OpenAI Blog
Aug 1
Ten advances in mathematics and theoretical computer science
OpenAI shares new results on long-standing open problems in mathematics and theoretical computer science, including advances in geometry, cryptography, and complexity.
An OpenAI model has disproved a central conjecture in discrete geometry
An OpenAI model solved the 80-year-old unit distance problem, disproving a major conjecture in discrete geometry and marking a milestone in AI-driven mathematics.
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arXiv Computation and Language
Sep 23
FrontierMath Erd\H{o}s
arXiv:2609. 25050v1 Announce Type: new Abstract: We introduce FrontierMath Erd\H{o}s (FME), a benchmark of 68 Erd\H{o}s problems that are open as of August 2026.
OpenAI Blog
Sep 21
Advisory Group on Mathematics and Artificial Intelligence
OpenAI is collaborating with an independent Advisory Group on Mathematics and Artificial Intelligence. The group’s role is to guide the review and communication of emerging AI results. This partnership aims to ensure rigorous oversight and clear dissemination of new developments in AI.
OpenAI Blog
Dec 11, 2025
Advancing science and math with GPT-5.2
GPT-5. 2 is OpenAI’s strongest model yet for math and science, setting new state-of-the-art results on benchmarks like GPQA Diamond and FrontierMath.
arXiv Machine Learning
Sep 3
Towards Solving the Gilbert-Pollak Conjecture via Large Language Models
The paper announces a new lower bound of 0.8559 for the Steiner ratio, improving on the previous 0.824 bound for the Gilbert‑Pollak Conjecture. It introduces an AI system that uses large language models to generate rule‑constrained geometric lemmas, which are then turned into executable verification functions that certify the bound. The approach relies on only thousands of LLM calls, highlighting the feasibility of LLM‑based methods for advanced mathematical research.
OpenAI Blog
Dec 11, 2025
Ten years
OpenAI reflects on ten years of progress, from early research breakthroughs to widely used AI systems that reshaped what’s possible. We share lessons from the past decade and why we remain optimistic about building AGI that benefits all of humanity.
OpenAI Blog
Dec 23, 2022
The power of continuous learning
Lilian Weng works on Applied AI Research at OpenAI.
OpenAI Blog
Sep 12, 2024
OpenAI o1-mini
Advancing cost-efficient reasoning
arXiv AI
Aug 26
Autonomous Mathematical Discovery in an Open-World Multi-Agent Environment
The paper reports on autonomous mathematical discovery within the Station, an open‑world multi‑agent environment where diverse AI agents pursue shared research goals without central coordination. Across 12 construction problems and two case studies, the agents produced novel results—including a new infinite family of finite‑field Kakeya sets, 604‑point kissing configurations in dimension 11, improved records for discretized Kakeya needle and sign uncertainty problems, a stronger lower bound for Erdős’s minimum‑overlap problem, and new infinite families for Book Ramsey numbers—alongside theorems and analyses that explain the constructions. All agent dialogues, proofs, and verification code are released to provide a transparent record of the discovery process.
OpenAI Blog
Nov 20, 2025
Early experiments in accelerating science with GPT-5
OpenAI introduces the first research cases showing how GPT-5 accelerates scientific progress across math, physics, biology, and computer science. Explore how AI and researchers collaborate to generate proofs, uncover new insights, and reshape the pace of discovery.
OpenAI Blog
Jun 11, 2020
OpenAI API
We’re releasing an API for accessing new AI models developed by OpenAI.
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.