mlsanityData to 7 Oct 2026

The Equational Theories Project: Advancing Collaborative Mathematical Research at Scale

arXiv 2512.07087 ↗First posted 8 Dec 2025math.RA cs.LOcited by 8

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Abstract (arXiv)

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.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). First posted on arXiv 8 Dec 2025.

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Citing papers per year: 2026: 8.

8 papers.

  1. 2026Automatic Textbook Formalizationcited by 5
  2. 2026DIVE: Unlocking Self-Improvement in Frozen Language Models Through Diversity-Driven Skill Evolutioncited by 2
  3. 2026Discovering mathematical concepts through a multi-agent systemcited by 1
  4. 2026ALPS: Measuring Valid Creativity in Large Language Models with Mathematical Constructioncited by 0
  5. 2026A Certificate-Producing Cascade for Equational Implication: The SAIR EQT2 Stage 2 Solvercited by 0
  6. 2026Choir: An Open Protocol for Distributed Multi-Agent Autoformalizationcited by 0
  7. 2026Fyan: A Human--AI Harness with Semantic Auditing for Document-Level Formalizationcited by 0
  8. 2026NanoProof: Open and Efficient Automated Theorem Proving in Lean 4cited by 0