OpenAI’s Astra model solved ten problems, prompting debate among mathematicians over access costs and credit for ideas
OpenAI’s Astra model solved ten problems, prompting debate among mathematicians over access costs and credit for ideas
On 11 August, The Verge collected mathematicians’ reactions to ten results that OpenAI had announced on 1 August. The discussion covered the cost of access to closed models, attribution of ideas, and the training of future mathematicians.
On 1 August, OpenAI announced that an experimental version of its forthcoming Astra model had found solutions to ten longstanding problems. Researchers then used the same model to prepare manuscripts, and the model expressed each argument as a Lean certificate. Lean is a program that checks a recorded sequence of logical steps.
A certificate verifies the reasoning in a written proof. The origin of the idea and the contribution of earlier work must be established from the literature. In Terence Tao’s proposal on priority, formal verification is likewise only one part of the required record: a colleague must also receive the manuscript and a clear account of the reasoning. One of the ten results showed why this matters. Mathematician Gábor Kun told The Verge that the detailed paper relied on his work from 2016 and 2019, with the second paper coauthored by Andreas Thom. OpenAI later revised its original announcement to acknowledge this work.
OpenAI estimated that finding the ten solutions would cost about $2 000 at the current rates for access to the Sol model. Colva Roney-Dougal, a mathematician at the University of St Andrews, stated the concern as follows:
“It is unclear whether universities will be willing to pay that much for our theorems.”
In June, the International Mathematical Union endorsed the Leiden Declaration on AI and Mathematics. The declaration calls for researchers to disclose the use of such tools, cite prior work, and leave responsibility for the correctness of proofs with humans. The cost of access and the rules for attribution determine who can obtain, verify, and build on a result.
Oxford mathematician András Juhász connects this debate to the training of graduate students. Problems that large language models are beginning to solve often serve as exercises through which researchers learn how to think. In his view, universities will need to combine access to such systems with work that teaches future mathematicians how to formulate a question, assess another person’s idea, and develop it further.