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

NeuralCert: certified computational discovery of extremal mathematical constructions

NeuralCert presents a framework that learns high‑dimensional variational trial functions in a compact separable form, then spectrally diagnoses, prunes, and exactly certifies them via multimodular evaluation. The method is fully explicit and independently verifiable, and can run on a standard personal computer. Applied to three extremal problems, it demonstrates that neural optimization can discover better constructions, reveal empirical invariants useful for proofs, and expose optimization barriers that inspire new analytic or numerical approaches.

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.

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.

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.