Harvard Mathematicians Divided Over AI’s Role in Research and Teaching After OpenAI Breakthrough

Harvard mathematicians are divided over how far artificial intelligence should go in their field, as OpenAI’s announcement of an AI-generated solution to a decades-old math problem raises questions about the future of research and teaching.

In September, OpenAI released what it said was a solution to the Navier-Stokes existence and smoothness problem, which asks whether equations governing fluid motion can develop mathematical breakdowns. The problem had remained unresolved for roughly 90 years and is one of seven Millennium Prize Problems, each carrying a $1 million prize from the Clay Mathematics Institute.

The Crimson interviewed a dozen Harvard mathematics faculty, researchers, and lecturers, who expressed differing views on the implications of OpenAI’s solution and how AI should be used in the field moving forward.

Some raised concerns that AI-generated proofs can lack proper citations and thorough explanations, making them difficult to evaluate.

“We should use AI as a tool to increase that human understanding, but not to replace it or give up our knowledge and let it only be stored in machines,” said Melanie Matchett Wood, a Harvard professor and member of the independent Advisory Group on Mathematics and Artificial Intelligence.

The advisory group, formed in September, aims to provide guidelines for the release of mathematical research by AI companies.

Others, like Ahsan Z. Khan, a research associate at Harvard’s Center of Mathematical Sciences and Applications, argued that accuracy is more important than how the proofs were derived.

“If someone is able to tell you the equations of general relativity, it doesn’t really matter whether it was Einstein or Hilbert or ChatGPT,” Khan said. “It’s still general relativity.”

Lorenzo Riva, another CMSA lecturer, said he has avoided using AI in his research in large part to avoid the issue of models potentially plagiarizing his research.

“Whatever I put out might or might not be used depending on how much of the internet the AI is allowed to search,” Riva said. “That’s something that authors should have control over: whether their papers are being used for training or not.”

Other faculty said AI has a role to play in supporting research by completing routine tasks, but they avoid relying on it to generate ideas, solutions, or proofs.

“I find its effectiveness for my research, so far, best served in things like literature search and coding,” Harvard mathematics professor Tomer M. Schlank said.

But Schlank cited “serious concerns” regarding the ethics of using AI models to solve mathematical problems, arguing that the profit incentive of AI companies conflict with the field’s pursuit of knowledge.

Michał P. Szachniewicz, a Benjamin Peirce Fellow in the Math department, said he uses AI for routine tasks like cleaning up lecture notes, but still prefers discussing problems with other mathematicians rather than just “sitting and typing” with ChatGPT.

Faculty and students are also grappling with how best to incorporate AI into areas beyond research, including teaching.

Brendan A. Kelly, the director of the Introductory Math Program, said he hopes to find a good balance between adopting AI tools and preserving meaningful learning. Several introductory math courses introduced tech-free policies during classes and sections this fall.

Kelly said the policies were intended to prioritize an education that “elevates students’ skills, dispositions, and academic identities.”

At a September summit co-hosted by the Harvard Math department and the CMSA, 24 mathematicians developed recommendations calling for greater emphasis on in-person written and oral assessments and training students to use AI tools in their research.

Laura G. DeMarco, the director of undergraduate studies in the Math department, said the department was “working hard” to determine how AI tools fit into the collaborative culture of mathematics.

“Being a mathematician is being part of a community of explorers together, and I am definitely optimistic about the future of this community,” DeMarco said.