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The Equational Theories Project: Advancing Collaborative Mathematical Research at Scale

Published: December 8, 2025 | arXiv ID: 2512.07087v1

By: Matthew Bolan , Joachim Breitner , Jose Brox and more

Potential Business Impact:

Helps math computers find new number rules.

Business Areas:
STEM Education Education, Science and Engineering

We report on the Equational Theories Project (ETP), an online collaborative pilot project to explore new ways to collaborate in mathematics with machine assistance. The project successfully determined all 22 028 942 edges of the implication graph between the 4694 simplest equational laws on magmas, by a combination of human-generated and automated proofs, all validated by the formal proof assistant language Lean. As a result of this project, several new constructions of magmas satisfying specific laws were discovered, and several auxiliary questions were also addressed, such as the effect of restricting attention to finite magmas.

Page Count
74 pages

Category
Mathematics:
Rings and Algebras