Why are mathematicians concerned about OpenAI’s AI solving problems that stumped researchers for years?

OpenAI has released more than 700 AI-generated mathematical research papers, raising hopes that artificial intelligence could accelerate scientific discovery while prompting concerns about the reliability of its findings and the future of mathematical research.

On 6 October, the company published 722 preprints covering 372 groups of mathematical results across fields including algebra, geometry, number theory and mathematical logic.

However, the release quickly drew scrutiny after researchers identified errors in some of the papers.

The announcement follows another claimed breakthrough in September, when OpenAI said an unreleased model had produced a proposed solution to the Navier-Stokes problem, an unresolved mathematical challenge dating back nearly 90 years.

The problem concerns whether equations describing fluid motion always produce well-behaved solutions. It is one of seven Millennium Prize Problems, each carrying a $1 million prize.

OpenAI said its model took about 88 hours to develop the solution, followed by 17 hours of formalisation and verification.

How did OpenAI's AI model solve hundreds of maths problems?

OpenAI used an internal AI model to tackle thousands of mathematical questions, producing papers that present results across several branches of mathematics.

The company also released formal versions of many proofs using Lean, a programming language and proof assistant that allows mathematical arguments to be checked for logical correctness.

However, formal verification does not remove the need for independent mathematicians to assess the findings, their assumptions and their significance.

Are all of OpenAI's mathematical discoveries verified?

No. The papers remain subject to independent scrutiny, and the initial release was followed by corrections and withdrawals.

According to Retraction Watch, OpenAI withdrew three preprints on October 7 after identifying a sign error that invalidated an argument in one paper and affected two related papers. The company also revised 14 other manuscripts to address problems with proofs, statements, hypotheses and citations.

Why are mathematicians concerned about AI solving maths problems?

One concern is the sheer volume of research being released. Reviewing hundreds of papers takes time, and researchers may struggle to verify the findings before the work attracts wider attention.

Mathematicians have also questioned whether AI-generated solutions provide enough clarity for others to understand the reasoning and build on the results.

As Nature reported, the scale of OpenAI's release prompted criticism within the mathematical community.

Another concern is that mathematics involves more than finding answers. Working through difficult problems can produce new techniques, reveal connections between different fields and inspire further questions.

Can AI replace mathematicians in the future?

AI could become a powerful research assistant, helping mathematicians test conjectures, explore possible proofs and tackle problems that would otherwise require substantial time and effort.

Human expertise is likely to remain important in evaluating discoveries.

OpenAI has also announced support for workshops, conferences and other programmes to help researchers examine its findings.