The rapid development of AI is of enormous public interest right now, with the possible existential risk to humanity being reported by mainstream news organisations. However, the discussion is often tempered with questions such as ‘haven’t we heard this before?’ or ‘isn’t this just hype from the AI companies or a desire to protect their interests?’. As discussed widely in this blog and elsewhere, we as mathematicians (perhaps more than other scientists) have a particularly close up view of the speed of development and many of us have concluded that we ought to be very worried. We should make this point loudly. 42 mathematician Fellows of the Royal Society have today written to the president of the society, Sir Paul Nurse, to put forward this view.
Mathematicians of all types are invited to support the letter, their names are displayed here. If you want to add your name, complete this form. The letter is reproduced below.
Dear Paul,
We, as mathematicians, write to express our extreme concern about the pace of development of AI and the implications of this for humanity and civilisation. None of us have any significant involvement with AI companies.1
In the last three months we have seen the leading models of OpenAI and Anthropic develop from around the level of a strong student to having solved multiple open questions at the forefront of research, including one of the seven Millennium Prize Problems. These models are now operating<sup>2</sup> at the level of the top human mathematicians in many parts of the subject and we must assume there is a significant chance of them developing superhuman abilities within a similarly short timeframe.
This has profound implications for mathematics, but highlighting that is not the purpose of our letter. It is highly likely that these systems are comparably strong in other technical domains such as (for example) cybersecurity, autonomous weapon control, development of biological and chemical agents and the targeted spread of misinformation. Moreover, we must assume that the rate of change of their capabilities will be similarly rapid in these areas.
We have all seen the concerns raised by former employees of the large AI companies, estimating the probability of human extinction to be as high as 10 per cent over the next decade. Our witnessing of the rise in capabilities of these models in our domain of expertise persuades us that such statements must not be dismissed as ‘hype’. By the time the situation becomes obvious to the wider public, it may be too late to act. We believe this is an emergency, and call on the Royal Society to use its influence to convey this view to government and the media.
- Most of us use AI tools and many of us have been provided access to the leading publicly available models for free. Some of us have informal and unpaid connections with mathematicians working at AI companies, resulting in early access to and subsequent free use of some of their models. ↩︎
- Whilst it is true that the leading AI companies employ top mathematicians, and we cannot be sure of the exact methodology behind the solution of the Navier-Stokes Millennium Problem, our remarks apply to the outputs of the leading publicly-available models such as ChatGPT6-Astra ↩︎
Signed by 42 Fellows and Foreign Members of the Royal Society:
Luis Fernando Alday
Martin Barlow
Emmanuel Breuillard
Tom Bridgeland
Mark Chaplain
Kevin Costello
Ingrid Daubechies
Marcus du Sautoy
Toby Gee
Mike Giles
Alain Goriely
Timothy Gowers
Ben Green
Geoffrey Grimmett
Mark Gross
Martin Hairer
Roger Heath-Brown
Dominic Joyce
Frank Kelly
Jens Marklof
Vladimir Marković
James Maynard
James McKernan
Jason Miller
Robert Morris
Jonathan Pila
Jeremy Quastel
Oscar Randal-Williams
Mary Rees
Richard Samworth
Peter Sarnak
Caroline Series
Peter Scholze
Gordon Slade
Ivan Smith
Endre Süli
Richard Thomas
Jack Thorne
Ulrike Tillmann
Burt Totaro
Claire Voisin
Wendelin Werner
Received 16 September 2026.