Mathematician Ernest Ryu used OpenAI’s GPT-5 to solve a 40-year-old open problem in convex optimization. The solution is now under formal verification. If confirmed, it marks one of the most significant demonstrations of AI’s capacity for genuine mathematical discovery.
This follows a trend. OpenAI’s internal models have produced over 10 new solutions to Erdős-style combinatorics problems, some being considered for top journals. At the 2025 International Mathematical Olympiad, models from OpenAI and Google DeepMind achieved gold-medal performance. DeepMind’s AlphaEvolve improved upon the best known results in 23 of 67 research-level problems.
Convex optimization underpins machine learning, finance, and logistics. A 40-year-old problem isn't an obscure curiosity; it's a bottleneck. That a general-purpose model like GPT-5 solved it, rather than a purpose-built one, raises the ceiling on what AI can achieve.
For crypto and cybersecurity, the implications are direct. Cryptography relies on assumptions about which problems are hard. While today's AI tackles optimization and combinatorics, not the number theory behind most encryption, the trajectory is clear. Enhanced AI reasoning could accelerate the development of new protocols like zero-knowledge proofs and post-quantum standards. It also strengthens formal verification for smart contracts, moving security from “we looked at it hard” to provable guarantees.
The mathematical capability demonstrated by GPT-5 and AlphaEvolve is an early indicator of a fundamental shift in what’s computationally possible. Crypto sits directly in the blast radius.