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

Harvard mathematicians disagree about how much artificial intelligence (AI) should be used in mathematics. OpenAI's announcement that its AI had solved a math problem that had gone unanswered for decades has raised questions about the future of mathematical research and teaching.

In September, OpenAI announced what it said was a solution to the Navier-Stokes existence and smoothness problem. This problem asks whether equations that describe how fluids move can develop mathematical breakdowns. It had remained unsolved for about 90 years and is one of the seven Millennium Prize Problems. Each problem carries a $1 million prize from the Clay Mathematics Institute.

The Crimson interviewed 12 Harvard mathematics professors, researchers, and lecturers. They shared different views on what OpenAI's solution means and how AI should be used in mathematics in the future.

Some worried that proofs created by AI may not include proper references or detailed explanations, making them hard to check and understand.

“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 was formed in September. It aims to create guidelines for how AI companies release mathematical research.

Others, including Ahsan Z. Khan, a research associate at Harvard’s Center of Mathematical Sciences and Applications (CMSA), argued that whether a proof is correct matters more than how it was created.

“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, partly because AI models might copy his work without proper permission or credit.

“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 members said AI can help with research by handling routine tasks, but they avoid depending on it to come up with ideas, find solutions, or create 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.

However, Schlank raised “serious concerns” about the ethics of using AI models to solve math problems. He argued that AI companies' desire to make money can conflict with mathematics' goal of gaining knowledge.

Michał P. Szachniewicz, a Benjamin Peirce Fellow in the Math department, said he uses AI for routine tasks, such as improving lecture notes. But he still prefers to discuss problems with other mathematicians instead of just “sitting and typing” with ChatGPT.

Faculty members and students are also trying to figure out how AI should be used outside research, including in teaching.

Brendan A. Kelly, director of the Introductory Math Program, said he hopes to find a good balance between using AI tools and protecting meaningful learning. Several introductory math courses introduced rules banning technology during classes and discussion sections this fall.

Kelly said the rules were meant to put first an education that “elevates students’ skills, dispositions, and academic identities.”

At a September meeting co-hosted by Harvard's Math department and the CMSA, 24 mathematicians developed recommendations. They called for more in-person written and oral tests and for training students to use AI tools in their research.

Laura G. DeMarco, director of undergraduate studies in the Math department, said the department was “working hard” to figure out how AI tools fit into the shared, cooperative 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.