When Machines Crack Classics: How an AI Proof Upset the Craft of Mathematics

The useful part

You can add math to the list after OpenAI said that, using thousands of agents, it had solved a decades-old puzzle known as the Navier-Stokes existence and smoothness problem. "The artists and the musicians have already gone through this," says Juspreet Singh Sandhu, a mathematician at Colorado State University. Despite what timed high school exams might have you believe, mathematicians aren't focused on getting the right answer as fast as possible.

How it works

• Mathematicians typically follow a thoughtful, deliberate process to develop their ideas.
• The draw of Navier-Stokes is similar to why people play Sudoku or chess, both of which have no utility other than being fun and intellectually stimulating.
• Mathematicians imagined how the equations would apply in a fringe, almost sci-fi context, just because it intrigued them.
• When humans write proofs, they organize their arguments based on previous research, which they cite.
• Consider it akin to workshopping a poem, but with logic instead of emotion.

What to take from it

They pursued answers to the problem, he says, because of the "mathematical richness, the puzzle aspect of it." The puzzle's solution will not help anybody design a more aerodynamic airplane wing. Mathematicians expect approximate equations like Navier-Stokes to imply such nonsensical situations, which they find particularly interesting because sometimes they can lead to brand-new mathematical ideas. They were on the verge of cracking the problem before OpenAI's proof found that yes, the Navier-Stokes equations did imply a sci-fi fluid explosion.

Example or evidence

• Centuries later, physicists would use imaginary numbers in the equations for describing quantum mechanics, and they were able to use mathematicians' theorems about i to build their understanding of...
• In fact, contrary to math's image as a practical subject, the development of new mathematical ideas often resembles artistic exploration, akin to inventing a game or puzzle.
• OpenAI approached the proof with brute force, which shortcut the process in a way that threatens to undermine human understanding.
• "A mathematician, like a painter or poet, is a maker of patterns," wrote the English mathematician G.

Details worth keeping

Solving Math's Greatest Problems Was an Art Form. Then Came AI | WIRED Skip to main content Save this story Save this story From Suno composing uncanny elevator music to Tilly Norwood delivering customer-service-inflected one-liners, artificial intelligence has rattled creative industries. Hardy in his 1940 essay, A Mathematician's Apology.

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• Nytimes: In our field of applied mathematics, the long, human process of trial and error — not just the solutions themselves — is often what has led to progress.
• Newscientist: Mathematicians now have a formidable tool for breaking open challenging problems, but working out how best to use it isn't going to be easy
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