Terence Tao at IMO 2024: AI and Mathematics

Introduction to Professor Terence Tao, his achievements at the IMO, and his current position at the University of California.

Discussion on AI and machine assistance in mathematics, its impact on research mathematics, and the evolution of using machines in mathematics over time.

Exploration of the historical use of machines, computers, and tables in mathematics, including examples from Roman times to the modern era.

Importance of tables and databases in mathematical research, including examples of fundamental results discovered through tables like the prime number theorem.

Explanation of computer-assisted proofs, including examples of the Four Color Theorem and the Kepler Conjecture, and the challenges and advancements in this field.

Discussion on using machine learning and formal proof assistants in mathematics, including examples, challenges, and the potential impact of these tools on the field.

Introduction to machine learning and the use of neural networks to predict answers to various questions.

Exploration of machine learning applications in knot theory, specifically in identifying knot invariants using neural networks.

Description of training a neural network on knot invariants and how it successfully predicted knot signatures.

Discussion on the identification of important knot invariants through saliency analysis of neural network outputs.

Exploration of machine learning's role in mathematics, providing hints and connections but still requiring human input for problem-solving.

Discussion on the capabilities and limitations of large language models like GPT-4 in solving mathematical questions.

Overview of challenges faced and progress made in using AI for mathematical problem-solving, including proof assistants and theorem verification.

Speculation on the future of AI in mathematics, including the potential for AI-generated conjectures and advancements in problem-solving approaches.

Conversation on formalizing mathematics using proof assistants based on homotopy type theory and the potential of AI in translation between proof languages.

Reflection on age and growth in mathematics, discussing the impact of starting university at a young age on mathematical development.

Insight into selecting research problems, including serendipitous discoveries through interactions in mathematics communities.