On the subject of AI: mathematics

In May 2026, OpenAI announced that its chatbot had solved an 80-year-old open problem in mathematics.

The news was particularly notable as the breakthrough came via on a single, open-ended prompt simply asking the AI to consider whether or not the geometry conjecture in question – first posed by the great Hungarian mathematician Paul Erdős – might or might not be true.

This was followed in July by ChatGPT disproving another decades-old conjecture, this time in graph theory. The result attracted attention not least due to the user giving the chatbot extremely rudimentary instructions (as can be seen here) such as “do a breakthrough” and “have a clear strategy from deeper understanding.” This was one among many discoveries which have been publicised over the last few months.

This has led to plenty of hyperbole in the press asking whether maths will be the “first academic profession to see its work taken over by AI” – but it has also caused leading voices in mathematics research, such as Terence Tao, to argue that the rapid progress of artificial intelligence is forcing a reckoning with fundamental questions in the discipline. Tao suggests that the mathematics community is currently at varying points on the “five stages of grief” spectrum, with denial beginning to fade away.

The most thorough response to the effect of AI on maths research so far has come in the form of the Leiden Declaration, a call for action developed collaboratively by mathematicians across the world which to date has attracted 3,600 signatories and endorsements from senior figures in the community.

The declaration begins by outlining the potential threats to research from the growing capability of artificial intelligence tools, and their proliferating use, in ways that will be familiar to other disciplines.

These include the risk that automated techniques can produce “plausible but unreliable (or even incorrect) arguments which are difficult to distinguish from correct mathematical proofs,” as well as disruption to established mechanisms for funding and professional recognition – especially where some researchers are unable or unwilling to use such tools.

Questions of authorship and the integrity of research loom large as well:

“Technologies that draw extensively on the published mathematical commons undermine the traditional system of attribution. Models trained on published works frequently return outputs that do not properly cite the human works they synthesize. Many current models are also built on data obtained by systematically exploiting licenses and access arrangements that were not made with artificial intelligence in mind, or indeed by simply violating copyright protections.”

The Leiden Declaration sees individual researchers asked to disclose tool use, put effort into proper attribution, participate in public discourse related to artificial intelligence-assisted methods and results, and be mindful of the benefits and drawbacks of different AI tools. Crucially, the declaration affirms that the “responsibility for correctness” must remain exclusively with human authors.

The declaration also has recommendations for mathematical organisations and research funders, including the need to insist on appropriate – peer-reviewed – publication platforms rather than press releases and blogposts.

The final section of the declaration tackles the relationship between academia and the commercial AI industry, arguing that the same standards should apply here as elsewhere. The authors warn:

“We recognize that industry has offered lucrative jobs, monetary rewards, computing resources, and intellectually stimulating opportunities that some mathematicians have found attractive. This has taken place in an era of underfunding of higher education and precarious academic employment. We also recognize that many mathematicians did not expect their work to become entangled with social and ethical implications of such magnitude, nor to be incorporated into systems used for purposes they may find deeply troubling.”

Earlier this month OpenAI said that it had “deep respect and understanding” for the signatories of the Leiden declaration and others concerned with the impact of AI on mathematics research.

Yet in the same statement the company unveiled ten new results from its latest models in a wide variety of mathematical fields, each of which “resolves or makes substantial progress on a long-standing open problem.”

“On the subject of AI” will be an ongoing series exploring how artificial intelligence is impacting on research in specific fields.

Look out for future instalments focused on other disciplines later in the autumn and beyond. If you have thoughts to share, please get in touch.