How GPT-5 helped mathematician Ernest Ryu solve a 40-year-old open problem

Mon, Apr 6 · 9:20 PM UTC 2 min read

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Abstract collage-style artwork featuring a large blurred gradient background in pink, orange, and blue tones. Overlapping panels include bold black text reading “Ryu Ernest” on a pale yellow block, a brown block with faint repeated “OpenAI for Science” text, and a minimalist diagram with curved arro.

How a mathematician used GPT‑5 to explore ideas faster and find a path to solving a long-standing optimization problem.

Key facts

With 15 years in applied mathematics and optimization theory, Professor Ernest Ryu of the University of California, Los Angeles (UCLA), was curious about the large language model (LLM) everyone
After thinking deeply about how to credit GPT‑5’s collaboration with helping to solve this proof, he ultimately decided it was used as a tool, which is why GPT‑5 is not listed as a co-author
In 2023, he decided to test ChatGPT‑3.5’s ability to solve simple math and logic problems, like scheduling meetings with multiple people across time zones
The pre-print paper on Ryu’s work to solve the NAG problem is available publicly and is working its way through the peer review process, which takes around 12-18 months

Summary

Every significant math problem has a story—someone who posed a question, someone who tried to solve it, someone who could not, and eventually, maybe, someone who could. With 15 years in applied mathematics and optimization theory, Professor Ernest Ryu of the University of California, Los Angeles (UCLA), was curious about the large language model (LLM) everyone was talking about. When OpenAI unveiled GPT‑5 two years later, Ryu began hearing about its rapidly advancing capabilities in mathematics. Ryu decided to tackle an “open” problem, meaning it was unsolved and recognized in the community as something of interest.

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