{"id":92212,"date":"2026-07-01T16:15:37","date_gmt":"2026-07-01T16:15:37","guid":{"rendered":"https:\/\/www.europesays.com\/ai\/92212\/"},"modified":"2026-07-01T16:15:37","modified_gmt":"2026-07-01T16:15:37","slug":"claudes-solution-to-decades-long-math-mystery-is-essentially-correct-physicists-say","status":"publish","type":"post","link":"https:\/\/www.europesays.com\/ai\/92212\/","title":{"rendered":"Claude’s Solution to Decades-Long Math Mystery Is ‘Essentially Correct,’ Physicists Say"},"content":{"rendered":"

As typically is the case with AI, whether it truly adds any value to human work depends on the user\u2019s intentions<\/a>. For science, that means that, technically, AI can try offering an answer to a question, but it\u2019s up to the experts to check its work and decide if there\u2019s more to be explored.<\/p>\n

A couple years ago, physicists Giorgio Parisi and Francesco Zamponi reached a stalemate in their attempt to solve the jamming problem, a mathematical issue in physics concerning systems that suddenly turn rigid while remaining disordered. The pair from La Sapienza University of Rome in Italy tried asking the AI model Claude to come up with a solution. Claude\u2019s initial proof reportedly had a lot of errors, but the underlying approach appeared to be a step in the right direction. Parisi and Zamponi pursued this idea and landed on a surprisingly simple resolution, showing their reasoning in a paper<\/a> published today in the Journal of Statistical Mechanics: Theory and Experiment.<\/p>\n

\u201cQuite quickly, Claude came up with an initial idea that was essentially correct,\u201d Zamponi said in a statement<\/a>. \u201cThe answer was right there, and we simply hadn\u2019t seen it.\u201d<\/p>\n

A mathematical traffic jam \"GranularA simple representation of jamming due to arch formation in a granular material. \u00a9 Gsrdzl via Wikimedia Commons <\/p>\n

In physics, jamming<\/a> refers to a process in which density increases in a granular material (think of a children\u2019s ball pit), resulting in a system becoming rigid, sort of like a \u201ctraffic jam\u201d of particles. Back in 2014, Parisi, Zamponi, and other collaborators mathematically described<\/a> jamming, finding in the process that two parameters of the model would always add up to one.<\/p>\n

\u201cThe result emerged clearly from numerical calculations from the very beginning, but no one could explain why it was true,\u201d according to the statement. \u201cFor years, researchers searched for a mathematical proof of the relation, convinced that some deeper structure of the theory lay behind its apparent simplicity.\u201d<\/p>\n

A fresh pair of eyes, kind of <\/p>\n

With quick advances in generative AI models, Parisi and Zamponi wondered if Claude\u2019s relatively more advanced mathematical reasoning abilities could offer anything useful for the jam in the jamming conjecture. Initially, the pair asked Claude to replicate the group\u2019s numerical calculations, then challenged the AI to try and come up with a proof for the two parameters always adding up to one.<\/p>\n

\u201cWe were hoping this would reveal some new understanding of the equations,\u201d Zamponi explained.<\/p>\n

In short, the proof \u201ccontained errors and required several rounds of verification and revision by the authors.\u201d However, the researchers were able to build upon the basic premises of Claude\u2019s suggestions to arrive at a more solid proof.<\/p>\n

AI and \u2018impossible\u2019 problems <\/p>\n

AI\u2019s increased use in mathematics seems to invoke both excitement and concern for experts. In an interview with Gizmodo<\/a>, Princeton mathematician Will Sawin said that AI is definitely effective at searching the literature and finding patterns that humans might not have noticed before. In other words, it\u2019s not necessarily that an AI model generated an entirely novel idea that humans couldn\u2019t have found on their own, at least for now.<\/p>\n

Something similar appears to have been the case for Parisi and Zamponi. In the paper, they write that it\u2019s \u201cdifficult to say\u201d why they hadn\u2019t realized what Claude seemingly did. However, the human pair admitted that they were \u201clooking for something deeper\u201d and overlooked a more \u201cconceptually simple case,\u201d which Claude\u2019s suggestion pointed them towards.<\/p>\n","protected":false},"excerpt":{"rendered":"As typically is the case with AI, whether it truly adds any value to human work depends on…\n","protected":false},"author":2,"featured_media":92213,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8],"tags":[24,53,3154,182,5809,37123],"class_list":["post-92212","post","type-post","status-publish","format-standard","has-post-thumbnail","category-anthropic","tag-ai","tag-anthropic","tag-anthropic-claude","tag-claude","tag-mathematics","tag-theoretical-physics"],"_links":{"self":[{"href":"https:\/\/www.europesays.com\/ai\/wp-json\/wp\/v2\/posts\/92212","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.europesays.com\/ai\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.europesays.com\/ai\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/ai\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/ai\/wp-json\/wp\/v2\/comments?post=92212"}],"version-history":[{"count":0,"href":"https:\/\/www.europesays.com\/ai\/wp-json\/wp\/v2\/posts\/92212\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/ai\/wp-json\/wp\/v2\/media\/92213"}],"wp:attachment":[{"href":"https:\/\/www.europesays.com\/ai\/wp-json\/wp\/v2\/media?parent=92212"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.europesays.com\/ai\/wp-json\/wp\/v2\/categories?post=92212"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.europesays.com\/ai\/wp-json\/wp\/v2\/tags?post=92212"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}