Verification, not ideation
Terence Tao warns AI shifted the bottleneck from idea generation to verification — we now need formal verification tools (like Lean) to validate AI‑produced math and proofs rather than just more model runs. For clinical and diabetes analytics that means building verification and audit pipelines, not only iterating models. (x.com)
In a March 6, 2026 essay for OpenAI’s Academy, Tao argued that the right response to machine‑generated proofs is formal verification — naming proof assistants such as Lean as tools that can “keep AI honest” when models produce polished but unreliable arguments. Tao published a Lean companion to his textbook Analysis I on May 31, 2025, laying out a formalized curriculum for undergraduates and researchers to use Lean alongside traditional exposition. That companion has an active GitHub repository — teorth/analysis — with roughly 1.6k stars and weekly commits that show ongoing maintenance and community contributions. The Equational Theories Project, which Tao helped lead, mechanically settled all 22,028,942 implication edges among 4,694 simple equational laws and reported those results as formally verified in a December 2025 arXiv paper. Tao is a co‑founder of the Foundation for Science and AI Research (SAIR), which launched a public “AI for Science: Kickoff 2026” program in early February 2026 and positions formal verification and rigorous benchmarks at the center of its agenda. (sair.foundation) SAIR’s first public competition — the Mathematics Distillation Challenge — presents the ~22 million equational yes/no problems from the Equational Theories Project and asks entrants to produce compact “cheat‑sheets” that improve weak open‑source model performance; the SAIR benchmark page lists a public release using 25 models and three runs per problem as of March 14, 2026. (competition.sair.foundation) Researchers packaged Tao’s formal work into evaluation suites such as TaoBench — a March 2026 arXiv benchmark based on 150 exercises from his Analysis I formalization — explicitly intended to measure whether automated theorem‑prover LLMs generalize beyond Mathlib.
