Earlier this year, a 23-year-old without any formal mathematics training made headlines by claiming he’d used OpenAI’s ChatGPT to solve one of the “Erdős problems” — a database of challenging conjectures left behind by Hungarian mathematician Paul Erdős.
Then, last month, scholars were taken aback when OpenAI claimed its AI had disproved an 80-year-old “unit distance” conjecture, also devised by Erdős.
“This marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics,” OpenAI boasted at the time.
But whether the frontier AI models powering tools like ChatGPT really represent a major leap in our ability to solve problems that have been plaguing mathematicians for decades remains hotly debated among experts.
In perhaps the strongest public rebuke yet, a new declaration signed by over 150 mathematics experts from around the world warned governments not to “believe the hype” when it comes to AI’s capabilities to solve complex mathematical problems, throwing cold water on claims of a revolution in the field.
In a statement accompanying the 11-page “Leiden Declaration on AI and Mathematics,” International Mathematical Union vice president Ulrike Tillmann argued that AI “raises questions that cannot be left unexamined.”
“The future of mathematical research must be guided by human judgment, fair and transparent practices, and the shared values of the global mathematical community,” Tillmann said.
“There is currently a strong commercial incentive on the part of the technology industry to overstate the capabilities of their products,” the declaration reads, advising policymakers to “consult with experts, including mathematicians, in forming policy decisions rather than relying on press releases or popular reporting of mathematical results.”
Worse yet, AI models may produce convincing-sounding solutions that don’t actually withstand scrutiny.
“Current automated techniques can produce plausible but unreliable (or even incorrect) arguments which are difficult to distinguish from correct mathematical proofs,” said signee and University of Oxford head of computer science Leslie Ann Goldberg in a statement. “This is a serious problem: research in mathematics (and in mathematical disciplines like theoretical Computer Science) almost always builds on previous research, so it is essential for researchers to know that the results in the literature are correct.”
The declaration highlighted the highly precarious position many academics are finding themselves in. Attracting new funding has proven difficult, while interest in AI continues to soar, often forcing them to endorse the tech at all costs.
“We recognize that industry has offered lucrative jobs, monetary rewards, computing resources, and intellectually stimulating opportunities that some mathematicians have found attractive,” it reads. “This has taken place in an era of underfunding of higher education and precarious academic employment.”
The document also noted there were plenty of other reasons to call for regulatory oversight beyond the field of mathematics, noting the AI industry’s “involvement in military and mass surveillance programs, development of technologies which promote misinformation and undermine democracy, and environmental costs.”
In short, it’s a ringing denunciation of the persistent hype surrounding AI, and a call for reining in its use that reverberates far beyond the world of mathematics. The broader scientific community has been reeling from a flood of papers that make heavy use of AI, risking contaminating the peer-review process with hallucinations.
It’s also a pertinent reminder that AI models are being trained on cutting-edge research, often without sign-off from the original authors.
“Mathematicians who never intended to contribute to AI development are having their work used for this purpose without their consent,” Leiden University anthropologist of AI Rodrigo Ochigame, who helped draft the declaration, told Scientific American. “I think that’s a deeply concerning situation.”
More on AI and mathematics: Mathematicians Claim Significant Discovery Using ChatGPT
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