![\"OpenAI](\"https:\/\/dataconomy.com\/wp-content\/uploads\/2026\/01\/OpenAI_s_GPT_5.2_solved_complex_math_problems.jpeg\" "\\"OpenAI")
<\/p>\n<\/p>\n
OpenAI\u2019s latest model demonstrated an unexpected capability in solving high-level mathematical problems, according to testing conducted by software engineer and former quant researcher Neel Somani.<\/p>\n
Somani observed the model generate a full solution after 15 minutes of processing a problem in ChatGPT, subsequently formalizing the proof with the Harmonic tool, confirming its accuracy. He stated he aimed to establish a baseline for large language models\u2019 (LLMs) capacity to solve open mathematical problems.<\/p>\n
The model\u2019s chain of thought invoked mathematical axioms including Legendre\u2019s formula, Bertrand\u2019s postulate, and the Star of David theorem. It located a 2013 Math Overflow post by Harvard mathematician Noam Elkies, which offered a similar problem\u2019s solution, but ChatGPT\u2019s final proof differed and provided a more complete solution to a version of a problem posed by mathematician Paul Erd\u0151s.<\/p>\n
Since the release of GPT 5.2, which Somani described as \u201canecdotally more skilled at mathematical reasoning than previous iterations,\u201d a growing volume of solved problems has raised inquiries about LLMs\u2019 ability to advance human knowledge. Somani focused on the Erd\u0151s problems, a collection of over 1,000 conjectures maintained online, which vary in subject matter and difficulty.<\/p>\n
The first autonomous solutions to these problems emerged in November from AlphaEvolve, a Gemini-powered model. More recently, Somani and others have found GPT 5.2 adept with high-level mathematics. Since December, 15 problems on the Erd\u0151s website have shifted from \u201copen\u201d to \u201csolved,\u201d with 11 solutions crediting AI models.<\/p>\n
Mathematician Terence Tao, on his GitHub page, noted eight problems where AI models made meaningful autonomous progress and six cases where progress involved locating and building on prior research. Tao conjectured on Mastodon that AI systems\u2019 scalable nature makes them \u201cbetter suited for being systematically applied to the \u2018long tail\u2019 of obscure Erd\u0151s problems, many of which actually have straightforward solutions,\u201d adding that \u201cmany of these easier Erd\u0151s problems are now more likely to be solved by purely AI-based methods than by human or hybrid means.\u201d<\/p>\n
A driving force in this advancement is a shift towards formalization, a labor-intensive process for verifying and extending mathematical reasoning. While not requiring AI, new automated tools have simplified this process. The open-source proof assistant Lean, developed at Microsoft Research in 2013, has gained wide use for formalizing proofs, and AI tools like Harmonic\u2019s Aristotle aim to automate much of this work.<\/p>\n
Tudor Achim, Harmonic\u2019s founder, stated the engagement of mathematicians and computer science professors with AI tools held more significance than the number of solved Erd\u0151s problems. Achim said, \u201cThese people have reputations to protect, so when they\u2019re saying they use Aristotle or they use ChatGPT, that\u2019s real evidence.\u201d<\/p>\n
Featured image credit<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":" OpenAI\u2019s latest model demonstrated an unexpected capability in solving high-level mathematical problems, according to testing conducted by software engineer and former quant researcher Neel Somani. Somani observed the model generate a full solution after 15 minutes of processing a problem in ChatGPT, subsequently formalizing the proof with the Harmonic tool, confirming its accuracy. He stated […]<\/p>\n","protected":false},"author":1,"featured_media":43390,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[37],"tags":[],"class_list":{"0":"post-43389","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-technologies"},"_links":{"self":[{"href":"https:\/\/agooka.com\/news\/wp-json\/wp\/v2\/posts\/43389","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/agooka.com\/news\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/agooka.com\/news\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/agooka.com\/news\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/agooka.com\/news\/wp-json\/wp\/v2\/comments?post=43389"}],"version-history":[{"count":0,"href":"https:\/\/agooka.com\/news\/wp-json\/wp\/v2\/posts\/43389\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/agooka.com\/news\/wp-json\/wp\/v2\/media\/43390"}],"wp:attachment":[{"href":"https:\/\/agooka.com\/news\/wp-json\/wp\/v2\/media?parent=43389"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/agooka.com\/news\/wp-json\/wp\/v2\/categories?post=43389"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/agooka.com\/news\/wp-json\/wp\/v2\/tags?post=43389"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}