Solving (some) formal math olympiad problems

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.

What is mathematics now, and what should it be?

Advances in neural theorem provers have been impressive, but the successes obscure a broader vision of what AI can do for mathematics and how mathematicians can engage with AI. This essay advances a m...

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.

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...

GamePad: A learning environment for theorem proving

Achieving Olympiad-Level Geometry Large Language Model Agent via Complexity Boosting Reinforcement Learning

The paper introduces InternGeometry, a large language model agent that achieves medalist-level performance on International Mathematical Olympiad geometry problems. It overcomes traditional heuristic limitations by iteratively proposing and verifying auxiliary constructions with a symbolic engine, supported by a dynamic memory mechanism that allows over 200 interactions per problem. Using Complexity-Boosting Reinforcement Learning, InternGeometry trains on only 13,000 examples—0.004% of the data used by AlphaGeometry 2—and solves 44 of 50 IMO geometry problems, surpassing the average gold medalist score.

Advanced version of Gemini with Deep Think officially achieves gold-medal standard at the International Mathematical Olympiad

The International Mathematical Olympiad (“IMO”) is the world’s most prestigious competition for young mathematicians, and has been held annually since 1959. Each country taking part is represented by six elite, pre-university mathematicians who compete to solve six exceptionally difficult problems in algebra, combinatorics, geometry, and number theory.

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.

ComBench: A Benchmark for Rigorous Proof Reasoning and Constructive Realization in Olympiad-Level Combinatorics

arXiv:2606. 10479v1 Announce Type: new Abstract: Combinatorics is central to Olympiad-level mathematical problem solving, requiring deep discrete reasoning, creative constructions, and rigorous structural insight.

LEAP: Supercharging LLMs for Formal Mathematics with Agentic Frameworks

arXiv:2606. 03303v1 Announce Type: new Abstract: Large Language Models (LLMs) exhibit strong informal mathematical reasoning but struggle to generate mechanically verifiable proofs in formal languages like Lean.

SorryDB: Can AI Provers Complete Real-World Lean Theorems?

arXiv:2603. 02668v2 Announce Type: replace Abstract: We present SorryDB, a dynamically-updating benchmark of open Lean tasks drawn from 78 real world formalization projects on GitHub.

Formally Solving Answer-Construction Problems in Lean

arXiv:2505. 18492v5 Announce Type: replace Abstract: Mathematical competition problems fall into two broad types: theorem proving, which asks for a proof of a given statement, and answer construction, which requires constructing a property-satifying object with proofs.