MATHEMATICS, A.I., AND THE LEIDEN DECLARATION PART 2

YESTERDAY IN PART 1, WE FOCUSED ON OpenAI’s achievement in disproving a previous conjecture in combinatorial geometry. Today, we continue Siobhan Roberts’ analysis of the Leiden Declaration, a response by the mathematics community to the OpenAI result. 

Addressing This Significance via the Leiden Declaration. Siobhan Roberts cites Harvard mathematician Melanie Matchett Wood: “ ‘It is a powerful tool, and I think it will be a great tool to accelerate mathematics research,’ Dr. Matchett Wood said in an interview. But she noted that the community needs to figure out how to use A.I. ‘in a way that will maintain human understanding of the mathematics.’ ”

Roberts continues, “Among the potential threats that the Leiden Declaration authors articulate are accuracy and reliability: Journal editors are already complaining about a flood of plausible seeming A.I.-generated papers and proofs that have turned out to be incorrect, and in ways that are difficult for mathematicians to discern.”

There’s also the matter of A.I.’s incentivizing for profit versus academe’s goal of enhancing scholarship. Roberts describes, “For Rodrigo Ochigame, a historian and anthropologist of computing and artificial intelligence at Leiden University in the Netherlands, and one of the statement’s authors, the latest OpenAI proof illustrates why this sort of collective reckoning in the discipline is necessary. ‘The story follows the same pattern as many other announcements by commercial A.I. developers,’ Dr. Ochigame said. ‘The A.I. model is proprietary and unavailable to anyone outside the company. We get a flashy promotional video, while basic information needed to assess the scientific meaning of the result is kept secret. The company disclosed nothing about the methods, human-written prompts, training data, or computational resources consumed.’ ”

Ouch.

A Gift Economy. Roberts cites mathematician Michael Harris of Columbia University, author of the Substack newsletter “Silicon Reckoner” and another member of the declaration’s working group: “An aspect of mathematics that is cherished by mathematicians is that it is one of few successful examples of a gift economy—that is to say, its economy is somehow an island of idealism in our society.”

With the exception of Anthropic, A.I. has expressed little interest in this aspect of academe. 

Professor Ochigame concurs: “Those companies have repeatedly articulated this strategy in pitches to investors, so it is perhaps not a coincidence that OpenAI’s announcement about the unit distance conjecture came out the same day the news broke that the company is preparing to file for an I.P.O.”

And, once more, the matter of A.I.’s unbridled scraping of the Internet arises. Ochigame observes, “This situation has put mathematicians in a troubling ethical position. Without their consent, their published work is being used as strategic training data for the development of general-purpose A.I. The resulting models are being commercialized for many purposes, including military applications, that raise grave ethical concerns. Most mathematicians never imagined, much less consented, that their work would be used for such purposes.”

Hear! Hear!

Ochigame continues, “Mathematics is a rich form of cultural expression with an ancient history, and I am not worried that any technology will ever render it obsolete.… What I am worried about is that a handful of corporations are mobilizing their vast financial resources to impose an impoverished view of mathematics so forcefully—at a moment when scientific research is already under political attack—that they may well end up destroying the social institutions that allow mathematics to flourish.” 

More than simply expressing envy over disproving an old conjecture, the Leiden Declaration is an example of a much-needed guardrail to this new technology. Indeed, similar statements would be appropriate in other areas of human thought. ds   

© Dennis Simanaitis, SimanaitisSays.com, 2026