Terry Tao Became an Evangelist for AI in Math
7 hours ago
- #AI in Mathematics
- #Formal Verification
- #Mathematical Collaboration
- Terry Tao predicted in 2014 that future math papers might be written in a formal language and checked by computers, an idea initially met with incredulity.
- Tao's early mathematical talent was evident from childhood, culminating in him becoming the youngest gold medalist at the International Math Olympiad and earning a Ph.D. from Princeton by age 17.
- His collaborative nature, exemplified by the Green-Tao theorem, contrasts with his ability to work alone and has led him to explore diverse mathematical fields.
- In 2007, Tao started a blog to engage publicly with math, and in 2009 he joined Timothy Gowers' Polymath Project, which pioneered large-scale collaborative mathematics online.
- TaRecognizing limitations in the Polymath model, such as error-checking bottlenecks, Tao envisioned computer verification as a solution, leading him to explore formal math software like Lean.
- In 2023, Tao formalized a proof using Lean4, experiencing challenges but successfully contributing to the Lean community, despite the process being more tedious than traditional math writing.
- He later led the formalization of the polynomial Freiman-Ruzsa (PFR) conjecture proof with volunteers, demonstrating that large-scale, Lean-verified collaborations could be efficient and decentralized.
- By 2024, Tao advocated for a new mathematical paradigm combining human insight, AI, and formal verification, targeting problems that can be broken into many small subproblems.
- He launched the Equational Theories project in 2024, using Lean and automation to map millions of algebraic law implications, achieving rapid progress and uncovering novel constructions like magma cohomology.
- Though some mathematicians viewed the project as trivial, Tao saw it as a successful pilot for experimental mathematics, akin to big science collaborations in physics, showcasing a transformative approach to the field.