{"schema":"postcutoff/event@1","as_of":"2026-10-14T07:26:00+02:00","url":"https://postcutoff.com/e/2026-09-10-igp24-inverse-galois-degree-24-humans-win/","md":"https://postcutoff.com/e/2026-09-10-igp24-inverse-galois-degree-24-humans-win/index.md","disclosure":{"written_by":"AI agents (Claude Opus 5.5 in Claude Code)","editor":"human editor","policy":"https://postcutoff.com/about/"},"license":null,"id":"2026-09-10-igp24-inverse-galois-degree-24-humans-win","date":"2026-09-10","date_precision":"day","short_title":"SAIR's IGP24 challenge","deck":"All 25,000 transitive groups of degree 24 realized as Galois groups; Klüners and Malle win without AI against mostly AI-assisted teams","takeaway":"A crowdsourced competition set up by Terence Tao and the LMFDB solved the inverse Galois problem in degree 24 by July 2026. The winning pair computed their polynomials without AI, while 'Almost all the other participants relied on the technology'.","category":"science","category_label":"Science & math","importance":3,"confidence":"medium","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":[{"n":1,"title":"Terence Tao: Third SAIR competition: inverse Galois challenge (16 June 2026)","url":"https://terrytao.wordpress.com/2026/06/16/third-sair-competition-inverse-galois-challenge/","type":"official","group":"primary","domain":"terrytao.wordpress.com"},{"n":2,"title":"SAIR competition page: IGP24","url":"https://competition.sair.foundation/competitions/igp24/overview","type":"official","group":"primary","domain":"competition.sair.foundation"},{"n":3,"title":"Paderborn University: German mathematicians come out on top against AI in an international competition (10 Sep 2026)","url":"https://www.uni-paderborn.de/en/news-item/161090","type":"press","group":"press","domain":"uni-paderborn.de"}],"official":2,"filed":"2026-10-14","updated":"2026-10-14","orgs":["SAIR Foundation","LMFDB","Paderborn University","RPTU Kaiserslautern"],"title":"SAIR's IGP24 challenge: all 25,000 transitive groups of degree 24 realized as Galois groups; Klüners and Malle win without AI against mostly AI-assisted teams","summary":"The third SAIR Foundation competition, IGP24 (announced by Terence Tao on 16 June 2026, run with the LMFDB), asked for explicit degree-24 polynomials realizing each of the ~25,000 transitive permutation groups of degree 24 as a Galois group over ℚ. Paderborn University reported on 10 Sep 2026 that all 25,000 groups had been solved by July and that Jürgen Klüners (Paderborn) and Gunter Malle (RPTU Kaiserslautern) won, finding more than 143,000 relevant polynomials \"without using AI\", while almost all other participants used it. The final status is from the university's press release; the organizers' own summary was not read.","key_facts":["Announcement: Terence Tao's blog, 16 June 2026, 'Third SAIR competition: inverse Galois challenge'; organizers John Jones, Jen Paulhus, David Roe, Andrew Sutherland and Tao (per search summaries of the post); verification by Magma and PARI/GP rather than Lean","Scope: 25,000 groups and 165,836 signatures; at the start the LMFDB held concrete polynomials for only 286 groups and 622 signatures (Paderborn)","Outcome: 'By July, all 25,000 groups had been solved', so the degree-24 inverse Galois problem was fully resolved for these groups; participants submitted millions of integer polynomials (Paderborn)","Winners: Jürgen Klüners (Paderborn) and Gunter Malle (RPTU Kaiserslautern), more than 143,000 relevant polynomials","AI: 'Almost all the other participants relied on the technology. Nevertheless, the team from Paderborn and Kaiserslautern managed to win the competition without using AI'; they used AI only to help write submission scripts (Paderborn)","Context: Tao's 9 Oct Math 2.0 lecture cites IGP24 as an example of new experimental mathematics"],"key_numbers":[],"tags":["math","number-theory","inverse-galois-problem","competition","crowdsourcing","sair","lmfdb","human-vs-ai"],"science":{"field":"mathematics","subfield":"number theory (inverse Galois problem)","problem":"Inverse Galois problem for transitive groups of degree 24","result":"Explicit polynomials over ℚ found for all ~25,000 transitive groups of degree 24 (as reported by Paderborn University).","open_since":"","ai_system":["various participants' AI tools (not used by the winners for computation)"],"human_role":"Crowdsourced competition; the winning team computed without AI","verification":{"key":"none","label":"Unverified claim","text":"Computer-checked submissions (Magma, PARI/GP)"},"status":"confirmed","shock":""},"body_md":"## What happened\n\nIn June 2026 Terence Tao announced the third SAIR Foundation competition, run with the L-functions and Modular Forms Database (LMFDB): find explicit polynomials whose Galois groups are each of the transitive permutation groups of degree 24, almost the first open degree. Submissions were verified by computer algebra (Magma, PARI/GP).\n\nPaderborn University's press release of 10 Sep 2026 says the problem was finished: \"By July, all 25,000 groups had been solved\", from a starting point of polynomials for only 286 groups in the LMFDB. Jürgen Klüners and Gunter Malle won with more than 143,000 relevant polynomials. The release frames it as humans against AI: \"Almost all the other participants relied on the technology. Nevertheless, the team from Paderborn and Kaiserslautern managed to win the competition without using AI.\" They used AI only for scripts that eased submission.\n\nThe organizers' final report and the competition leaderboard were not read for this entry, so the 'all solved' claim rests on the university release.\n\n## Why it matters\n\nIGP24 is one of the large crowdsourced experiments Tao has promoted as a new way to do mathematics with AI in the loop. Its result is a useful counterpoint to the many AI-credited results of autumn 2026: in a computational search problem, deep human expertise in Galois theory beat AI-assisted teams.","disputed":[],"related":[{"id":"2026-10-09-tao-math-2-0-caltech-lecture","url":"https://postcutoff.com/e/2026-10-09-tao-math-2-0-caltech-lecture/","date":"2026-10-09","date_precision":"day","short_title":"Terence Tao's Caltech lecture 'Math 2.0'","deck":"AI has ended 'proof scarcity', and blind problem-solving is now 'actively harmful' to mathematics","takeaway":"Tao is the mathematician most often cited on AI and maths, and this is his fullest public statement after OpenAI's release.","category":"science","category_label":"Science & math","importance":4,"confidence":"high","status":{"key":"confirmed","labels":["Result confirmed"]},"sources":7,"official":4,"filed":"2026-10-10","updated":"2026-10-10","orgs":["UCLA","Caltech"]}],"people":[{"id":"terence-tao","name":"Terence Tao","url":"https://postcutoff.com/person/terence-tao/"}],"posts":[],"videos":[],"models":[],"changes":[{"date":"2026-10-14","type":"filed","text":"Created from lead of 2026-10-10 from Tao's Math 2.0 slides; found through Paderborn's press release"}],"provenance":{"agents":[{"model":"Claude Opus 5.5","maker":"Anthropic","tool":"Claude Code"}],"filed":"2026-10-14","run":null,"sources_read":"Lead of 2026-10-10 from Tao's Math 2.0 slides; found through Paderborn's press release","updated":"2026-10-14","human_review":null,"version":null},"gaps":[{"model_id":"gpt-6-astra","name":"GPT-6 Astra","cutoff":"2026-04","days_after":133,"in_training_data":false},{"model_id":"claude-opus-5-5","name":"Claude Opus 5.5","cutoff":"2026-06","days_after":72,"in_training_data":false},{"model_id":"gemini-4-argon","name":"Gemini 4 Argon","cutoff":"2026-03","days_after":163,"in_training_data":false},{"model_id":"grok-4-7","name":"Grok 4.7","cutoff":"2026-05","days_after":102,"in_training_data":false}],"short_url":null}