In early October, the artificial-intelligence firm OpenAI posted more than 700 AI-generated mathematical manuscripts on an online public repository. The arguments — if found to be correct after verification — contain an extraordinary trove of new mathematical knowledge. The reaction to these developments from the maths community has ranged from exhilaration to despair. Some researchers worry they have spent their lifetimes attempting to solve problems and their work might now suddenly seem meaningless. Others have expressed concern about the negative impact on young colleagues who are entering the field during a period of flux. And there’s been widespread anger at the manner in which AI companies are releasing such findings.
As one of the authors of the Leiden Declaration on Artificial Intelligence and Mathematics, which was published in June, I think some of the field’s concerns over OpenAI’s approach to announcing its discoveries could have been anticipated. In our declaration, we did not oppose the use of AI but put forwards several practical safeguards. These included the need for clear citation policies, precise disclosures on how AI is used and a renewed commitment to the long-standing expectation that all arguments made in a maths proof should be independently verifiable and answerable by a human author. Some AI companies have agreed to follow the declaration. OpenAI has not.
Mathematicians are developing rules for AI use — other fields should follow
Now that mathematicians have started analysing the AI-assisted proofs, it’s clear that many of the 700 preprints are presented in a sloppy, rough-and-ready style, making them hard to understand. The inner workings of OpenAI’s closed models are unknown, and there is also no human author named who might take responsibility for explaining or correcting the content if flaws emerge. It will take mathematicians a lot of time and effort to check the work in the preprints and rewrite it in a professional format that is suitable for judgement by peer reviewers. Unsurprisingly, many mathematicians are unenthusiastic about clearing up OpenAI’s mess, however exciting the underlying mathematics might be.
So, what does this mean for the future of mathematics? Creatively rethinking how the field must evolve will require action at every level. Outstanding leadership by individuals such as mathematician Terence Tao, and grassroots initiatives such as the Leiden declaration, need to be complemented with high-level engagement from stakeholder institutions such as the International Mathematical Union. It would be a disservice to the field if AI companies are allowed to set the norms on how to do mathematics without wide-ranging input from academics.
Can maths survive AI? Fields medallist Terence Tao calls for a ‘Maths 2.0’ world
