GPT-5 and the Future of Mathematical Discovery

UCLA professor Ernest Ryu succeeded in solving a 40-year-old open problem in the field of optimization theory using GPT-5. He confirmed that GPT-5 is a powerful tool that can quickly find ideas and techniques from a vast amount of mathematical papers and suggest new avenues of exploration.

The problem solved concerns the stability of Nesterov Accelerated Gradient (NAG). Introduced by Yurii Nesterov in 1983, NAG speeds up the convergence of algorithms through a 'look-ahead' method, but for decades there had been no mathematical proof of why the added momentum does not undermine the algorithm's stability.

During this process, GPT-5 proposed creative and unconventional approaches, providing decisive help in solving the complex mathematical problem.