# Open problems from the 2010s > 31 AI-made results on questions first raised the 2010s, each explained in plain English. Results on questions first raised the 2010s, going by the… Canonical: https://closedform.nishachay.tech/open-since/2010s/ Last updated: 2026-10-14 Results on questions first raised the 2010s, going by the earliest step each entry records. 31 AI-made results on questions first raised the 2010s, from 66 papers in the OpenAI math collection, each explained in plain English. 20 have a formal Lean proof listed; 11 are claimed in a paper and not yet machine-checked. They span 12 fields, led by algebraic and complex geometry (9), probability and statistical mechanics (4) and theoretical computer science (4). The oldest question here dates back to 2010: [Irrational cubic fourfolds with Hodge-theoretic and categorical K3 associations](https://closedform.nishachay.tech/e/openai-math-2026-054/). ## Results (31) - [Numerical semiampleness and generalized minimal models](https://closedform.nishachay.tech/e/openai-math-2026-036/) - Entry 036 · Nef adjoint divisors with an extra nef part are claimed to be numerically semiample; minimal models are claimed too. (Claimed, not checked) - [The ordinary-double-point volume gap](https://closedform.nishachay.tech/e/openai-math-2026-037/) - Entry 037 · Every singular point of a mild kind is at most as roomy as a double cone, in any dimension. (Claimed, not checked) - [P = W for fixed-determinant SL n moduli spaces](https://closedform.nishachay.tech/e/openai-math-2026-043/) - Entry 043 · Two ways of layering the cohomology of SL_n Higgs moduli are claimed to agree in every composite coprime rank. (Claimed, not checked) - [The equivariant cohomological Hikita conjecture](https://closedform.nishachay.tech/e/openai-math-2026-044/) - Entry 044 · For every finite quiver, the cohomology of a Nakajima variety is claimed to equal functions on a Coulomb fixed scheme. (Claimed, not checked) - [Kobayashi’s canonical-ampleness conjecture](https://closedform.nishachay.tech/e/openai-math-2026-051/) - Entry 051 · Compact Kähler manifolds with no entire curves have ample canonical bundle, as Kobayashi conjectured. (Claimed, not checked) - [A counterexample to Pixton completeness in Chow](https://closedform.nishachay.tech/e/openai-math-2026-053/) - Entry 053 · A tautological relation in genus 10^60 that Pixton’s original relations miss, in Chow and in cohomology. (Claimed, not checked) - [Irrational cubic fourfolds with Hodge-theoretic and categorical K3 associations](https://closedform.nishachay.tech/e/openai-math-2026-054/) - Entry 054 · Very general cubic fourfolds of large admissible discriminant are irrational despite a K3 derived category. (Claimed, not checked) - [Gepner symmetry and large-volume stability on threefolds](https://closedform.nishachay.tech/e/openai-math-2026-055/) - Entry 055 · A stability condition on every smooth quintic threefold with Toda’s exact 2/5 Gepner symmetry. (Claimed, not checked) - [Semialgebraic universal covers and bounded domains](https://closedform.nishachay.tech/e/openai-math-2026-058/) - Entry 058 · Unrolled shapes with a polynomial description split into just three kinds of pieces. (Formal proof listed) - [Annular variation and dyadic absolute bounds for the triangular Hilbert transform](https://closedform.nishachay.tech/e/openai-math-2026-082/) - Entry 082 · A triangle-shaped singular integral stays bounded at the symmetric L³ point, whatever cutoffs each point picks. (Formal proof listed) - [Logarithmic and L p Brunn–Minkowski inequalities and the B-conjecture](https://closedform.nishachay.tech/e/openai-math-2026-091/) - Entry 091 · Blending two symmetric shapes the thrifty way never loses volume below their geometric mean. (Formal proof listed) - [The Courtade–Kumar and Hellinger conjectures](https://closedform.nishachay.tech/e/openai-math-2026-119/) - Entry 119 · No yes-or-no summary of random bits survives noise better than simply keeping one bit. (Formal proof listed) - [A quasilinear PCP theorem for PPAD](https://closedform.nishachay.tech/e/openai-math-2026-136/) - Entry 136 · End-of-Line puzzles turn into number circuits only slightly bigger that tolerate many broken gates, the paper claims. (Claimed, not checked) - [Subpolynomial query complexity for log-concave sampling](https://closedform.nishachay.tech/e/openai-math-2026-139/) - Entry 139 · Sampling from a gently curved bowl needs no fixed power of the dimension in queries. (Formal proof listed) - [Memory–sample lower bounds for noiseless Gaussian regression](https://closedform.nishachay.tech/e/openai-math-2026-140/) - Entry 140 · Exact clues still cost more reading for each extra digit of accuracy when memory is limited. (Formal proof listed) - [Talagrand’s expectation thresholds, discrete convexity, and graph decompositions](https://closedform.nishachay.tech/e/openai-math-2026-175/) - Entry 175 · Spreading credit fractionally beats whole-set covers by at most a fixed factor in Talagrand's threshold theory. (Formal proof listed) - [Bounded-degree coboundary expanders](https://closedform.nishachay.tech/e/openai-math-2026-177/) - Entry 177 · Large higher-dimensional expanders with a bounded number of faces at each point exist in every dimension. (Formal proof listed) - [Saxl’s conjecture and universal tensor squares](https://closedform.nishachay.tech/e/openai-math-2026-205/) - Entry 205 · The staircase representation's tensor square contains every irreducible representation, proving Saxl's conjecture. (Formal proof listed) - [The geometric phase diagram, diffusion, and spectra of random planar maps](https://closedform.nishachay.tech/e/openai-math-2026-211/) - Entry 211 · Random FK planar maps are claimed to look like random surfaces for q ≤ 4 and like a random tree above 4. (Formal proof listed) - [Conformal universality for weakly interacting and random-bond Ising models](https://closedform.nishachay.tech/e/openai-math-2026-218/) - Entry 218 · Weak extra interactions or weak random bonds leave the critical Ising interface's conformal limit, SLE₃, unchanged. (Formal proof listed) - [The double-dimer loop ensemble converges to CLE 4](https://closedform.nishachay.tech/e/openai-math-2026-226/) - Entry 226 · Loops from two overlaid random domino tilings of the half-plane converge, as curves, to nested CLE₄. (Claimed, not checked) - [The free uniform spanning forest is a factor of IID](https://closedform.nishachay.tech/e/openai-math-2026-231/) - Entry 231 · One fixed rule builds the free uniform spanning forest from independent random labels on every infinite graph. (Formal proof listed) - [An infinite finitely presented simple amenable group](https://closedform.nishachay.tech/e/openai-math-2026-253/) - Entry 253 · One infinite group that is simple, amenable and described by finitely many rules at once. (Formal proof listed) - [Classical capacity of generalized amplitude damping](https://closedform.nishachay.tech/e/openai-math-2026-276/) - Entry 276 · Proves an exact formula for the classical capacity of every generalized amplitude-damping qubit channel. (Formal proof listed) - [The optimal quartic separation between randomized and quantum queries](https://closedform.nishachay.tech/e/openai-math-2026-284/) - Entry 284 · Claims functions where randomized queries need nearly the fourth power of quantum queries, refuting a cubic conjecture. (Claimed, not checked) - [The Kirchberg–Rørdam character criterion and infinite tensor-power Jiang–Su stability](https://closedform.nishachay.tech/e/openai-math-2026-299/) - Entry 299 · Proves a separable C*-algebra absorbs the Jiang–Su algebra exactly when its central-sequence algebra has no characters. (Formal proof listed) - [Trace cones and Razak–Jacelon stabilization](https://closedform.nishachay.tech/e/openai-math-2026-301/) - Entry 301 · Claims the trace cone determines every separable nuclear C*-algebra once stabilized by the Razak–Jacelon algebra. (Formal proof listed) - [Markov type characterizes superreflexivity](https://closedform.nishachay.tech/e/openai-math-2026-327/) - Entry 327 · Proves that a Banach space with nontrivial Markov type is superreflexive, answering a question of Naor. (Formal proof listed) - [Reflexive midpoint convexity and diamond distortion](https://closedform.nishachay.tech/e/openai-math-2026-331/) - Entry 331 · Proves a reflexive Banach space can be midpoint convex far out yet admit no asymptotically uniformly convex norm. (Formal proof listed) - [Gigli’s characterization of Alexandrov curvature](https://closedform.nishachay.tech/e/openai-math-2026-356/) - Entry 356 · Claims Gigli's conjecture: Alexandrov curvature bounds match RCD spaces with a distributional sectional curvature bound. (Formal proof listed) - [A three-manifold without conjugate points or nonpositive curvature](https://closedform.nishachay.tech/e/openai-math-2026-358/) - Entry 358 · Proves that a closed three-manifold can carry a metric without conjugate points yet no metric of nonpositive curvature. 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