Terry Tao is at the forefront of exploring how AI can transform mathematical research, emphasizing the use of interactive theorem provers like Lean and Coq. While we may not yet be able to fully replicate a mathematician's brain, LLMs could serve as invaluable assistants in the research process. By digitizing mathematical proofs into formal programming languages, these tools can not only verify proofs but also suggest incremental improvements, streamlining the exploration and formulation of complex mathematical ideas.
The interaction with the theorem provers allows not just verification, but also incremental suggestions, facilitating the proving process for mathematicians working on complex problems.
Tao emphasizes that while digitizing the brain of a brilliant mathematician like himself isn't feasible yet, advancements in AI can potentially transform mathematical research methods.
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