GPT-5 and the future of mathematical discovery

Accelerating discovery with the AI for Math Initiative

The initiative brings together some of the world's most prestigious research institutions to pioneer the use of AI in mathematical research.

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.

Long-Horizon AI Research for Grothendieck Constant: A Case Study in Human-AI Mathematical Collaboration

AI agents are increasingly used in mathematics research, but it is often unclear how to use them effectively. Towards this, we present an extensive case study of how AI was used to improve bounds on the Grothendieck constant $K_G$, which captures the hardness between combinatorial problems and their continuous relaxations.

Long-Horizon AI Research for Grothendieck Constant: A Case Study in Human-AI Mathematical Collaboration

arXiv:2608. 11195v1 Announce Type: new Abstract: AI agents are increasingly used in mathematics research, but it is often unclear how to use them effectively.

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.

GPT-4o mini: advancing cost-efficient intelligence

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.

Introducing GPT-5

We are introducing GPT‑5, our best AI system yet. GPT‑5 is a significant leap in intelligence over all our previous models, featuring state-of-the-art performance across coding, math, writing, health, visual perception, and more.

Can AI Follow In Einstein's Footsteps?

AI is accelerating physics discovery, but perhaps away from Einstein-level theory building. To understand this gap, we must recognize a striking trend: while being very successful, the most visible AI contributions to physics discovery appear to mirror the historical development of physics, but in reverse.

Scientific discovery as meta-optimization: a combinatorial optimization case study

Scientific discovery is fundamentally an optimization problem, defined by a vast "state space" of theories and experiments, and an evaluation criterion based on quality, novelty, and validity. Large language models (LLMs) have enabled automated exploration of this space, but we argue that simultaneous modification of the evaluation criteria is equally important.

Structured Scaling of AI Discovery Across Diverse Scientific Domains

arXiv:2604. 19341v2 Announce Type: replace-cross Abstract: Scientific discovery often requires many cycles of proposing, testing, and refining candidate solutions.

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.