{"status":"public","abstract":[{"lang":"eng","text":"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."}],"date_updated":"2026-03-12T08:36:21Z","citation":{"chicago":"Bolan, Matthew, Joachim Breitner, Jose Brox, Nicholas Carlini, Mario Carneiro, Floris van Doorn, Martin Dvorak, et al. “The Equational Theories Project: Advancing Collaborative Mathematical Research at Scale.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2512.07087\">https://doi.org/10.48550/arXiv.2512.07087</a>.","ista":"Bolan M, Breitner J, Brox J, Carlini N, Carneiro M, Doorn F van, Dvorak M, Goens A, Hill A, Husum H, Mejia HI, Kocsis ZA, Floch BL, Bar-on A, Luccioli L, McNeil D, Meiburg A, Monticone P, Nielsen PP, Osazuwa EO, Paolini G, Petracci M, Reinke B, Renshaw D, Rossel M, Roux C, Scanvic J, Srinivas S, Tadipatri AR, Tao T, Tsyrklevich V, Vaquerizo-Villar F, Weber D, Zheng F. The equational theories project: Advancing collaborative mathematical research at scale. arXiv, <a href=\"https://doi.org/10.48550/arXiv.2512.07087\">10.48550/arXiv.2512.07087</a>.","ieee":"M. Bolan <i>et al.</i>, “The equational theories project: Advancing collaborative mathematical research at scale,” <i>arXiv</i>. .","mla":"Bolan, Matthew, et al. “The Equational Theories Project: Advancing Collaborative Mathematical Research at Scale.” <i>ArXiv</i>, doi:<a href=\"https://doi.org/10.48550/arXiv.2512.07087\">10.48550/arXiv.2512.07087</a>.","ama":"Bolan M, Breitner J, Brox J, et al. The equational theories project: Advancing collaborative mathematical research at scale. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2512.07087\">10.48550/arXiv.2512.07087</a>","apa":"Bolan, M., Breitner, J., Brox, J., Carlini, N., Carneiro, M., Doorn, F. van, … Zheng, F. (n.d.). The equational theories project: Advancing collaborative mathematical research at scale. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2512.07087\">https://doi.org/10.48550/arXiv.2512.07087</a>","short":"M. Bolan, J. Breitner, J. Brox, N. Carlini, M. Carneiro, F. van Doorn, M. Dvorak, A. Goens, A. Hill, H. Husum, H.I. Mejia, Z.A. Kocsis, B.L. Floch, A. Bar-on, L. Luccioli, D. McNeil, A. Meiburg, P. Monticone, P.P. Nielsen, E.O. Osazuwa, G. Paolini, M. Petracci, B. Reinke, D. Renshaw, M. Rossel, C. Roux, J. Scanvic, S. Srinivas, A.R. Tadipatri, T. Tao, V. Tsyrklevich, F. Vaquerizo-Villar, D. Weber, F. Zheng, ArXiv (n.d.)."},"oa_version":"Preprint","article_processing_charge":"No","author":[{"last_name":"Bolan","first_name":"Matthew","full_name":"Bolan, Matthew"},{"first_name":"Joachim","full_name":"Breitner, Joachim","last_name":"Breitner"},{"full_name":"Brox, Jose","first_name":"Jose","last_name":"Brox"},{"first_name":"Nicholas","full_name":"Carlini, Nicholas","last_name":"Carlini"},{"last_name":"Carneiro","full_name":"Carneiro, Mario","first_name":"Mario"},{"last_name":"Doorn","first_name":"Floris van","full_name":"Doorn, Floris van"},{"full_name":"Dvorak, Martin","orcid":"0000-0001-5293-214X","first_name":"Martin","id":"40ED02A8-C8B4-11E9-A9C0-453BE6697425","last_name":"Dvorak"},{"full_name":"Goens, Andrés","first_name":"Andrés","last_name":"Goens"},{"first_name":"Aaron","full_name":"Hill, Aaron","last_name":"Hill"},{"full_name":"Husum, Harald","first_name":"Harald","last_name":"Husum"},{"last_name":"Mejia","first_name":"Hernán Ibarra","full_name":"Mejia, Hernán Ibarra"},{"full_name":"Kocsis, Zoltan A.","first_name":"Zoltan A.","last_name":"Kocsis"},{"last_name":"Floch","first_name":"Bruno Le","full_name":"Floch, Bruno Le"},{"last_name":"Bar-on","full_name":"Bar-on, Amir","first_name":"Amir"},{"first_name":"Lorenzo","full_name":"Luccioli, Lorenzo","last_name":"Luccioli"},{"first_name":"Douglas","full_name":"McNeil, Douglas","last_name":"McNeil"},{"first_name":"Alex","full_name":"Meiburg, Alex","last_name":"Meiburg"},{"first_name":"Pietro","full_name":"Monticone, Pietro","last_name":"Monticone"},{"first_name":"Pace P.","full_name":"Nielsen, Pace P.","last_name":"Nielsen"},{"first_name":"Emmanuel Osalotioman","full_name":"Osazuwa, Emmanuel Osalotioman","last_name":"Osazuwa"},{"last_name":"Paolini","first_name":"Giovanni","full_name":"Paolini, Giovanni"},{"last_name":"Petracci","full_name":"Petracci, Marco","first_name":"Marco"},{"last_name":"Reinke","first_name":"Bernhard","full_name":"Reinke, Bernhard"},{"last_name":"Renshaw","full_name":"Renshaw, David","first_name":"David"},{"last_name":"Rossel","first_name":"Marcus","full_name":"Rossel, Marcus"},{"last_name":"Roux","full_name":"Roux, Cody","first_name":"Cody"},{"first_name":"Jérémy","full_name":"Scanvic, Jérémy","last_name":"Scanvic"},{"first_name":"Shreyas","full_name":"Srinivas, Shreyas","last_name":"Srinivas"},{"last_name":"Tadipatri","full_name":"Tadipatri, Anand Rao","first_name":"Anand Rao"},{"last_name":"Tao","first_name":"Terence","full_name":"Tao, Terence"},{"first_name":"Vlad","full_name":"Tsyrklevich, Vlad","last_name":"Tsyrklevich"},{"first_name":"Fernando","full_name":"Vaquerizo-Villar, Fernando","last_name":"Vaquerizo-Villar"},{"first_name":"Daniel","full_name":"Weber, Daniel","last_name":"Weber"},{"first_name":"Fan","full_name":"Zheng, Fan","last_name":"Zheng"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2512.07087"}],"month":"12","title":"The equational theories project: Advancing collaborative mathematical research at scale","external_id":{"arxiv":["2512.07087"]},"date_published":"2025-12-16T00:00:00Z","publication":"arXiv","oa":1,"date_created":"2026-03-04T12:00:16Z","type":"preprint","department":[{"_id":"GradSch"},{"_id":"VlKo"}],"_id":"21399","publication_status":"submitted","day":"16","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"arxiv":1,"year":"2025","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","OA_place":"repository","doi":"10.48550/arXiv.2512.07087","language":[{"iso":"eng"}]}