Terry Tao on the future of mathematics | Math, Inc.

In this interview, Terry Tao discusses his evolving perspective on mathematics, influenced by machine-assisted proof and formalization. He reflects on the initial drudgery in mathematical problem-solving, such as literature reviews and adapting existing techniques, and how tools like Lean and AI are changing the landscape. Tao shares his experiences learning Lean, emphasizing its potential to clean up mathematical writing and enable new styles of proof. He also touches on the concept of pre-rigorous, rigorous, and post-rigorous stages in learning mathematics and how formalization helps eliminate unnecessary hypotheses. Tao envisions a future where mathematics is more collaborative and modular, with specialized roles and increased accessibility for citizen mathematicians, and shares his excitement about formalizing bounds for analytic number theory, aiming for a dynamic, state-of-the-art field that leverages automation to overcome tedious computations and trust issues.