GPT-5 mathematical discovery is reshaping how mathematicians solve complex problems faster and more efficiently. Professor Ernest Ryu from UCLA used GPT-5 to tackle a decades-old optimization theory challenge, exploring ideas faster and uncovering new pathways that were previously hidden due to human limitations. This AI-driven approach is making waves in mathematical research.
The optimization problem that Ryu addressed involves the Nesterov Accelerated Gradient (NAG) method, a phenomenon known for its speed without compromising algorithm stability. This longstanding puzzle has intrigued researchers since 1983 when Yurii Nesterov first introduced the method. The mystery: why does adding momentum in NAG not destabilize the process while speeding it up?
Ryu’s curiosity about GPT’s evolving mathematical abilities started in 2023 with ChatGPT-3.5, and by the time GPT-5 launched, its enhanced capacities inspired him to revisit difficult questions in optimization theory. GPT-5’s ability to surface diverse mathematical approaches from vast literature gave Ryu new inspiration, accelerating his progress on the problem significantly.
Throughout his work, GPT-5 served not as an inventor but as a powerful assistant capable of pulling relevant ideas from various fields. It offered creative, sometimes unconventional proposals that Ryu evaluated for their potential. This iterative process of rapid idea generation and filtering sped up what would usually take weeks into mere days.
The breakthrough happened when GPT-5 suggested restructuring key equations governing the NAG method. While not entirely correct initially, Ryu refined the idea into a rigorous mathematical proof. The collaboration felt like working with a talented student who could brainstorm and ask questions—only much faster and tireless in generating possibilities.
Despite its strengths, GPT-5’s outputs required careful human verification. Its arguments occasionally contained errors or plausible-looking but flawed logic. Ryu maintained strict oversight, discarding dead-end ideas and developing promising ones. This combined approach leveraged AI’s speed and human intuition, proving powerful in navigating complex mathematical challenges.
Looking ahead, Ryu plans to continue integrating AI tools like GPT-5 in his research. He urges mathematicians to embrace this technology with patience and rigor, emphasizing the value of collaboration between humans and AI. His experience highlights the potential for AI to unlock new horizons in math, sparking innovations across disciplines.
