philip lelyveld The world of entertainment technology

A.I. Is Coming for Mathematics, Too

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Akshay Venkatesh, a mathematician at the Institute for Advanced Study in Princeton and a winner of the Fields Medal in 2018, isn’t currently interested in using A.I., but he is keen on talking about it.“I want my students to realize that the field they’re in is going to change a lot,” he said in an interview last year. He recently added by email: “I am not opposed to thoughtful and deliberate use of technology to support our human understanding. But I strongly believe that mindfulness about the way we use it is essential.”

In February, Dr. Avigad attended a workshop about “machine-assisted proofs” at the Institute for Pure and Applied Mathematics, on the campus of the University of California, Los Angeles. (He visited the Euclid portrait on the final day of the workshop.) The gathering drew an atypical mix of mathematicians and computer scientists. “It feels consequential,” said Terence Tao, a mathematician at the university, winner of a Fields Medal in 2006 and the workshop’s lead organizer. ...

One conspicuous workshop attendee sat in the front row: a trapezoidal box named “raise-hand robot” that emitted a mechanical murmur and lifted its hand whenever an online participant had a question. “It helps if robots are cute and nonthreatening,” Dr. Tao said. ...

Early during Dr. Williamson’s DeepMind collaboration, the team found a simple neural net that predicted “a quantity in mathematics that I cared deeply about,” he said in an interview, and it did so “ridiculously accurately.” Dr. Williamson tried hard to understand why — that would be the makings of a theorem — but could not. Neither could anybody at DeepMind. Like the ancient geometer Euclid, the neural net had somehow intuitively discerned a mathematical truth, but the logical “why” of it was far from obvious.

At the Los Angeles workshop, a prominent theme was how to combine the intuitive and the logical. If A.I. could do both at the same time, all bets would be off.

But, Dr. Williamson observed, there is scant motivation to understand the black box that machine learning presents. “It’s the hackiness culture in tech, where if it works most of the time, that’s great,” he said — but that scenario leaves mathematicians dissatisfied.

He added that trying to understand what goes on inside a neural net raises “fascinating mathematical questions,” and that finding answers presents an opportunity for mathematicians “to contribute meaningfully to the world.”

See the full article here; https://www.nytimes.com/2023/07/02/science/ai-mathematics-machine-learning.html