Swarms of agents spent weeks on the work. Human review started to fall behind.
In June 2025, an agent improved a math result that was 56 years old. In October 2026, one model published 719 manuscripts. A machine could check the work.
June 2025: AlphaEvolve
Google built an agent. The name of the agent is AlphaEvolve.
AlphaEvolve uses a large language model to change code. An automatic check scores each change. The agent keeps the best changes. Then the agent repeats the loop.
AlphaEvolve found a way to multiply two 4×4 complex matrices. The method uses 48 scalar multiplications. No one had improved Strassen’s method for this case in 56 years.
The same agent worked on systems that already run at Google.
- It found a better way to schedule work in data centers.
- It found a simpler circuit for a hardware accelerator.
- It reduced the time to train its language model.
October 2026: 719 manuscripts
On 6 October 2026, OpenAI published results on open problems in mathematics. An internal model produced the results. OpenAI has not released that model.
The manuscripts are in a GitHub repository. The catalogue holds 719 manuscripts. Those manuscripts form 372 families. OpenAI gave the model approximately 4,000 problems. The average result needed approximately 3 hours of compute on ChatGPT Pro.
OpenAI also shares Lean proofs for many results. Lean is a language. A computer can use Lean to check a proof. Today, approximately 42% of the main results have a Lean proof. OpenAI says that some other results can contain errors. OpenAI says that it will correct those errors quickly.
The Institute for Advanced Study has an Advisory Group on Mathematics and AI. OpenAI asked that group for advice. OpenAI used the advice to decide how to share the results.
Will Depue’s list
Will Depue showed this list. He is the reference. It is Fable 5.1’s ranking of discoveries from the last 3 years. The list has 100 lines. He marked each line with one color.
| Source | Meaning |
|---|---|
| People | A person found the result. |
| AI before 6 Oct | An AI found the result before 6 October 2026. |
| OpenAI repository | An AI found the result. It is in the OpenAI math repository. |
He writes that 59% of the list has a release date of that day. He also writes that 87% came from AI and 13% came from people. The table shows the first few lines. Scroll to read the rest. The ranks come from the model. They are not a checked list from mathematicians.
| Rank | Source | Result |
|---|---|---|
| 1 | AI before 6 Oct | Finite-time blowup for 3D incompressible Navier–Stokes with smooth forcing (Clay statements C/D), OpenAI internal multi-agent model, Lean-formalized, 2026 |
| 2 | OpenAI repository | Rational Hodge conjecture for CM abelian varieties, implying the Tate conjecture for abelian varieties over finite fields and the Hodge standard conjecture, openai/math family 032, 2026 |
| 3 | OpenAI repository | Quasi-Riemann hypothesis: all Dirichlet L-functions zero-free in Re s > 7/8, no Landau–Siegel zeros, openai/math family 003, 2026 |
| 4 | People | Geometric Langlands conjecture (de Rham, unramified), Gaitsgory, Raskin, Arinkin, Beraldo, Campbell, Chen, Faergeman, Lin, Rozenblyum, 2024 |
| 5 | OpenAI repository | Unique Games Conjecture and optimal approximation thresholds, openai/math family 102, 2026 |
| 6 | OpenAI repository | Hilbert's tenth problem over Q is undecidable, openai/math family 004, 2026 |
| 7 | OpenAI repository | Log abundance conjecture in characteristic zero and effective Iitaka fibrations, openai/math family 034, 2026 |
| 8 | OpenAI repository | Zilber–Pink conjecture for abelian varieties over Q̄ and for curves in A₂, openai/math family 016, 2026 |
| 9 | OpenAI repository | Erdős's reciprocal-sum (Erdős–Turán) conjecture on arithmetic progressions, with quasipolynomial Szemerédi bounds, openai/math family 159, 2026 |
| 10 | OpenAI repository | The irrationality exponent of π is exactly 2, openai/math family 017, 2026 |
| 11 | People | Kakeya set conjecture in R³, Wang, Zahl, 2025 |
| 12 | OpenAI repository | Kakeya maximal conjecture in R³ and Hausdorff conjecture in R⁴, openai/math family 074, 2026 |
| 13 | People | Hilbert's sixth problem: derivation of the Boltzmann equation from hard-sphere dynamics, Deng, Hani, Ma, 2025 |
| 14 | AI before 6 Oct | Jacobian conjecture is false in dimension ≥ 3 (explicit counterexample), Alpöge with Claude Fable 5 (Anthropic), 2026 |
| 15 | OpenAI repository | Matrix multiplication exponent ω ≤ 9/4, openai/math family 107, 2026 |
| 16 | OpenAI repository | Modularity of all elliptic curves over imaginary quadratic fields, openai/math family 030, 2026 |
| 17 | OpenAI repository | Artin's primitive root conjecture: infinitely many primes for every admissible base, openai/math family 029, 2026 |
| 18 | OpenAI repository | Full BSD formula and finiteness of Sha for elliptic curves of Selmer corank ≤ 1, openai/math family 002, 2026 |
| 19 | OpenAI repository | Fontaine–Mazur conjecture at the prime 2 (odd, regular, two-dimensional), openai/math family 010, 2026 |
| 20 | People | Large value estimates for Dirichlet polynomials, first zero-density improvement over Ingham since 1940, Guth, Maynard, 2024 |
| 21 | AI before 6 Oct | First non-sofic group (Gromov's question), OpenAI Astra, Lean-certified, 2026 |
| 22 | OpenAI repository | L = RL = BPL, openai/math family 103, 2026 |
| 23 | OpenAI repository | Kaplansky's zero-divisor conjecture disproved (with direct-finiteness and Gottschalk surjunctivity counterexamples), openai/math families 196 and 197, 2026 |
| 24 | OpenAI repository | Hilbert's sixteenth problem: uniform bound on limit cycles depending only on degree, openai/math family 143, 2026 |
| 25 | People | Bourgain's slicing conjecture and the KLS conjecture, Klartag, Lehec (building on Guan), 2024 |
| 26 | OpenAI repository | Counterexamples to coefficient-free Baum–Connes and Kadison–Kaplansky, openai/math family 285, 2026 |
| 27 | OpenAI repository | A torsion-free hyperbolic group that is not residually finite, openai/math family 252, 2026 |
| 28 | OpenAI repository | Thompson's group F is nonamenable, openai/math family 248, 2026 |
| 29 | OpenAI repository | Cannon's conjecture, openai/math family 246, 2026 |
| 30 | OpenAI repository | Free group factor isomorphism L(F₂) ≅ L(F₃), openai/math family 287, 2026 |
| 31 | OpenAI repository | Existence of minimal models and Mori fibre spaces for generalized log canonical pairs, openai/math family 036, 2026 |
| 32 | People | Marton's conjecture (polynomial Freiman–Ruzsa over F₂ⁿ), Gowers, Green, Manners, Tao, 2023 |
| 33 | People | Exponential improvement for diagonal Ramsey numbers, Campos, Griffiths, Morris, Sahasrabudhe, 2023 |
| 34 | OpenAI repository | Two-point Chowla conjecture and the binary corrected Elliott conjecture, openai/math family 007, 2026 |
| 35 | OpenAI repository | Falconer distance conjecture in every dimension, openai/math family 073, 2026 |
| 36 | OpenAI repository | Symmetric and nonsymmetric Mahler conjectures in every dimension, openai/math family 087, 2026 |
| 37 | AI before 6 Oct | Finite-time blowup for 3D Euler, 2D Boussinesq and IPM with smooth forcing, Buckmaster, Alpöge with Claude, Lean-verified, 2026 |
| 38 | OpenAI repository | Hadwiger's conjecture disproved (even fractionally), openai/math family 157, 2026 |
| 39 | People | McKay conjecture, Cabanes, Späth, 2024 |
| 40 | OpenAI repository | Anderson localization in 2D at all disorder and delocalization in 3D at weak disorder, openai/math family 261, 2026 |
| 41 | OpenAI repository | Hilbert–Smith conjecture in every dimension, openai/math family 304, 2026 |
| 42 | People | Modularity of abelian surfaces over Q, Boxer, Calegari, Gee, Pilloni, 2025 |
| 43 | OpenAI repository | Deligne–Drinfeld conjecture on the Grothendieck–Teichmüller Lie algebra, openai/math family 008, 2026 |
| 44 | OpenAI repository | Restricted geometric Langlands in positive characteristic and generic Ramanujan for exceptional groups over function fields, openai/math family 014, 2026 |
| 45 | AI before 6 Oct | Proportion of zeta zeros on the critical line raised from 41.6% to 67.2%, Anthropic (unreleased Claude), Lean-formalized, 2026 |
| 46 | OpenAI repository | Yau's uniformization conjecture, openai/math family 338, 2026 |
| 47 | OpenAI repository | Fujita's freeness conjecture at the sharp bound, openai/math family 038, 2026 |
| 48 | OpenAI repository | Bloch's conjecture for surfaces with p_g = 0, openai/math family 040, 2026 |
| 49 | People | Kervaire invariant one in dimension 126, Lin, Wang, Xu, 2024 |
| 50 | OpenAI repository | Spin-one Haldane gap, openai/math family 268, 2026 |
| 51 | OpenAI repository | Positive-temperature Bose–Einstein condensation for the 3D hard-sphere gas, openai/math family 267, 2026 |
| 52 | OpenAI repository | Log-Brunn–Minkowski inequality and the B-conjecture, openai/math family 091, 2026 |
| 53 | AI before 6 Oct | Erdős unit distance conjecture disproved (n^{1+δ} unit distances), OpenAI internal model, verified by Alon, Sawin and others, 2026 |
| 54 | OpenAI repository | Sidorenko's conjecture and the forcing conjecture disproved, openai/math family 161, 2026 |
| 55 | OpenAI repository | The plane cannot be 5-colored (chromatic number of the plane ≥ 6), openai/math family 158, 2026 |
| 56 | People | Hilbert's tenth problem undecidable over rings of integers of every number field, Koymans, Pagano, 2024; Alpöge, Bhargava, Ho, Shnidman, 2025 |
| 57 | OpenAI repository | Local p-adic section conjecture and the section conjecture for modular curves, openai/math family 019, 2026 |
| 58 | AI before 6 Oct | Connes rigidity conjecture disproved, OpenAI Astra, Lean-certified, 2026 |
| 59 | OpenAI repository | Integer multiplication in o(n log n) on a multitape Turing machine, openai/math family 109, 2026 |
| 60 | People | Kelley–Meka bound for sets without 3-term progressions, Kelley, Meka, 2023 |
| 61 | OpenAI repository | Shelah's eventual categoricity conjecture in ZFC, openai/math family 240, 2026 |
| 62 | OpenAI repository | LeBrun–Salamon conjecture and classification of contact Fano manifolds, openai/math family 062, 2026 |
| 63 | People | MNOP conjecture (GW/DT correspondence for Calabi–Yau threefolds), Pardon, 2023 |
| 64 | OpenAI repository | Nagata's conjecture and maximal Seshadri constants, openai/math family 039, 2026 |
| 65 | OpenAI repository | Goldfeld's conjecture for quadratic twists, openai/math family 006, 2026 |
| 66 | OpenAI repository | Sogge's local smoothing conjecture in three dimensions, openai/math family 079, 2026 |
| 67 | OpenAI repository | Three-dimensional Bochner–Riesz conjecture, openai/math family 078, 2026 |
| 68 | People | Furstenberg set conjecture in the plane, Ren, Wang, 2023 |
| 69 | OpenAI repository | De Giorgi's conjecture in dimension 8, openai/math family 375, 2026 |
| 70 | OpenAI repository | Global regularity for 3D relativistic Vlasov–Maxwell, openai/math family 362, 2026 |
| 71 | AI before 6 Oct | High-dimensional sphere packing upper bound improved (first since Kabatiansky–Levenshtein, 1978), OpenAI Astra, Lean-certified, 2026 |
| 72 | OpenAI repository | Purely cosmetic surgery conjecture, openai/math family 306, 2026 |
| 73 | People | Supercritical sharpness for percolation on all infinite transitive graphs, Diskin, Easo, Radhakrishnan, Sudakov, Tassion, 2026 |
| 74 | OpenAI repository | Benjamini–Schramm nonuniqueness conjecture p_c < p_u, openai/math family 214, 2026 |
| 75 | OpenAI repository | Kadison's similarity conjecture, openai/math family 288, 2026 |
| 76 | OpenAI repository | Dixmier's unitarizability problem for all discrete groups, openai/math family 251, 2026 |
| 77 | OpenAI repository | Rigidity of the Turing degrees, openai/math family 241, 2026 |
| 78 | People | Graham's rearrangement conjecture, Sauermann, Pham; Bedert; Kravitz; Müyesser, Pokrovskiy, 2026 |
| 79 | OpenAI repository | Catalan's constant is irrational, openai/math family 005, 2026 |
| 80 | OpenAI repository | Serre's positivity conjecture for intersection multiplicities, openai/math family 193, 2026 |
| 81 | OpenAI repository | Blockwise Alperin weight conjecture, openai/math family 202, 2026 |
| 82 | People | Komlós conjecture: discrepancy bound improved to (log N)^{1/4}, Bansal, Jiang, 2025 |
| 83 | People | Finite-time blowup for 3D Euler with C^{1,1/2−ε} forcing, Córdoba, Martínez-Zoroa, 2024 |
| 84 | OpenAI repository | Shafarevich holomorphic convexity conjecture disproved, openai/math family 046, 2026 |
| 85 | OpenAI repository | Periodic tiling conjecture fails in Z³, openai/math family 155, 2026 |
| 86 | AI before 6 Oct | Exponential threshold parallel repetition for entangled two-player games, OpenAI Astra, Lean-certified, 2026 |
| 87 | People | Unknotting number is not additive, Brittenham, Hermiller, 2025 |
| 88 | People | Aperiodic monotile ("hat" and "spectre"), Smith, Myers, Kaplan, Goodman-Strauss, 2023 |
| 89 | People | Lattice sphere packings of density ≳ n log n / 2ⁿ (beyond Rogers 1947), Klartag, 2025 |
| 90 | AI before 6 Oct | 4×4 complex matrix multiplication with 48 scalar multiplications (beating Strassen), AlphaEvolve, Google DeepMind, 2025 |
| 91 | People | Bunkbed conjecture disproved, Gladkov, Pak, Zimin, 2024 |
| 92 | People | Order of magnitude of r(4,t), Mattheus, Verstraete, 2023 |
| 93 | People | Moving sofa problem solved (Gerver's sofa is optimal), Baek, 2024 |
| 94 | People | ω < 2.371339, Alman, Duan, Vassilevska Williams, Xu, Xu, Zhou, 2024 |
| 95 | AI before 6 Oct | Hadamard matrices of order 668 and every open order up to 2000, Alpöge, Reynolds-Haertle, "tehwalris" with Claude (Anthropic), 2026 |
| 96 | AI before 6 Oct | Erdős problems #124, #1051, #728, #619, #146, #183 resolved, Harmonic Aristotle, DeepMind Aletheia, OpenAI GPT-5.2 and Astra, Anthropic Claude Fable 5, 2025–2026 |
| 97 | People | Pólya's eigenvalue conjecture for the disk, Filonov, Levitin, Polterovich, Sher, 2023 |
| 98 | AI before 6 Oct | New cap set lower bounds (dimension 8 and asymptotic), FunSearch, Google DeepMind, 2023 |
| 99 | People | BB(5) = 47,176,870 (Coq-verified), bbchallenge collaboration, 2024 |
| 100 | People | Elliptic curve over Q of rank ≥ 29, Elkies, Klagsbrun, 2024 |
One day holds most of a ranking of three years. That is the speed.
Who sees this
Andrej Karpathy describes who can see this work. He calls the gap a sharp funnel. The numbers below are his estimates.
| Who | Number of people | Share |
|---|---|---|
| People who almost never use a language model | 6 billion | ~75% |
| People who sometimes use a free chatbot | 1–2 billion | ~20% |
| People who use frontier models for math and code | 20 million | ~0.2% |
| People with access to the newest internal systems | 5,000 | ~0.00006% |
The public has seen a preview of the narrow end of that funnel. Karpathy says it looks like swarms of thousands of agents. The agents work together for weeks on very large software projects. They mint zero-days, which are software flaws no one has patched yet. They run cyber attacks and defenses at the speed of a machine. They discover new science. They advance the frontier of mathematics.
The impact grows with ambition, with the size of the problem, and with how long the work runs. The system is jagged. It is strong on some tasks and weak on others. A small sliver of professionals feels what he calls “the vertigo of the curve going vertical.” Meanwhile, human review and comprehension are starting to fall behind.
What changes next
A search for an answer becomes cheaper. The check becomes the hard part. OpenAI says that it will fund workshops and programs. The goal is to help people understand major results from AI.
A hard problem that needs weeks of work shows the difference. The gap between users will grow. A team that gives hard problems to agents will move faster. A team that uses a chatbot for small tasks will move more slowly.
Our view
If you develop AI agents, or if you want to build a business on AI, do not judge the potential from a simple question. Test what an agent can do on a large, real task.
One question
“What are the major causes of water pollution?”
The full path
- Find relevant public data on the environment.
- Download the data and clean it.
- Review the scientific literature.
- Develop hypotheses about pollution patterns.
- Write code to analyze the data.
- Run statistical tests.
- Generate visualizations.
- Compare the findings with existing research.
- Identify the limits and the uncertainty.
- Prepare a draft report for a human researcher to review.
The first column tests whether an AI can answer a question. The second column tests whether an agent can take part in a full research workflow.
A system that finishes these steps does not automatically make a valid discovery. A person must still check the data, the methods, the statistics, and the conclusions.
This difference matters. The value of an agent system may not come from a better single answer. It may come from doing more of the work that a real result needs.
Three practical lessons follow.
- Focus on hard problems. Look for tasks that need time, technical knowledge, or coordination. These are places where agents can add real value.
- Choose tasks where someone can check the result. Scientific analysis can use statistical tests, code that another person can run, independent data, and expert review.
- Build systems that finish a workflow, not only a conversation. An agent platform should collect information, run analysis, use tools, check the work, and produce a useful output. The more reliably it finishes these steps, the more valuable it can become.
Sources
- Will Depue, Fable 5.1 list on X, 6 October 2026
- Andrej Karpathy, post on X, 11 October 2026
- OpenAI, Sharing AI progress in mathematics, 6 October 2026
- OpenAI math repository
- Novikov et al., AlphaEvolve: A coding agent for scientific and algorithmic discovery, arXiv:2506.13131, June 2025