The Human/AI Frontier: A Conversation with Bogdan Grechuk

Bogdan Grechuk, an Associate Professor of Mathematics at the University of Leicester, explores the use of artificial intelligence in solving complex mathematical problems, specifically Diophantine equations. Despite AI's potential, Grechuk highlights challenges, such as models producing incorrect yet convincing solutions, which wastes time and requires verification through formal proof systems. He collaborates with Surge AI to push AI capabilities by creating problems that current models struggle to solve without guidance. Grechuk successfully guided GPT-5 through a complex problem by transforming it into an elliptic curve and finding solutions, illustrating that while AI can handle PhD-level problems with direct inputs, it still requires further development to independently solve research-level questions. He envisions a future where AI could autonomously contribute to mathematical research beyond executing existing methods.