Cuts up, cuts out

Recently some leading mathematicians have been studying the use, impact, and risks of using artificial intelligence in mathematical research and institutions.

They have now published the Leiden Declaration to articulate their concerns and to make recommendations.

I learned about this today from the New York Times, and you can learn a lot by reading their article. But you can learn more by reading the Declaration.

I feel that the Declaration is directly relevant not only to the mathematical community, but also, in reality, to all of us who regard thinking as an integral part of what we do. And that, in the end, is really all of us.

I strongly suggest that you study the Declaration and adopt its recommendations.

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. Perhaps most pointedly, the authors raise the question of whether the many A.I. companies tackling mathematics — major players such as OpenAI, Google DeepMind and Anthropic, or start-ups such as Harmonic, Math, Inc. and Axiom Math — are keeping the field’s best interests in mind. “Technology companies’ involvement in research,” they write, “raises the risk that research questions are prioritized and incentivized because of their amenability to A.I. methods and models, rather than their deeper significance to understanding.” In turn, they point out, this disadvantages researchers who choose not to use the technology, and those who do not have access to it.

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