AI for Science
permanent hub

This is the permanent hub tracking how AI is attacking open problems in mathematics, physics and biology. It collects the deep dives and the state of each field. Last updated: October 3, 2026.

Math: proofs and counterexamples

Result	When	Who
Unit distance conjecture disproved (~80 years)	May 2026	OpenAI internal model
Ten open problems resolved or advanced (with Lean proofs)	Aug 2026	Internal Astra
Zeta-zeros lower bound raised 41.6% → 67.2%	Aug 2026	Anthropic (unreleased Claude)
Fermat's Last Theorem fully formalized	Sep 2026	Anthropic (~13M lines of Lean)
AI-generated proof of the Navier–Stokes problem	Sep 2026	OpenAI internal system (~10,000 agents)

For Navier–Stokes, correctness is broadly accepted because the Lean code compiles, but a later paper showed the method cannot reach the unforced problem, so the debate over meaning continues.

OpenAI shifts toward "responsible release" of AI mathematics (October 2026)Verified

OpenAI publicly released a broad range of mathematical results from an internal frontier model. Where earlier releases drew criticism for leading with a press release, this one publishes to a GitHub repository with protocols for revisions and citations. Many proofs are formalized in Lean, and the company published ten reasoning summaries, compute estimates in terms of ChatGPT Pro usage, and statistics on attempted problems — with the average result using roughly three hours of ChatGPT Pro thinking. Source: OpenAI

The move follows advice from the independent Advisory Group on Mathematics and AI (AGMAI) at IAS. In recommendations dated September 29, 2026, AGMAI set out norms for releasing AI-generated mathematics that no human yet understands: (1) scour and cite the literature; (2) rewrite proofs in conventional paper style; (3) disclose the model, prompts, a summarized chain of thought, time and compute cost; (4) formalize where possible; (5) when releasing many results at once, state how many comparable problems were tried and failed, and how problems were chosen — plus funding for human-understanding activities such as conferences and expositions. Source: AGMAI

AIfrontier view This is a concrete response to the math community's criticism. The demand to publish failed attempts is especially notable, as it counters success-only publicity. OpenAI says it will fund workshops and conferences too.

Physics: simplification and exact solutions

• Gluon scattering amplitudes (Feb): a configuration textbooks treat as zero is shown to be nonzero in a special kinematic regime. GPT-5.2 Pro simplified the expressions and conjectured a formula for all n; an internal model proved it.
• Gravitational waves from cosmic strings (Mar): Gemini Deep Think plus tree search derived exact analytical solutions for arbitrary loop geometries.
• Potts model (2025): the 1D frustrated Potts model exactly solved with o3-mini-high.

Biology and chemistry: design and validation

• Claude protein binder design (Aug): 14 of 15 targets; hit rates 22.6–35.1% versus 10–15% typical. Outside labs synthesized and tested the designs.
• Google Co-Scientist (May, Nature): generates, debates and refines hypotheses, with wet-lab validation in AML drug repurposing, liver fibrosis and antimicrobial resistance.
• Around the edges: OpenAI's GPT-Rosalind, models trained on pharma's private data, and Arc Institute's Virtual Cell Challenge.

Pushback: the math community

On September 11, 2026, 28 Fields Medalists published "A Severe Misalignment of AI in Mathematics," warning that "solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight," and citing rushed announcements and attribution concerns. OpenAI set up an independent mathematics advisory group on September 21, but it will not advise on how OpenAI paces its internal progress. Anthropic CEO Dario Amodei's essay "We Must Pace the Frontier" argues for slowing the rate of capability improvement itself.

Deep dives

Sources

• 本特集「AI for science特集」 https://aifrontier.co.jp/ai-news/ai-for-science-open-problems-2026-10-01.html
• OpenAI「Ten advances in mathematics」 https://openai.com/index/ten-advances-in-mathematics/
• OpenAI「On the Navier–Stokes Millennium Prize Problem」 https://openai.com/index/navier-stokes-solution/
• Anthropic「Riemann zeta」 https://www.anthropic.com/research/riemann-zeta
• Anthropic「Claude accelerates protein design」 https://www.anthropic.com/research/Claude-accelerates-protein-design
• Nature「Co-Scientist」 https://www.nature.com/articles/s41586-026-10644-y
• フィールズ賞受賞者声明 https://mathandai.org/
• darioamodei.com「We Must Pace the Frontier」 https://darioamodei.com/post/we-must-pace-the-frontier