{"id":247302,"date":"2026-11-13T23:17:40","date_gmt":"2026-11-14T05:17:40","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2026\/11\/ai-rivals-tackle-one-of-physics-deepest-mathematical-challenges"},"modified":"2026-11-13T23:17:40","modified_gmt":"2026-11-14T05:17:40","slug":"ai-rivals-tackle-one-of-physics-deepest-mathematical-challenges","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2026\/11\/ai-rivals-tackle-one-of-physics-deepest-mathematical-challenges","title":{"rendered":"AI rivals tackle one of physics\u2019 deepest mathematical challenges"},"content":{"rendered":"\n<p><iframe title=\"AI rivals tackle one of physics\u2019 deepest mathematical challenges\" style=\"display: block; margin: 0 auto; width: 100%; aspect-ratio: 4\/3; object-fit: contain;\" src=\"https:\/\/www.youtube.com\/embed\/vMiY7zlBOFI?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope;\n   picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<p>One by one, artificial intelligence (AI) is felling some of the biggest trees in the mathematical forest. In September, OpenAI announced it had cracked the notoriously difficult <a href=\"https:\/\/www.science.org\/content\/article\/how-ai-math-breakthrough-ignited-controversy\">Navier-Stokes fluid dynamics problem<\/a>, one of math\u2019s seven Millennium Prize challenges. A month later, the company released more than 700 math papers, including a <a href=\"https:\/\/www.science.org\/content\/article\/ai-edges-closer-solving-riemann-hypothesis-one-math-s-hardest-problems\">major advance on the Riemann hypothesis<\/a>, another famous unsolved Millennium Prize Problem involving prime numbers. Its latest release, on 28 October, included a <a href=\"https:\/\/www.science.org\/content\/article\/ai-cracks-27-year-old-pillar-computer-science-openai-and-anthropic-claim\">refutation of a decades-old conjecture in computer science <\/a>\u2014as well as a proof that one of physics\u2019 most successful theories is on firm mathematical footing.<\/p>\n<p>Controversially, OpenAI did not release the 1147-page proof of the physics result, known as the 4D Yang-Mills existence problem. Instead, it appointed a committee of physicists and mathematicians headed by Nobel laureate David Gross to \u201cshepherd\u201d the result. On 10 November, the group released a <a href=\"https:\/\/github.com\/yang-mills-group\/YM\/blob\/main\/docs\/assessment-1.pdf\">validation<\/a> of a formalized version of the proof in Lean, a computer language that can check mathematical arguments against a set of axioms. Although it doesn\u2019t mean the still-unreleased proof is correct, it\u2019s a sign of its logical consistency.<\/p>\n<p>For physicists, the result is unlikely to change their day-to-day work: The Yang-Mills theory has already been remarkably successful at explaining the behavior of particles at accelerators such as the Large Hadron Collider. But important mysteries still remain, including how most of the mass of protons and neutrons arises, and why the quarks that make them up can never be found alone. A rigorous proof could offer fresh insights into these phenomena. \u201cMaybe there\u2019s something we\u2019re missing,\u201d says David Tong, a physicist at the University of Cambridge.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>One by one, artificial intelligence (AI) is felling some of the biggest trees in the mathematical forest. In September, OpenAI announced it had cracked the notoriously difficult Navier-Stokes fluid dynamics problem, one of math\u2019s seven Millennium Prize challenges. A month later, the company released more than 700 math papers, including a major advance on the [\u2026]<\/p>\n","protected":false},"author":662,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2229,48,6],"tags":[],"class_list":["post-247302","post","type-post","status-publish","format-standard","hentry","category-mathematics","category-particle-physics","category-robotics-ai"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/247302","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/users\/662"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=247302"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/247302\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=247302"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=247302"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=247302"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}