Twenty-five leading mathematicians signed an open letter arguing that AI labs threatened their intellectual work as they seek to one-up each other with solutions to famous math problems.
“We are witnessing a general threat to intellectual work, with misalignment between the outcome of the use of AI and its initial purpose,” the signatories said in a letter available online.
They noted that in recent months, the success of AI in solving major mathematical problems has made headlines even outside mathematical circles.
“But solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight. Forgetting this in the world of AI may turn the tool against the primary goal. Indeed, the mass production at faster and faster pace of “true/false” statements could destroy fertile ground instead of breathing life into new ideas,” they argued in the letter.
While the ability of AI models to solve the world’s outstanding mathematical challenges could be a boon to humanity, the signatories of the new letter argued that this will only be the case if those solutions can be understood and communicated by the math community and, ultimately, the rest of the world.
“Often these solutions are announced in a rush, leaving no time for a proper writeup, the isolation of new methods and ideas, and citing relevant previous work of others,” they wrote.
“As in all creative professions, this raises severe attribution and plagiarism questions. Moreover, without the willing mathematicians who must take care of their development and integration into the mathematical canon, AI-conceived ideas would never become fully alive and the crucial human transmission chain between mathematicians would be lost,” they added.
They said, “The issues the mathematical community faces now are similar to issues that other scientific and creative professions are facing, and indicate issues that all of humanity might face: how to make sure that, as AI changes the way work is done, we do not lose sight of what that work was meant to achieve in the first place.”
The group highlighted the importance of human interference even as “AI offers the potential of enhancing and accelerating genuine mathematical study and understanding.”
“Mathematics as a profession will need to adapt to these changes in several ways. However, whether these changes ultimately benefit the field or have a destructive effect will in large part be determined by the decisions of the humans in control of this new technology,” the group stated.
Leiden Declaration
This letter follows the Leiden Declaration, released by a working group of mathematicians in June. That document also grapples with the ways that LLM proofs will change their work and offers a set of recommendations for mathematicians, institutions, and policymakers.
The declaration called for action to address the challenges posed by the use of artificial intelligence within mathematics research. It is the result of a community initiative and is endorsed by the International Mathematical Union (IMU).
‘OpenAI fought on career-making math problem’
This week, NYU professor Tristan Buckmaster accused OpenAI of pressuring him not to credit a collaborator, who works for Anthropic, for solving an important math problem.
Tech Crunch reported on September 8 that Professor Buckmaster declared three proofs with a preliminary finding on one of the major unsolved problems in theoretical mathematics.
The findings, made in collaboration with Anthropic mathematician Levent Alpöge and using both Codex and Claude AI models, are significant in themselves — but they were also accompanied by an unusual controversy surrounding OpenAI’s attempts to solve the same problem.
According to the statement, a parallel effort by OpenAI built on their work before it became public, leading to a tangle of academic rivalries and conflicting claims.
“There is another part of this story, and one that, honestly, I very much wish I did not have to be concerned with,” Buckmaster wrote in his statement announcing the proofs.
“I am not happy about the presentation quality in these papers. Ideally, we would have preferred to spend weeks turning the LLM generated proofs into something readable from the very first page.
This level of care is what these problems and the community devoted to these problems deserves.,” Buckmaster wrote.
He said, “The various Boussines and Euler write-ups in particular are much closer to what models produce under human direction than to a paper written by a person. The Euler writeup, in particular, can only be described as AI slop. I am sorry for this. The reasons…involve our being pressured by outside factors. I say this not as an excuse but as an explanation,” the letter said.
Shortly after the Buckmaster’s statement, OpenAI published a full proof of the Navier–Stokes existence and smoothness problem, which Buckmaster’s findings had taken steps towards.
According to OpenAI, the proof was discovered by an unreleased next-generation model, which has tackled a range of different unsolved problems over the past week. All told, the week-long effort consumed 300 billion output tokens — $22.5 million worth of compute, if charged at current Astra rates.
Buckmaster said the important thing was, instead the significance that a mathematician and an LLM model can now do all this work in a month.
OpenAI withdraws sponsorship of math event
On Thursday, OpenAI withdrew its sponsorship of a math event at CalTech after the company was criticized by researchers at the university.
“We recognize that the rapid progress of AI in mathematics is disruptive. We’re looking to engage with the math community more on the best way to integrate this technology and communicate its impacts. After considering concerns raised by members of the mathematics community, we’ve decided to withdraw OpenAI’s sponsorship of the Caltech Mathathon and have notified the organizers,” Dan Roberts, a scientist at OpenAI, wrote on X.
https://x.com/danintheory/status/2098125701782372640
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