Terry Tao Launches 22 Million-Check Equational Theories Project for AI-Assisted Algebra
Updated
Updated · Quanta Magazine · Jun 8
Terry Tao Launches 22 Million-Check Equational Theories Project for AI-Assisted Algebra
1 articles · Updated · Quanta Magazine · Jun 8
Summary
September 2024 brought Tao’s new “Equational Theories” collaboration, built to map how 4,694 algebraic laws imply one another through AI tools, automated theorem provers and Lean-style formal verification.
The project targeted a scale humans struggle to manage alone: roughly 22 million possible implications, with Tao framing it as a test of machine-assisted, massively collaborative mathematics.
Volunteers first screened laws against simple magmas with Python scripts, resolving more than 99% of cases within days; the remaining questions were then attacked by automated provers and human contributors.
By late 2024 the effort had cut the open cases to 138, and by early 2025 only a handful remained, even as participation slowed once the easiest tasks were exhausted.
Tao sees the project less as a one-off result than as a prototype for “experimental” mathematics, after it already surfaced at least one apparently new construction, magma cohomology.
If AI can now author elegant proofs, what is the future role for human mathematicians?
If no human can grasp a full proof, only a computer, is it still true knowledge?
Mapping 22 Million Implications: The Equational Theories Project and the Future of Collaborative, AI-Assisted Mathematics
Overview
The Equational Theories Project (ETP), launched in September 2024, set out to pioneer new ways of collaborative mathematical research by combining human expertise with machine assistance. Inspired by a MathOverflow question about associative and constant identities, the project chose a goal well-suited for crowdsourcing and computer-aided methods, ensuring both broad participation and deep research value. ETP quickly attracted attention for its innovative approach, with coverage in major media outlets. By strategically blending crowdsourced efforts and advanced computational tools, the project established a new model for large-scale, collaborative mathematical discovery.