DeepMind Blog
Oct 24, 2025
Discovering new solutions to century-old problems in fluid dynamics
Our new method could help mathematicians leverage AI techniques to tackle long-standing challenges in mathematics, physics and engineering.
On the Navier–Stokes Millennium Prize Problem
OpenAI shares an AI-generated solution to the Navier–Stokes Millennium Prize Problem, providing both a writeup and a formal proof written in Lean.
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OpenAI Blog
Feb 2, 2022
Solving (some) formal math olympiad problems
We built a neural theorem prover for Lean that learned to solve a variety of challenging high-school olympiad problems, including problems from the AMC12 and AIME competitions, as well as two problems adapted from the IMO.
OpenAI Blog
Feb 20
Our First Proof submissions
We share our AI model’s proof attempts for the First Proof math challenge, testing research-grade reasoning on expert-level problems.
arXiv AI
Jun 17
First Proof Second Batch
arXiv:2606. 18119v1 Announce Type: new Abstract: To assess the ability of current AI systems to correctly solve research-level mathematics problems, we tested several AI systems on a set of ten problems in a broad range of mathematical fields; these problems arose naturally in the research process of the contributors.
Simon Willison
Sep 8
Some thoughts on the Navier–Stokes Millennium Prize Problem
On the Navier–Stokes Millennium Prize Problem introduces an impressive result from OpenAI, who used an unreleased model to produce a resolution to the Navier–Stokes existence and smoothness problem, o...
Simon Willison
Sep 8
On the Navier–Stokes Millennium Prize Problem
Simon Willison reports that OpenAI used an unreleased model to produce a claimed resolution to the Navier–Stokes existence and smoothness problem, one of the seven Millennium Prize Problems. The claim has been met with controversy, as NYU professor Tristan Buckmaster and mathematician Levent Alpöge—who had been working on related problems with Claude and Codex—accused OpenAI of using their unpublished work. OpenAI has denied accessing their data and has offered to wait for Buckmaster’s publication, but will not include Alpöge as a co‑author due to a competitive relationship with his employer.
arXiv AI
Sep 3
AI Mathematician: Towards Fully Automated Frontier Mathematical Research
The paper introduces the AI Mathematician (AIM) framework, which leverages Large Reasoning Models (LRMs) to tackle frontier mathematical research. AIM addresses the complexity and procedural rigor of research problems through an exploration mechanism for longer solution paths and a pessimistic reasonable verification method for reliability. Early experiments show AIM can autonomously construct significant proof components and uncover non‑trivial insights across real‑world mathematical topics.
arXiv AI
Jun 9
Advancing Mathematics Research with AI-Driven Formal Proof Search
arXiv:2605. 22763v2 Announce Type: replace Abstract: Large language models (LLMs) increasingly excel at mathematical reasoning, but their unreliability limits their utility in mathematics research.
arXiv AI
Jun 30
QED: An Open-Source Multi-Agent System for Generating Mathematical Proofs on Open Problems
arXiv:2604. 24021v4 Announce Type: replace Abstract: We present QED, an open-source multi-agent system that turns human-provided research questions into complete mathematical proofs without further human guidance.
arXiv AI
Aug 17
The Past and Future of AI Scientists
arXiv:2608. 14407v1 Announce Type: new Abstract: We present a survey of the past and future of AI Scientists: machines capable of automating science.
arXiv AI
Aug 25
What is mathematics now, and what should it be?
arXiv:2608.23218v1 Announce Type: new Abstract: Advances in neural theorem provers have been impressive, but the successes obscure a broader vision of what AI can do for mathematics and how mathemati...
arXiv Machine Learning
Jun 5
LeanMarathon: Toward Reliable AI Co-Mathematicians through Long-Horizon Lean Autoformalization
arXiv:2606. 05400v1 Announce Type: cross Abstract: Long-horizon autoformalization of research mathematics fails not only at hard lemmas, but at scale: statements drift, dependencies tangle, context decays, and local repairs corrupt distant work.