# Open problems from the 1990s

> 55 AI-made results on questions first raised the 1990s, each explained in plain English. Results on questions first raised the 1990s, going by the…

Canonical: https://closedform.nishachay.tech/open-since/1990s/
Last updated: 2026-10-14

Results on questions first raised the 1990s, going by the earliest step each entry records.

55 AI-made results on questions first raised the 1990s, from 97 papers in the OpenAI math collection, each explained in plain English. 30 have a formal Lean proof listed; 25 are claimed in a paper and not yet machine-checked. They span 15 fields, led by theoretical computer science (7), combinatorics (6) and probability and statistical mechanics (6). The oldest question here dates back to 1990: [The Deligne–Drinfeld conjecture](https://closedform.nishachay.tech/e/openai-math-2026-008/). Results rated Landmark include [Modularity of elliptic curves over imaginary quadratic fields](https://closedform.nishachay.tech/e/openai-math-2026-030/) and [Local smoothing in three dimensions](https://closedform.nishachay.tech/e/openai-math-2026-079/).

## Results (55)

- [The Deligne–Drinfeld conjecture](https://closedform.nishachay.tech/e/openai-math-2026-008/) - Entry 008 · A short list of braid equations has exactly the solutions Deligne and Drinfeld predicted, in every size. (Formal proof listed)
- [Function-field reconstruction from Milnor K-theory and Galois data](https://closedform.nishachay.tech/e/openai-math-2026-009/) - Entry 009 · A field of functions can be rebuilt from its multiplication, blurred by powers, plus one trace of addition. (Formal proof listed)
- [Unrestricted pro-modularity at the prime two](https://closedform.nishachay.tech/e/openai-math-2026-010/) - Entry 010 · Odd two-dimensional 2-adic Galois representations are claimed to come from modular forms, with no condition mod 2. (Claimed, not checked)
- [Modularity of elliptic curves over imaginary quadratic fields](https://closedform.nishachay.tech/e/openai-math-2026-030/) - Entry 030 · Every elliptic curve over every imaginary quadratic field is claimed to match an automorphic form, place by place. (Claimed, not checked)
- [Projective contact classification and the LeBrun–Salamon conjecture](https://closedform.nishachay.tech/e/openai-math-2026-062/) - Entry 062 · Contact Fano manifolds are homogeneous, which settles the LeBrun–Salamon conjecture on quaternionic-Kähler spaces. (Claimed, not checked)
- [Virasoro constraints for complete intersections and projective-bundle towers](https://closedform.nishachay.tech/e/openai-math-2026-065/) - Entry 065 · Claimed proofs that curve counts on complete intersections and on projective bundles obey the Virasoro equations. (Claimed, not checked)
- [Bounded klt complements for Fano contractions](https://closedform.nishachay.tech/e/openai-math-2026-066/) - Entry 066 · One complement index, fixed by dimension and singularity bound, works for every mildly singular Fano contraction. (Formal proof listed)
- [The Campana–Peternell conjecture in dimension six](https://closedform.nishachay.tech/e/openai-math-2026-067/) - Entry 067 · A claimed proof that every six-dimensional Fano manifold with nef tangent bundle is a symmetric, homogeneous space. (Claimed, not checked)
- [Anticanonical nonvanishing in every dimension](https://closedform.nishachay.tech/e/openai-math-2026-068/) - Entry 068 · A claimed proof that a smooth nonnegatively curved anticanonical bundle always has a section of some power. (Claimed, not checked)
- [Local smoothing in three dimensions](https://closedform.nishachay.tech/e/openai-math-2026-079/) - Entry 079 · A claimed proof of Sogge's local smoothing conjecture for waves in 3D space, including the critical case p = 3. (Claimed, not checked)
- [Riesz transforms and rectifiability in higher codimension](https://closedform.nishachay.tech/e/openai-math-2026-081/) - Entry 081 · A bounded Riesz transform forces surfaces in higher codimension to contain big flat-like pieces. (Formal proof listed)
- [An L 3 bound for the trilinear Hilbert transform](https://closedform.nishachay.tech/e/openai-math-2026-086/) - Entry 086 · A singular average of three shifted functions obeys an L³ × L³ × L³ to L¹ size bound, the paper claims. (Claimed, not checked)
- [Quasipolynomial algorithms for mean-payoff, stochastic and parity games](https://closedform.nishachay.tech/e/openai-math-2026-104/) - Entry 104 · Who wins a mean-payoff game can be found in quasipolynomial time, however large the scores. (Formal proof listed)
- [Bin packing and unbounded configuration-LP gaps](https://closedform.nishachay.tech/e/openai-math-2026-118/) - Entry 118 · Rounding up the fractional bin count can be wrong by any fixed number of bins. (Formal proof listed)
- [Exponential semidefinite complexity of perfect matching](https://closedform.nishachay.tech/e/openai-math-2026-126/) - Entry 126 · Exact semidefinite descriptions of perfect matching need exponential size, a new paper claims. (Formal proof listed)
- [Average sensitivity of polynomial threshold functions](https://closedform.nishachay.tech/e/openai-math-2026-127/) - Entry 127 · Yes-or-no rules built from degree-d polynomials on n inputs have average sensitivity at most 8d√n. (Formal proof listed)
- [Rapid mixing of graph switches for every degree sequence](https://closedform.nishachay.tech/e/openai-math-2026-131/) - Entry 131 · Random rewiring reaches a fair random network quickly, for every possible list of degrees. (Formal proof listed)
- [A superquadratic separation of sensitivity and block sensitivity](https://closedform.nishachay.tech/e/openai-math-2026-132/) - Entry 132 · Block sensitivity can outgrow any constant times sensitivity squared. (Formal proof listed)
- [Homogeneous depth-five lower bounds for iterated matrix multiplication](https://closedform.nishachay.tech/e/openai-math-2026-135/) - Entry 135 · Five-layer recipes for multiplying n matrices need n to a power that grows like √n. (Formal proof listed)
- [Pointwise multiple ergodic averages for mixing transformations](https://closedform.nishachay.tech/e/openai-math-2026-154/) - Entry 154 · For mixing systems, averages along k, 2k, …, nk are claimed to settle at almost every starting point, for every n. (Claimed, not checked)
- [A counterexample to periodic tiling in dimension three](https://closedform.nishachay.tech/e/openai-math-2026-155/) - Entry 155 · Proves a finite tile in three dimensions can tile space, yet never in a fully repeating pattern. (Formal proof listed)
- [Borsuk's conjecture fails in dimension nine](https://closedform.nishachay.tech/e/openai-math-2026-156/) - Entry 156 · A set in nine-dimensional space cannot be cut into ten smaller pieces, so Borsuk's conjecture fails there. (Formal proof listed)
- [Counterexamples to Sidorenko’s conjecture and the forcing conjecture](https://closedform.nishachay.tech/e/openai-math-2026-161/) - Entry 161 · A 35-vertex bipartite pattern appears less often in some graph than random would predict. (Formal proof listed)
- [Combinatorial invariance of Kazhdan–Lusztig polynomials](https://closedform.nishachay.tech/e/openai-math-2026-168/) - Entry 168 · Proves a Kazhdan–Lusztig polynomial depends only on the shape of its Bruhat interval, settling combinatorial invariance. (Formal proof listed)
- [Shareshian–Wachs elementary positivity](https://closedform.nishachay.tech/e/openai-math-2026-169/) - Entry 169 · A coloring count with an extra q-weight always splits into elementary pieces with nonnegative coefficients. (Formal proof listed)
- [Seymour’s second-neighborhood conjecture](https://closedform.nishachay.tech/e/openai-math-2026-173/) - Entry 173 · In every network of one-way arrows, some point reaches at least as many points in two steps as in one. (Formal proof listed)
- [Eisenbud–Green–Harris and lex-plus-powers](https://closedform.nishachay.tech/e/openai-math-2026-200/) - Entry 200 · Two papers claim the Eisenbud–Green–Harris and lex-plus-powers conjectures over every field of characteristic zero. (Claimed, not checked)
- [Critical percolation on every quasi-transitive graph](https://closedform.nishachay.tech/e/openai-math-2026-213/) - Entry 213 · At the exact tipping point, random networks of a broad, symmetric kind form no endless cluster. (Formal proof listed)
- [The Benjamini–Schramm nonuniqueness conjecture](https://closedform.nishachay.tech/e/openai-math-2026-214/) - Entry 214 · Percolation on every fast-spreading symmetric graph has a range with infinitely many endless clusters. (Formal proof listed)
- [The low-temperature Sherrington–Kirkpatrick fluctuation law](https://closedform.nishachay.tech/e/openai-math-2026-217/) - Entry 217 · The typical spread of the low-temperature Sherrington–Kirkpatrick free energy grows like n^(1/6), with a limiting law. (Claimed, not checked)
- [GOE bulk universality for regular graphs with weak Anderson disorder](https://closedform.nishachay.tech/e/openai-math-2026-219/) - Entry 219 · Eigenvalue spacings of random regular graphs, even with weak random potentials, match those of Gaussian random matrices. (Claimed, not checked)
- [Critical and quenched near-critical universality for Poisson–Voronoi percolation](https://closedform.nishachay.tech/e/openai-math-2026-224/) - Entry 224 · Cardy's formula holds for Poisson–Voronoi percolation, and near-critical thresholds match the triangular lattice. (Claimed, not checked)
- [Limiting random SAT thresholds, sharp variance and computability](https://closedform.nishachay.tech/e/openai-math-2026-235/) - Entry 235 · Random k-SAT has a single limiting satisfiability threshold for every k ≥ 3, and the 3-SAT one is computable. (Formal proof listed)
- [Separating choiceless counting from polynomial time and witnessed choice](https://closedform.nishachay.tech/e/openai-math-2026-243/) - Entry 243 · Claims a polynomial-time query that choiceless polynomial time with counting cannot express. (Formal proof listed)
- [Weak normalization implies strong normalization in pure type systems](https://closedform.nishachay.tech/e/openai-math-2026-245/) - Entry 245 · Claims that in every pure type system, if every legal term can finish computing, then every way of computing finishes. (Formal proof listed)
- [Cannon's conjecture](https://closedform.nishachay.tech/e/openai-math-2026-246/) - Entry 246 · A hyperbolic group whose boundary is a sphere acts geometrically on hyperbolic three-space. (Formal proof listed)
- [Gersten’s conjecture and virtual compact specialness of one-relator groups](https://closedform.nishachay.tech/e/openai-math-2026-258/) - Entry 258 · Claims one-relator groups without Baumslag–Solitar subgroups are hyperbolic and virtually compact special. (Claimed, not checked)
- [A group without fixed price](https://closedform.nishachay.tech/e/openai-math-2026-259/) - Entry 259 · Claims a finitely generated group with two free measure-preserving actions of different costs, so fixed price fails. (Claimed, not checked)
- [Exactly three mutually unbiased bases in dimension six](https://closedform.nishachay.tech/e/openai-math-2026-266/) - Entry 266 · Dimension six fits only three mutually unbiased bases, by a computer-assisted search. (Formal proof listed)
- [Threshold and positive-energy bound states of the BFSS matrix model](https://closedform.nishachay.tech/e/openai-math-2026-270/) - Entry 270 · Claims the BFSS matrix model has one zero-energy bound state for every N, and many positive-energy states at N = 2. (Claimed, not checked)
- [Parity is not in QAC 0](https://closedform.nishachay.tech/e/openai-math-2026-274/) - Entry 274 · Proves constant-depth quantum circuits with polynomially many qubits cannot compute parity, settling Moore's conjecture. (Formal proof listed)
- [Threshold repetition for entangled games](https://closedform.nishachay.tech/e/openai-math-2026-277/) - Entry 277 · Proves that winning well above the entangled value in many repeated two-player games is exponentially unlikely. (Formal proof listed)
- [Exact quantum factoring over a fixed finite gate set](https://closedform.nishachay.tech/e/openai-math-2026-279/) - Entry 279 · Proves polynomial-size quantum circuits over a fixed gate set factor every integer with probability exactly one. (Formal proof listed)
- [Cuntz comparison, nuclear dimension, and equivariant Jiang–Su stability](https://closedform.nishachay.tech/e/openai-math-2026-291/) - Entry 291 · Claims amenable actions on Jiang–Su-stable algebras absorb the Jiang–Su algebra, plus three regularity theorems. (Formal proof listed)
- [Two notions of free entropy differ even when both are finite](https://closedform.nishachay.tech/e/openai-math-2026-298/) - Entry 298 · Proves two standard notions of free entropy can differ by at least 1/2 even when both are finite. (Formal proof listed)
- [The purely cosmetic surgery conjecture](https://closedform.nishachay.tech/e/openai-math-2026-306/) - Entry 306 · Claims that two different surgeries on a nontrivial knot never give the same oriented three-dimensional space. (Claimed, not checked)
- [Failure of rational injectivity for maximal coarse assembly](https://closedform.nishachay.tech/e/openai-math-2026-307/) - Entry 307 · Graph families where coarse assembly forgets a class of infinite order; Lean checks the reduced version. (Formal proof listed)
- [The Hovey–Strickland and Chai conjectures](https://closedform.nishachay.tech/e/openai-math-2026-311/) - Entry 311 · Claims Chai's invariant-ideal conjecture at every prime and height, and with it the Hovey–Strickland classification. (Claimed, not checked)
- [Finite generation for the K(n)-local sphere](https://closedform.nishachay.tech/e/openai-math-2026-313/) - Entry 313 · Claims every homotopy group of the K(n)-local sphere is finitely generated over the p-adic integers. (Claimed, not checked)
- [Chromatic splitting: filtrations and counterexamples](https://closedform.nishachay.tech/e/openai-math-2026-318/) - Entry 318 · Five papers claim Hopkins' chromatic splitting conjecture fails in its strong and weak forms, and offer a filtered fix. (Claimed, not checked)
- [Metric Markov cotype of ℓ 1 and Hilbert-space Lipschitz extension](https://closedform.nishachay.tech/e/openai-math-2026-332/) - Entry 332 · Claims to prove that ℓ1 has metric Markov cotype two, settling Ball's extension problem for maps into ℓ1. (Claimed, not checked)
- [The Solomon–Yau least-volume conjecture](https://closedform.nishachay.tech/e/openai-math-2026-349/) - Entry 349 · Claims the Solomon–Yau conjecture: after the equator, the next minimal hypersurface of a sphere is a Clifford product. (Claimed, not checked)
- [Scalar curvature and finite-time Ricci-flow singularities](https://closedform.nishachay.tech/e/openai-math-2026-351/) - Entry 351 · Claims four-dimensional Ricci flow continues while scalar curvature is bounded, but not in some high dimension. (Claimed, not checked)
- [Unique tangent flows at the first surface singularity](https://closedform.nishachay.tech/e/openai-math-2026-355/) - Entry 355 · Claims that blow-up limits of surface mean curvature flow are unique at the first singular time, in fixed coordinates. (Claimed, not checked)
- [Bi-Lipschitz coordinates at every regular RCD point](https://closedform.nishachay.tech/e/openai-math-2026-357/) - Entry 357 · Claims bi-Lipschitz coordinate charts around every regular point of a noncollapsed RCD space. (Claimed, not checked)

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