AI声称解决500个数学开放问题中的90个
Suddenly, AI has solved 90 of the 500 most important open problems in mathematic…
Suddenly, AI has solved 90 of the 500 most important open problems in mathematics
突然之间，人工智能已经解决了数学领域500个最重要的开放问题中的90个
Highest ranked problems:
排名最高的问题：
#2 Riemann Hypothesis — PARTIAL #4 Hodge Conjecture — PARTIAL #5 Birch and Swinnerton-Dyer Conjecture — PARTIAL #10 Extended Riemann hypothesis for Dedekind zeta functions — PARTIAL #12 Generalized Riemann Hypothesis for Dirichlet L-functions — PARTIAL #15 Tate Conjecture for Algebraic Cycles — PARTIAL #22 Hilbert's Tenth Problem over the Rationals — FULL CLAIM #24 Grothendiecks Generalized Hodge Conjecture — PARTIAL #28 Matrix-Multiplication Exponent Equals Two — PARTIAL #29 Unique Games Conjecture — FULL CLAIM #31 Anderson Model Extended States in Dimension at Least Three — FULL CLAIM #37 Prove the Penrose inequality or present a counterexample — FULL CLAIM #38 Higher-dimensional Euclidean Kakeya conjecture — PARTIAL #39 Modularity of Elliptic Curves over Number Fields (End_K(E)=Z) — PARTIAL #40 Hilbert's Sixteenth Problem, Second Part — PARTIAL #46 Fourier restriction conjecture — PARTIAL #47 The Fontaine-Mazur Conjecture on Geometric Galois Representations — PARTIAL #48 Nonexistence of Landau–Siegel zeros for quadratic Dirichlet L-functions — FULL CLAIM #52 The Baum-Connes Conjecture for the K-Theory of Reduced Group C*-Algebras — FULL CLAIM #62 Permanent versus Determinant over C — PARTIAL #69 Finiteness of the Tate-Shafarevich Group for Elliptic Curves — PARTIAL #72 Termination of Flips Conjecture in the Minimal Model Program — PARTIAL #77 Chowla conjecture on correlations of the Liouville function — PARTIAL #78 Abundance Conjecture for the minimal model program — FULL CLAIM #80 Hadwiger Conjecture — FULL CLAIM #83 Zilber-Pink Conjecture on Unlikely Intersections — PARTIAL #87 Bose-Einstein Condensation in Interacting Continuous Bose Gases — FULL CLAIM #92 Entanglement Area Law for 2D Gapped Quantum Systems — FULL CLAIM #94 Grothendieck Standard Conjecture of Hodge Type — PARTIAL #95 Kannan-Lovasz-Simonovits conjecture on isoperimetry of log-concave measures — PARTIAL #99 Grothendiecks Section Conjecture in Anabelian Geometry — PARTIAL #112 The Haldane Conjecture on Spectral Gaps of Antiferromagnetic Quantum Spin Chains — PARTIAL #114 Iitaka conjecture C_{n,m} on subadditivity of Kodaira dimension — FULL CLAIM #119 The Borel Conjecture on Topological Rigidity of Aspherical Manifolds — FULL CLAIM #124 Aspherical Manifolds Admit No Metric of Positive Scalar Curvature — FULL CLAIM #130 Polynomial Bound for Limit Cycles of Planar Polynomial Vector Fields — PARTIAL #136 Erdős problem 3: divergent harmonic series and long arithmetic progressions — FULL CLAIM #139 Cannon's conjecture — FULL CLAIM #145 Residual Finiteness of Hyperbolic Groups — FULL CLAIM #153 Congruent Number Problem — PARTIAL #161 BPL = L (Derandomizing Bounded-Error Logspace) — FULL CLAIM #163 NP versus the Existential Theory of the Reals — PARTIAL #169 The Free Group Factor Isomorphism Problem — FULL CLAIM #172 Conformal Invariance of the Critical Random-Cluster Model with q <= 4 — FULL CLAIM #179 Arnold Conjecture on Hamiltonian Fixed Points — FULL CLAIM #181 Polyakov Conjecture: Absence of a Phase Transition for Planar O(n) Models with n >= 3 — FULL CLAIM #183 Smooth anisotropic Calderón uniqueness from full boundary data — FULL CLAIM #193 Nonvanishing conjecture for projective log canonical pairs — FULL CLAIM #195 Parity conjecture for elliptic curves — PARTIAL #198 Long-Range Order in the Quantum Heisenberg Ferromagnet — FULL CLAIM #203 Bochner-Riesz conjecture — PARTIAL #205 Local Smoothing Conjecture for Wave Equations — PARTIAL #206 Kaplansky's Zero-Divisor Conjecture for Torsion-Free Groups — FULL CLAIM #210 Artin's primitive root conjecture — PARTIAL #211 Hilbert-Smith Conjecture — FULL CLAIM #213 Falconer distance set conjecture — FULL CLAIM #222 Virasoro Conjecture for Gromov–Witten Invariants — PARTIAL #224 Wall's Poincare Duality Group Conjecture — FULL CLAIM #225 K(pi,1) conjecture for Artin groups — FULL CLAIM #234 Unconditional 2−epsilon Inapproximability of Minimum Vertex Cover — FULL CLAIM #235 Chromatic Number of the Plane (Hadwiger--Nelson Problem) — PARTIAL #237 Global Existence of Classical Solutions to the Relativistic Vlasov-Maxwell System — PARTIAL #239 Universal Optimality of the Hexagonal Lattice in Dimension Two — FULL CLAIM #246 De Giorgi Conjecture for the Allen-Cahn Equation in Dimensions 4 to 8 — FULL CLAIM #254 Exact satisfiability threshold for random k-SAT for small k (k = 3) — PARTIAL #256 Polynomial-Time Decidability of Semidefinite Programming Feasibility — PARTIAL #260 RL versus L — FULL CLAIM #261 Kadison Similarity Problem for C*-Algebras — FULL CLAIM #267 Sidorenko Conjecture on Bipartite Homomorphism Densities — FULL CLAIM #268 Shafarevich Holomorphic-Convexity Conjecture — FULL CLAIM #270 Kuznetsov Rationality Conjecture for Cubic Fourfolds — FULL CLAIM #271 All groups are good: the four-dimensional disc-embedding conjecture — FULL CLAIM #278 Planar homogeneous Mumford–Shah local-structure conjecture — PARTIAL #284 Nearby Lagrangian Conjecture — FULL CLAIM #285 Cartan-Hadamard isoperimetric conjecture — FULL CLAIM #289 Sharp Upper Bound in Yau's Conjecture on Nodal Sets of Laplace Eigenfunctions — FULL CLAIM #290 Kaplansky's Idempotent Conjecture — FULL CLAIM #291 Calderón uniqueness for bounded measurable real isotropic conductivities — FULL CLAIM #292 Global Attractor Conjecture for Complex-Balanced Mass-Action Systems — FULL CLAIM #295 Zariski Multiplicity Conjecture for Hypersurface Singularities — FULL CLAIM #297 Amenability of Thompson's Group F — FULL CLAIM #298 Griffiths Positivity Conjecture for Ample Vector Bundles — FULL CLAIM #300 The Singer Conjecture on Vanishing of L2-Cohomology of Aspherical Manifolds — PARTIAL #305 Birkhoff Conjecture (Near-Boundary Continuous Invariant Foliation) — FULL CLAIM #306 Secret key from all entangled states — FULL CLAIM #311 Mahler Conjecture on the Volume Product of a Convex Body — FULL CLAIM #321 Finiteness of Finitely Presented Periodic Groups — FULL CLAIM #328 Sinai's Positive Metric Entropy Conjecture for the Chirikov Standard Map — FULL CLAIM #334 Unrestricted Linear-Circuit Lower Bound for the Discrete Fourier Transform — FULL CLAIM #343 Koebe circle-domain uniformization conjecture — FULL CLAIM #351 Kobayashi Conjecture: Hyperbolic Compact Kähler Manifolds Have Ample Canonical Bundle — FULL CLAIM #356 Bott Conjecture: nonnegatively curved simply connected manifolds are rationally elliptic — PARTIAL #357 Strong Hyperplane Conjecture for Isotropic Constants — FULL CLAIM #358 CAT(0) Models for All Word-Hyperbolic Groups — FULL CLAIM #359 Hopf Conjecture: no metric of positive sectional curvature on S^2 x S^2 — PARTIAL #361 Alperins Weight Conjecture for Modular Representations of Finite Groups — FULL CLAIM #364 Log-Brunn-Minkowski Inequality for Symmetric Convex Bodies — FULL CLAIM #366 Hyperkähler SYZ (Lagrangian Fibration) Conjecture — FULL CLAIM #368 Benjamini-Schramm conjecture p_c<p_u for non-amenable Cayley graphs — FULL CLAIM #369 Dixmier unitarisability problem for discrete groups — FULL CLAIM #374 Fujita Freeness Conjecture — FULL CLAIM #375 Nagata Conjecture on Plane Curve Linear Systems — FULL CLAIM #378 Toms–Winter: Strict Comparison Implies Z-Stability — FULL CLAIM #379 Margulis–Platonov normal-subgroup conjecture — FULL CLAIM #388 Shelah's Categoricity Conjecture for L_omega1,omega — PARTIAL #392 Measure-zero singular set of stationary integral varifolds — FULL CLAIM #401 Serres Positivity Conjecture for Intersection Multiplicities over Regular Local Rings — FULL CLAIM #403 Rokhlin problem on multiple mixing — FULL CLAIM #419 Lück's Determinant Conjecture for Discrete Groups — FULL CLAIM #420 Absolute continuity of Bernoulli convolutions outside reciprocal Pisot parameters — FULL CLAIM #421 GNRS Conjecture — PARTIAL #424 Irrationality of Catalan's Constant — FULL CLAIM #425 Separable Quotient Problem for Banach Spaces — FULL CLAIM #430 Long-Time Existence of the Calabi Flow on Compact Kaehler Manifolds — FULL CLAIM #432 Combinatorial Invariance of Kazhdan-Lusztig Polynomials — FULL CLAIM #434 Realizable Limit Shapes in Two-Dimensional First-Passage Percolation — PARTIAL #438 Zariski Cancellation Problem (characteristic zero, dimension ≥ 3) — FULL CLAIM #440 Stein's Conjecture on the Hilbert Transform along Lipschitz Vector Fields — FULL CLAIM #448 Smooth Realization of Finite-Entropy Ergodic Transformations — FULL CLAIM #450 Deligne–Drinfeld Freeness Conjecture for grt_1 — FULL CLAIM #453 Shub entropy conjecture — FULL CLAIM #456 Maximal Number of Mutually Unbiased Bases in Composite Dimensions — PARTIAL #458 LeBrun-Salamon Conjecture: positive quaternion-Kahler manifolds are symmetric spaces — FULL CLAIM #461 Kaplansky's Direct Finiteness Conjecture — FULL CLAIM #465 David–Semmes Riesz-transform problem in intermediate dimensions — FULL CLAIM #467 Small Cohen-Macaulay Conjecture — FULL CLAIM #468 Ergodicity of Irrational Triangular Billiards — FULL CLAIM #472 CAT(0) Conjecture for All Artin Groups — FULL CLAIM #475 Katok entropy rigidity conjecture — FULL CLAIM #476 Polynomial-Time Solvability of Condon's Simple Stochastic Games — PARTIAL #480 Furstenberg No-Bigeodesics (Planar FPP, Standard Minimum Moment) — FULL CLAIM #483 Gaboriau's Fixed Price Problem for Countable Groups — FULL CLAIM #484 Persistence Conjecture for Weakly Reversible Mass-Action Systems — FULL CLAIM #486 Campana-Peternell Conjecture — PARTIAL #497 Maximum Number of k-sets and Complexity of k-levels — PARTIAL
#2 黎曼猜想 — PARTIAL #4 霍奇猜想 — PARTIAL #5 Birch and Swinnerton-Dyer 猜想 — PARTIAL #10 Dedekind zeta 函数的扩展黎曼猜想 — PARTIAL #12 Dirichlet L 函数的广义黎曼猜想 — PARTIAL #15 代数环面的 Tate 猜想 — PARTIAL #22 有理数域上的希尔伯特第十问题 — FULL CLAIM #24 格罗滕迪克的广义霍奇猜想 — PARTIAL #28 矩阵乘法指数等于二 — PARTIAL #29 唯一游戏猜想 — FULL CLAIM #31 至少三维的 Anderson 模型扩展态 — FULL CLAIM #37 证明彭罗斯不等式或提出反例 — FULL CLAIM #38 高维欧几里得 Kakeya 猜想 — PARTIAL #39 数域上椭圆曲线的模性 (End_K(E)=Z) — PARTIAL #40 希尔伯特第十六问题，第二部分 — PARTIAL #46 傅里叶限制猜想 — PARTIAL #47 Fontaine-Mazur 关于几何伽罗瓦表示的猜想 — PARTIAL #48 二次 Dirichlet L 函数不存在 Landau–Siegel 零点 — FULL CLAIM #52 约化群 C*-代数的 K-理论的 Baum-Connes 猜想 — FULL CLAIM #62 复数域上永久式与行列式的比较 — PARTIAL #69 椭圆曲线的 Tate-Shafarevich 群的有限性 — PARTIAL #72 最小模型纲领中翻转终止猜想 — PARTIAL #77 Chowla 关于 Liouville 函数相关性的猜想 — PARTIAL #78 最小模型纲领的丰度猜想 — FULL CLAIM #80 Hadwiger 猜想 — FULL CLAIM #83 Zilber-Pink 关于非典型相交的猜想 — PARTIAL #87 相互作用连续玻色气体中的玻色-爱因斯坦凝聚 — FULL CLAIM #92 二维带隙量子系统的纠缠面积律 — FULL CLAIM #94 格罗滕迪克霍奇型标准猜想 — PARTIAL #95 Kannan-Lovasz-Simonovits 关于对数凹测度等周问题的猜想 — PARTIAL #99 Anabelian 几何中的格罗滕迪克截面猜想 — PARTIAL #112 Haldane 关于反铁磁量子自旋链谱隙的猜想 — PARTIAL #114 Iitaka 关于 Kodaira 维度次可加性的 C_{n,m} 猜想 — FULL CLAIM #119 Borel 关于非紧致流形拓扑刚性性的猜想 — FULL CLAIM #124 非紧致流形不允许多于零标量曲率的度量 — FULL CLAIM #130 平面多项式向量场极限环的多项式界 — PARTIAL #136 Erdős 问题 3：发散的调和级数和长算术级数 — FULL CLAIM #139 Cannon 猜想 — FULL CLAIM #145 双曲群的剩余有限性 — FULL CLAIM #153 同余数问题 — PARTIAL #161 BPL = L（去随机化有界误差对数空间） — FULL CLAIM #163 NP 与实数的存在理论 — PARTIAL #169 自由群因子同构问题 — FULL CLAIM #172 q <= 4 的临界随机团模型的共形不变性 — FULL CLAIM #179 Arnold 关于哈密顿不动点的猜想 — FULL CLAIM #181 Polyakov 猜想：n >= 3 的平面 O(n) 模型不存在相变 — FULL CLAIM #183 从完整边界数据得出光滑各向异性 Calderón 唯一性 — FULL CLAIM #193 射影对数典范对的非消失猜想 — FULL CLAIM #195 椭圆曲线的奇偶性猜想 — PARTIAL #198 量子海森堡顺磁体中的长程序 — FULL CLAIM #203 Bochner-Riesz 猜想 — PARTIAL #205 波动方程的局部平滑猜想 — PARTIAL #206 Kaplansky 关于无挠群零因子问题的猜想 — FULL CLAIM #210 Artin 的原根猜想 — PARTIAL #211 Hilbert-Smith 猜想 — FULL CLAIM #213 Falconer 距离集猜想 — FULL CLAIM #222 Gromov–Witten 不变量的 Virasoro 猜想 — PARTIAL #224 Wall 的庞加莱对偶群猜想 — FULL CLAIM #225 Artin 群的 K(pi,1) 猜想 — FULL CLAIM #234 最小顶点覆盖无条件 2−epsilon 不可近似性 — FULL CLAIM #235 平面的色数（Hadwiger--Nelson 问题） — PARTIAL #237 相对论性 Vlasov-Maxwell 系统经典解的全局存在性 — PARTIAL #239 二维六角晶格的普遍最优性 — FULL CLAIM #246 四维至八维 Allen-Cahn 方程的 De Giorgi 猜想 — FULL CLAIM #254 小 k（k = 3）随机 k-SAT 的精确可满足阈值 — PARTIAL #256 半定规划可行性多项式时间判定 — PARTIAL #260 RL 与 L 的比较 — FULL CLAIM #261 C*-代数的 Kadison 相似性问题 — FULL CLAIM #267 Sidorenko 关于二分图同态密度的猜想 — FULL CLAIM #268 Shafarevich 全纯凸性猜想 — FULL CLAIM #270 三次四重体的 Kuznetsov 有理猜想 — FULL CLAIM #271 所有群都是好的：四维圆盘嵌入猜想 — FULL CLAIM #278 平面齐次 Mumford–Shah 局部结构猜想 — PARTIAL #284 邻近拉格朗日猜想 — FULL CLAIM #285 Cartan-Hadamard 等周猜想 — FULL CLAIM #289 Yau 关于拉普拉斯特征函数节点集的猜想中的尖锐上界 — FULL CLAIM #290 Kaplansky 的幂等元猜想 — FULL CLAIM #291 有界可测实各向同性电导率的 Calderón 唯一性 — FULL CLAIM #292 复平衡质量作用系统的全局吸引子猜想 — FULL CLAIM #295 超曲面奇点的 Zariski 多重性猜想 — FULL CLAIM #296 Thompson 群 F 的可 amenability — FULL CLAIM #298 充裕向量丛的 Griffiths 正性猜想 — FULL CLAIM #300 Singer 关于非紧致流形 L2-上同调消失的猜想 — PARTIAL #305 Birkhoff 猜想（近边界的连续不变叶状结构） — FULL CLAIM #306 来自所有纠缠态的密钥 — FULL CLAIM #311 Mahler 关于凸体体积乘积的猜想 — FULL CLAIM #321 有限展示周期群的有限性 — FULL CLAIM #328 Sinai 关于 Chirikov 标准映射的正度量熵猜想 — FULL CLAIM #334 离散傅里叶变换的无限制线性电路下界 — FULL CLAIM #343 Koebe 圆域一致化猜想 — FULL CLAIM #351 Kobayashi 猜想：双曲紧凯勒流形具有充裕典范丛 — FULL CLAIM #356 Bott 猜想：非负曲率单连通流形是有理椭圆的 — PARTIAL #357 各向同性常数的强超平面猜想 — FULL CLAIM #358 所有字双曲群的 CAT(0) 模型 — FULL CLAIM #359 Hopf 猜想：S^2 x S^2 上没有正截面曲率的度量 — PARTIAL #361 Alperin 关于有限群模表示的权重猜想 — FULL CLAIM #362 对称凸体的对数 Brunn-Minkowski 不等式 — FULL CLAIM #366 超凯勒 SYZ（拉格朗日纤维化）猜想 — FULL CLAIM #368 Benjamini-Schramm 猜想 p_c < p_u 对于非 amenability Cayley 图 — FULL CLAIM #369 离散群的 Dixmier 酉可问题 — FULL CLAIM #374 Fujita 自由性猜想 — FULL CLAIM #375 Nagata 关于平面曲线线性系的猜想 — FULL CLAIM #378 Toms–Winter：严格比较蕴含 Z-稳定性 — FULL CLAIM #379 Margulis–Platonov 正规子群猜想 — FULL CLAIM #388 Shelah 关于 L_omega1,omega 的分类学猜想 — PARTIAL #392 平稳积分变形的零测奇异集 — FULL CLAIM #401 Serre 关于正则局部环上交乘正性的猜想 — FULL CLAIM #403 Rokhlin 关于多重混合的问题 — FULL CLAIM #419 Lück 关于离散群的行列式猜想 — FULL CLAIM #420 互逆 Pisot 参数外的伯努利卷积的绝对连续性 — FULL CLAIM #421 GNRS 猜想 — PARTIAL #424 卡塔兰常数的无理性 — FULL CLAIM #425 Banach 空间的分离商空间问题 — FULL CLAIM #430 紧凯勒流形上 Calabi 流的长时间存在性 — FULL CLAIM #432 Kazhdan-Lusztig 多项式的组合不变性 — FULL CLAIM #434 二维首达渗流中可实现极限形状 — PARTIAL #438 Zariski 消去问题（特征零，维度 ≥ 3） — FULL CLAIM #440 Stein 关于沿 Lipschitz 向量场的希尔伯特变换的猜想 — FULL CLAIM #448 有限熵遍历变换的光滑实现 — FULL CLAIM #450 grt_1 的 Deligne–Drinfeld 自由性猜想 — FULL CLAIM #453 Shub 熵猜想 — FULL CLAIM #454 复合维度中最大数量的相互无偏基 — PARTIAL #456 LeBrun-Salamon 猜想：正四元数凯勒流形是对称空间 — FULL CLAIM #461 Kaplansky 的直接有限性猜想 — FULL CLAIM #462 David–Semmes 中间维度的 Riesz 变换问题 — FULL CLAIM #467 小 Cohen-Macaulay 猜想 — FULL CLAIM #468 无理三角台球桌的遍历性 — FULL CLAIM #472 所有 Artin 群的 CAT(0) 猜想 — FULL CLAIM #475 Katok 熵刚性猜想 — FULL CLAIM #476 Condon 简单随机博弈的多项式时间可解性 — PARTIAL #480 Furstenberg 无大测地线（平面 FPP，标准最小矩） — FULL CLAIM #483 Gaboriau 关于可数群的固定价格问题 — FULL CLAIM #484 弱可逆质量作用系统的持久性猜想 — FULL CLAIM #486 Campana-Peternell 猜想 — PARTIAL #497 k-集的最大数量与 k-层的复杂性 — PARTIAL
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