GPT‑5 didn't solve a 40-year math mystery—it baited the hook

For decades, the Nesterov Accelerated Gradient has been a kind of magic trick in optimization theory. Put simply, it makes algorithms run faster without making them blow up. Since 1983, the question of why this momentum didn’t introduce catastrophic instability remained an open wound in the field. Ernest Ryu, a UCLA professor with 15 years in applied math, had taken his own swings at the proof and whiffed, just like everyone else.

Ryu’s early experiments with LLMs were a bust. Back in 2023, he found ChatGPT‑3.5 understood logic but face-planted on accuracy. He wasn’t expecting a revolution when he fired up GPT‑5 two years later. What he got was a research partner with a bizarrely wide reading list. The model wasn’t conjuring new mathematics from the ether. Its value was far more grounded: it acted as a searchlight sweeping across adjacent fields, dredging up equations and obscure techniques from papers Ryu might never have found on his own.

That process was messy and late-night, often after his kids were asleep. GPT‑5 would spit out an approach, and Ryu would immediately spot the flaw in its reasoning. It was frequently wrong. But occasionally, it was wrong in an interesting way. “It had an interesting approach that I had not thought about,” Ryu said, treating the model less like an oracle and more like a brainstorming partner who had read everything but understood very little. Its power, he noted, was its willingness to try weird things and pull from a massive scale of reading.

This isn’t a story about AI replacing mathematicians. It’s about a tool that baited the hook with unconventional ideas, letting a human expert finally set it. Ryu used the model’s creative misfires to push his own thinking in new directions, eventually finding a path to the proof. The machine didn’t connect the final dots, but it handed Ryu a new pen when his own had run dry.