result 095
Geometric-progression case of the Erdős similarity conjecture
Proved in result 084
Gersten's conjecture
Proved in result 258
Gigli's characterization conjecture
Proved in result 356
Global section conjecture for smooth proper geometrically connected curves of genus at least two over number fields when their finite-cover descent locus equals their rational points
Partial progress in result 019
Global Spherical Shell conjecture
Proved in result 060
Goldfeld's analytic density conjecture
Proved in result 006
Goldfeld's mean analytic-rank conjecture
Proved in result 006
Gopalan–Servedio square-root conjecture
Disproved in result 192
Gorenstein-projective conjecture
Disproved in result 199
Gottschalk's surjunctivity conjecture
Disproved in result 197
Griffiths' positivity conjecture
Disproved in result 050
Gromov's integral scalar-curvature inequality
Proved in result 335
Gromov–Lawson aspherical conjecture
Proved in result 335
Gromov–Lawson conjecture
Proved in result 335
Gromov's scalar-curvature conjecture in every dimension n ≥ 4
Proved in result 336
Grothendieck homotopy hypothesis
Proved in result 312
Grothendieck's section conjecture over ℚ for the modular curves and of genus at least two
Proved in result 019
Gupta–Newman–Rabinovich–Sinclair conjecture for graphs of bounded treewidth
Proved in result 089
Gupta–Newman–Rabinovich–Sinclair conjecture for planar graphs
Proved in result 089
Gwynne and Miller's graph-metric conjecture for critical Fortuin–Kasteleyn maps at each fixed and for uniform spanning-tree-decorated maps
Proved in result 211
Gyárfás's monochromatic tree-cover conjecture
Disproved in result 162
H
Hadwiger's conjecture
Disproved in result 157
Hadwiger–Nelson problem
Partial progress in result 158
Hahn–Wilson conjecture at height two
Disproved in result 319
Hajłasz–Onninen maximal-function regularity problem in the planar centered-disk case
Proved in result 085
Half-area cylinder-covering conjecture
Disproved in result 100
Half-plane Temperleyan form of the double-dimer CLE4 scaling-limit conjecture
Proved in result 226
Harary–Hill conjecture
Proved in result 165
He–Schramm conjecture
Partial progress in result 071
Heilbronn's triangle problem
Disproved in result 191
Hellinger conjecture
Proved in result 119
Henry's pushout conjecture
Proved in result 312
Higher-dimensional Duke equidistribution problem
Proved in result 015
Higher-dimensional Erdős distinct-distances conjecture
Proved in result 166
Higher-dimensional Thomason model-structure conjecture of Ara and Maltsiniotis
Proved in result 317
Higher-finiteness strengthening of the Boone–Higman conjecture
Proved in result 250
Hilbert–Smith conjecture
Proved in result 304
Hilbert’s tenth problem over ℚ
Disproved in result 004
Hindman’s finite sums and products conjecture
Proved in result 164
Hodge standard conjecture for abelian varieties in arbitrary characteristic
Proved in result 032
Höring's conjecture on rationally connected projective manifolds
Proved in result 052
Hovey–Strickland conjecture
Proved in result 311
Howie's conjecture on nonsingular systems
Proved in result 256
Hutchcroft's stronger operator-threshold conjecture
Proved in result 214
Hyperinvariant-subspace problem
Disproved in result 293
I
Integral Donovan finiteness over Witt Vectors
Proved in result 203
Ionization conjecture
Proved in result 263
Irrationality exponent of π
Proved in result 017
Irrationality of Catalan's constant
Proved in result 005
Isoperimetric conjecture for the cubic flat three-torus
Proved in result 354
J
Jacobsthal's quadratic-bound question
Proved in result 021
Joó’s partitional-matroid question
Disproved in result 185
Joos–Kühn sharp-constant conjecture
Partial progress in result 188
K
K3 Oka conjecture
Proved in result 042
Kadison–Kaplansky projection conjecture
Disproved in result 285
Kadison–Ringrose cohomology conjecture
Proved in result 295
Kadison's similarity conjecture
Proved in result 288
Kakeya maximal conjecture in three dimensions
Proved in result 074
Kalton's question
Disproved in result 330
Kaplansky's direct-finiteness conjecture
Disproved in result 197
Kaplansky's idempotent conjecture in characteristic zero
Proved in result 207
Kaplansky's quasitrace conjecture
Disproved in result 294
Kaplansky's zero-divisor conjecture
Disproved in result 196
Katok's entropy rigidity conjecture for closed connected Riemannian manifolds of dimension at least three with strictly negative sectional curvature
Proved in result 339
Kerr–Newman Penrose inequality
Partial progress in result 260
Kerr–Newman Penrose inequality with bare gravitational ADM angular momentum
Disproved in result 260
Kervaire conjecture
Proved in result 256
Kervaire invariant problem at the prime three
Proved in result 309
Khot's 2-to-1 Games Conjecture
Proved in result 105
Khot's Unique Games Conjecture
Proved in result 102
Kirchberg's norm-ultrapower embedding problem
Disproved in result 292
Kirchberg–Rørdam character question
Proved in result 299
Kirchberg–Rørdam's comparison question
Proved in result 303
Kirk's reflexive-space fixed-point problem
Proved in result 328
Kobayashi's canonical-ampleness conjecture
Proved in result 051
Koebe's circle-domain conjecture
Proved in result 071
Kohn–Sham ensemble representability
Disproved in result 278
Kollár–Pardon conjecture
Proved in result 058
Kraetzer's conjectured spectrum at p = −1
Disproved in result 072
Kuhn and Lloyd's equality
Proved in result 314
Kurosh's division-ring problem on local finiteness
Disproved in result 201
Kuznetsov's rationality conjecture
Disproved in result 054
L
sufficiency conjecture
Proved in result 075
Lang–Plaut problem
Disproved in result 098
Large-data global classical regularity problem for the three-dimensional, one-species relativistic Vlasov–Maxwell system
Proved in result 362
Leader–Russell–Walters conjecture
Disproved in result 172
LeBrun–Salamon conjecture
Proved in result 062
Lech's multiplicity conjecture
Proved in result 194
Letrouit's conjectured uniform square-root estimate
Disproved in result 374
Lex-plus-powers conjectures
Proved in result 200
Linear List Hadwiger conjecture
Proved in result 157
Lins Neto–de Melo–Pugh conjecture for degree-five classical Liénard systems
Proved in result 143
Lipman–Zariski conjecture in characteristic zero
Disproved in result 048
Litt's integral-density question
Proved in result 027
Little finitistic-dimension conjecture
Disproved in result 198
Local p-adic section conjecture
Proved in result 019
Local strong cosmic censorship near each fixed rotating subextremal Kerr bridge
Proved in result 264
Log abundance for normal compact Kähler log canonical pairs with effective rational boundary
Proved in result 034
Log abundance for projective log canonical threefold pairs in numerical dimension one over algebraically closed fields of characteristic p > 3
Proved in result 035
Logarithmic Brunn–Minkowski conjecture
Proved in result 091
Low-temperature ordering problem
Proved in result 271
Lyons's question
Proved in result 236
M
Mahler conjecture for general convex bodies
Proved in result 087
Margulis–Platonov conjecture over global fields
Proved in result 018
Margulis–Platonov conjecture over global function fields
Proved in result 018
Margulis–Platonov conjecture over number fields
Proved in result 018
Matolcsi–Ruzsa–Weiner Fourier-vanishing conjecture
Proved in result 266
Mendel and Naor's question
Proved in result 332
Metric Blaschke conjecture
Proved in result 344
Milne's rationality conjecture
Proved in result 001
Minimal-model conjecture for projective generalized log canonical ℚ-pairs
Proved in result 036
Modified integer round-up conjecture of Scheithauer and Terno
Disproved in result 118
Modularity conjecture for elliptic curves over imaginary quadratic fields
Proved in result 030
Moore's parity conjecture in the measured-output model
Proved in result 274
Morse-number form of the Arnold conjecture
Disproved in result 347
N
Nagata–Biran conjecture for surfaces
Proved in result 039
Nagata–Biran–Szemberg assertion in higher dimensions
Proved in result 039
Nagata's conjecture for plane curves
Proved in result 039
Naimark's problem
Disproved in result 297
Naor's renorming question
Proved in result 327
Naor's sublinear-dimension question for
Proved in result 094
Near-boundary Birkhoff conjecture
Proved in result 147
Nearby Lagrangian conjecture
Disproved in result 340
Negatively pinched Kähler uniformization question
Disproved in result 359
Nienhuis's predicted three-quarter exponent
Proved in result 237
Nuclear-dimension equivalence in the nonsimple Toms–Winter regularity question
Proved in result 291
Numerical blockwise Alperin weight conjecture
Proved in result 202
Numerical-dimension-one case of the minimal-model conjecture
Proved in result 036
O
Odd, regular two-dimensional Fontaine–Mazur conjecture over ℚ at 2
Proved in result 010
One-phase Bernoulli problem
Proved in result 367
One-sided bounded-holomorphic-function question
Disproved in result 359
Ordinary-double-point volume-gap conjecture
Proved in result 037
Ordinary finite-assembly question for chromatic overlaps at the prime three and height three
Disproved in result 318
Ordinary Iitaka subadditivity conjecture
Proved in result 033
Ordinary two-point Chowla conjecture
Proved in result 007
Ostmann's inverse Goldbach conjecture
Proved in result 013
P
P = 2 case of Emerton's dimension conjecture
Proved in result 010
Parabolic Intersection Conjecture
Proved in result 254
Patterson's first-moment conjecture
Proved in result 023
Perfect-matching entropy conjecture of Anari, Oveis Gharan, and Vinzant
Proved in result 113
Periodic tiling conjecture
Disproved in result 155
Permanence conjecture for finite weakly reversible mass-action systems
Proved in result 149
Persistence conjecture for finite weakly reversible mass-action systems
Proved in result 149
Petty's projection-volume conjecture in dimensions at least four
Proved in result 088
Phan's Conjecture C for and
Proved in result 370
Phillips–Toms conjecture
Proved in result 302
Pietsch's dimension-free duality conjecture for metric entropy
Disproved in result 329
Pixton's completeness conjecture for his original relation system in Chow
Disproved in result 053
Pixton's completeness conjecture for his original relation system in rational cohomology
Disproved in result 053
Planar Cohn–Elkies sharpness conjecture
Proved in result 090
Planar Mumford–Shah regularity conjecture
Proved in result 366
Planar no-bigeodesics conjecture under that moment assumption
Proved in result 212
Planar unit-distance problem
Partial progress in result 167
Polynomial ordered binary matrix-removal conjecture
Disproved in result 190
Polynomial-sample question for binary trace reconstruction
Disproved in result 122
Popa's logarithmic additivity conjecture
Proved in result 033
Popa's logarithmic variation conjecture
Proved in result 033
Popa–Vaes quadratic strong-operator paving conjecture
Proved in result 300
Positive-b2 Global Spherical Shell conjecture
Proved in result 060
Positive-characteristic form of the qualitative Nagata–Biran–Szemberg assertion at geometric generic tuples
Proved in result 039
Prescribed-threshold form of Shelah's categoricity conjecture
Disproved in result 240
Problem XXI of Schafhauser, Tikuisis and White
Proved in result 291
Projected Lax conjecture
Disproved in result 095
Projective-space base conjecture for projective Lagrangian fibrations
Proved in result 041
Purely cosmetic surgery conjecture
Proved in result 306
Q
Quadratic strengthening of the Sensitivity Conjecture
Disproved in result 132
Quasi-Riemann hypothesis
Proved in result 003
Quasilinear PCP-for-PPAD conjecture
Proved in result 136
Question of Burger, Ozawa, and Thom
Proved in result 251
Question of Zhu, Fang, and Shi
Disproved in result 293
Quillen's conjecture in rational homology
Proved in result 310
R
Rational-boundary log abundance conjecture
Proved in result 034
Rational coarse Novikov conjecture
Disproved in result 307
Rational Hodge conjecture
Partial progress in result 032
Rational Hodge conjecture for complex CM abelian varieties
Proved in result 032
Rational Hodge conjecture for finite products of projective complex K3 surfaces
Proved in result 032
Rational Hodge conjecture for self-powers of a projective complex K3 surface on the K3 quadratic locus
Proved in result 032
Rational Hodge conjecture for the full two-dimensional rational Weil space in codimension four on split abelian eightfolds of Weil type
Proved in result 032
Rational Hodge conjecture on self-powers of a complex abelian sixfold with an imaginary-quadratic action and a compatible polarization whose rational homological Hermitian form is hyperbolic of signature
Proved in result 032
Rational Hodge conjecture on self-powers of a complex abelian variety of dimension at most five admitting an imaginary-quadratic action
Proved in result 032
Rational Hodge conjecture on self-powers of a very general member of the full smooth labelled family of diagonal complete intersections cut out by at most two equations of a common degree
Proved in result 032
Rational Hodge conjecture on self-powers of the Jacobian at each tensor Hodge-generic point of the full marked variation of a connected abelian cover of curves
Proved in result 032
Rationality conjecture of Gaitsgory–Lafforgue–Raskin
Proved in result 014
Reflexive diamond converse for asymptotic uniform convexifiability
Disproved in result 331
Regular-point bi-Lipschitz conjecture in the noncollapsed setting
Proved in result 357
Relative bicentralizer conjecture
Proved in result 290
Residual-finiteness question for hyperbolic groups
Disproved in result 252
Restricted geometric Langlands equivalence
Proved in result 014
Riemannian Penrose inequality
Proved in result 260
Rigidity conjecture for the Turing degrees
Proved in result 241
Robert and Tikuisis's Conjecture (C1)
Proved in result 291
Robert's trace-cone classification question
Proved in result 301
Rohde–Schramm prediction
Proved in result 223
Rokhlin's multiple-mixing problem for a single transformation
Proved in result 145
Rothvoss's polynomial-size lift question
Disproved in result 126
Ryser's covering conjecture
Disproved in result 162
S
Sakoda–Sipser state-succinctness conjecture
Proved in result 129
Sandier–Serfaty conjecture
Proved in result 090
Satisfiability conjecture for random 3-SAT
Proved in result 235
Satisfiability conjecture for random k-SAT
Proved in result 235
Saturation conjecture for Spin (2n), n ≥ 2
Proved in result 204
Saxl's conjecture
Proved in result 205
Scalar Calderón problem at bounded measurable regularity
Disproved in result 365
Scalar-curvature extension conjecture in its unrestricted all-dimensions form
Disproved in result 351
Scalar-curvature extension problem in dimension four
Proved in result 351
Scalar-dilation B-conjecture
Proved in result 091
Scalar one-dimensional Lieb–Thirring conjecture
Proved in result 262
Schönhage–Strassen optimality conjecture
Disproved in result 109
Schramm's Hausdorff-measure existence problem
Proved in result 230
Schramm's Problem 2.2
Proved in result 232
Schramm's Problem 2.3
Proved in result 232
Second Kahn–Kalai conjecture
Proved in result 176
Selmer converse in coranks zero and one for every elliptic curve over ℚ and every prime p
Proved in result 002
Separable Banach-space Lipschitz-isomorphism problem
Disproved in result 324
Separable C∗-algebraic spatial form of the Kadison–Kastler conjecture
Disproved in result 289
Separable Lipschitz-isomorphism problem
Disproved in result 324
Separable quotient problem
Addressed in result 323
Serre's intersection multiplicity conjecture
Proved in result 193
Seymour's second-neighborhood conjecture
Proved in result 173
Shafarevich conjecture on holomorphic convexity in complex dimension two
Disproved in result 046
Shafarevich holomorphic-convexity conjecture under the large-fundamental-group hypothesis
Disproved in result 046
Shelah's eventual categoricity conjecture
Proved in result 240
Shokurov’s bounded-klt-complement conjecture
Proved in result 066
Shub's entropy conjecture
Disproved in result 151
Sidorenko's conjecture
Disproved in result 161
Siegel and Yao's Conjecture A
Proved in result 343
Siegel–Yao conjecture
Proved in result 343
Simon’s continuum problem
Proved in result 228
Simon’s Problem 1
Proved in result 261
Simple-undirected Kannan–Tetali–Vempala conjecture
Proved in result 131
Sinai's positive-parameter-measure conjecture
Proved in result 146
Single-fold conjecture
Proved in result 242
Small Cohen–Macaulay module conjecture
Disproved in result 195
Smooth anisotropic Calderón uniqueness problem
Proved in result 365
Smooth three-dimensional isotropic elastic Calderón uniqueness problem
Proved in result 372
Snaky achievement problem
Proved in result 187
Sogge's Euclidean local smoothing conjecture in dimension three
Proved in result 079
Solomon–Yau least-volume conjecture
Proved in result 349
Spacetime Penrose inequality
Proved in result 260
Spherical magnetization law
Proved in result 271
Spin-one Haldane gap conjecture
Proved in result 268
Squarefree-values conjecture for irreducible integer quartics
Proved in result 020
Stable Coordinate Conjecture in ambient dimension five
Disproved in result 047
Stable Coordinate conjecture in four variables
Disproved in result 049
Stable-Morse lower bound for nondegenerate Hamiltonian fixed points
Disproved in result 347
Stein's weak- conjecture
Proved in result 083
Strict convexity and differentiability conjectures for the planar exponential model
Proved in result 212
Strict hot spots conjecture for smooth bounded simply connected planar domains
Proved in result 369
Strong chromatic splitting at height three for primes p ≥ 5
Disproved in result 318
Strong hyperkähler SYZ conjecture
Proved in result 041
Strong isotropic constant conjecture
Proved in result 101
Strong Kadison–Kastler conjecture
Proved in result 289
Strong-locality conjecture
Partial progress in result 280
Strong-locality conjecture for simple unitary strongly rational complex vertex operator algebras
Proved in result 280
Strong Nakayama conjecture
Disproved in result 199
Strong thin-tree conjecture
Proved in result 174
Strong Ulam stability for countable discrete groups
Proved in result 251
Subcritical Hénon–Lane–Emden conjecture
Proved in result 370
Subcritical Lane–Emden conjecture
Proved in result 370
Sufficiency of the associated-K3 criterion for rationality
Disproved in result 054
Surface case of the μ-constant problem
Proved in result 064
Symmetric Mahler conjecture
Proved in result 087
Symmetric scalar triangular Hilbert transform problem
Proved in result 082
Szabó's conjecture
Partial progress in result 291
T
Tachikawa's second conjecture
Disproved in result 199
Talagrand's conjecture that integral and fractional expectation thresholds are within a universal constant factor
Proved in result 175
Talagrand's discrete-convexity conjecture
Proved in result 175
Tate conjecture for abelian varieties over finite fields
Proved in result 032
Tensor square conjecture for symmetric groups
Proved in result 205
Three-dimensional Ball–Evans approximation problem
Proved in result 368
Three-dimensional Bochner–Riesz conjecture
Proved in result 078
Three-processor unit-job scheduling problem of Garey and Johnson
Proved in result 124
Threshold-bound-state conjecture
Proved in result 270
Tingley’s problem
Proved in result 322
Toda's Gepner conjecture
Proved in result 055
Toms–Winter regularity problem
Partial progress in result 291
Triangle case of the Joos–Kühn sharp-constant conjecture
Proved in result 188
Trilinear Hilbert transform conjecture for slopes 1, 2, 3 in the L3 exponent case
Proved in result 086
Turán's brickyard problem
Proved in result 165
Turyn's bounded-merit-factor conjecture
Disproved in result 076
Two-dimensional Anderson localization conjecture for the uniform single-site law
Proved in result 261
Two-dimensional Brauchart–Hardin–Saff conjecture on the linear term
Proved in result 090
Two-primary Birch and Swinnerton-Dyer leading-term formula for elliptic curves over the rationals whose two-power Selmer group has corank at most one
Proved in result 002
Type-D part of the simply-laced saturation conjecture
Proved in result 204
U
Uchida's conjecture
Proved in result 031
Uniform boundedness assertion in Hilbert's sixteenth problem
Proved in result 143
Uniform-boundedness version of the generalized star-height problem
Proved in result 134
Unital, stably finite case of Szabó's Conjecture A on automatic equivariant Jiang–Su stability
Proved in result 291
Unital Toms–Winter conjecture
Proved in result 291
Unramified de Rham quantum geometric Langlands equivalence at irrational level
Proved in result 069
Unrestricted critical-number form of the Arnold conjecture
Disproved in result 347
Unrestricted group-ring Determinant Conjecture
Disproved in result 197
Unrestricted infinite matroid intersection conjecture
Disproved in result 185
Unrestricted infinite matroid packing/covering conjecture
Disproved in result 185
Unrestricted integral Gersten conjecture in degree 3
Disproved in result 209
Unrestricted integral Gersten conjecture in degree 5
Disproved in result 209
Unrestricted rational cup-length form of the Arnold conjecture
Disproved in result 347
Unrestricted small-spatial-embedding problem for one-sided near inclusions of von Neumann algebras
Disproved in result 289
Unrestricted smooth local isometric realization problem for surfaces
Disproved in result 334
Unrestricted two-map PPT-composition conjecture
Disproved in result 272
V
Variational equality conjecture
Proved in result 221
Villani’s conjecture in this setting
Proved in result 360
Virasoro conjecture for smooth complete intersections in projective space
Proved in result 065
Voiculescu’s finite-entropy equality question
Disproved in result 298
W
Wakamatsu tilting conjecture
Disproved in result 199
Wall's conjecture
Disproved in result 305
Wall's finite D(2) conjecture
Disproved in result 321
Wall's manifold-realization question in dimension four
Disproved in result 305
Weak chromatic splitting for the derived p-completed sphere at height p+1 for primes p ≥ 7
Disproved in result 318
Weak chromatic splitting for the derived p-completed sphere at height p for primes p ≥ 5
Disproved in result 318
Weak inhomogeneous Duffin–Schaeffer conjecture
Proved in result 022
Weak pinned Erdős distinct-distance conjecture
Proved in result 167
Whether every word-hyperbolic group is a CAT(0) group
Disproved in result 257
Williams's question for this model
Proved in result 137
Wise's virtual free-by-cyclic conjecture for hyperbolic one-relator groups
Proved in result 258
Y
Yau's conjecture for smooth closed surfaces
Proved in result 350
Yau's integer-degree dimension comparison question
Disproved in result 361
Yau's nodal-set conjecture
Disproved in result 350
Yau's nodal upper bound in dimensions three and four
Disproved in result 350
Yau's uniformization conjecture
Proved in result 338
Z
Zarankiewicz crossing-number conjecture
Proved in result 165
Zariski's affine-space cancellation problem over ℂ in dimension four
Disproved in result 047
Zariski's multiplicity conjecture
Disproved in result 059
Zauner's dimension-six mutually unbiased bases conjecture
Proved in result 266
Zilber–Pink conjecture for curves in
Proved in result 016
#
Β-Barendregt–Geuvers–Klop conjecture
Proved in result 245
Μ-constant problem
Partial progress in result 064
ℓ1-Bass conjecture for every discrete group
Proved in result 207