{"id":47409,"date":"2026-05-21T20:54:08","date_gmt":"2026-05-21T20:54:08","guid":{"rendered":"https:\/\/www.europesays.com\/ai\/47409\/"},"modified":"2026-05-21T20:54:08","modified_gmt":"2026-05-21T20:54:08","slug":"openai-makes-breakthrough-in-80-year-old-math-problem-with-ingenious-ideas","status":"publish","type":"post","link":"https:\/\/www.europesays.com\/ai\/47409\/","title":{"rendered":"OpenAI makes breakthrough in 80-year-old math problem with ‘ingenious ideas’"},"content":{"rendered":"

OpenAI <\/a>claims its model solved a famous geometry problem that has eluded the world\u2019s greatest mathematicians for 80 years \u2014 a breakthrough hailed as evidence of the bot\u2019s creativity and \u201cintuition.\u201d<\/p>\n

The company<\/a> published its findings on Wednesday, demonstrating that one of its models cracked the planar unit distance problem, first posed by legendary Hungarian mathematician Paul Erd\u0151s in 1946. <\/p>\n

The puzzle poses a deceptively simple question that boils down to: How many pairs of dots on a piece of paper can be the same distance apart?<\/p>\n

OpenAI said one of its models helped disprove a conjecture centered on an 80-year-old geometry problem. OpenAI<\/p>\n

The prevailing theory suggested that a \u201csquare grid\u201d was the key to creating the maximum number of pairs listed in the problem, and Erd\u0151s himself proposed that the number of pairs could increase only slightly faster than the number of dots as more points were added.<\/p>\n

OpenAI\u2019s work, however, disproved the idea and proposed its own layout.<\/p>\n

University of Toronto mathematician Arul Shankar, one of the experts who reviewed OpenAI\u2019s work, went as far as to suggest the model used its own \u201cintuition\u201d to arrive at the surprising solution.<\/p>\n

\u201cIn my opinion, this paper demonstrates that current AI models go beyond just helpers to human mathematicians \u2013 they are capable of having original, ingenious ideas, and then carrying them out to fruition,\u201d he said in a statement.<\/p>\n

Fellow Toronto professor Jacob Tsimerman said he was wowed by the results, noting that he had once tried to disprove the distance problem himself to no avail.\u00a0<\/p>\n

it was long believed that a \u201csquare grid\u201d was the ideal method to demonstrate the planar unit distance problem. OpenAI<\/p>\n

\u201cIt is definitely an intimidating construction to see through, even if you know what is going on, and even harder to go play for yourself,\u201d he noted.\u00a0\u00a0<\/p>\n

OpenAI has repeatedly touted its model\u2019s use to help solve math problems and prove or disprove decades-old conjectures that were previously deemed too complicated to approach.<\/p>\n

The breakthrough came just days after it was revealed that OpenAI\u2019s ChatGPT<\/a> was used to help solve another decades-old problem, allowing the mathematician who first thought up the solution to see his \u201csensational\u201d idea proven right.<\/p>\n

Michel Talagrand was thrilled to find his \u201cconvexity conjecture\u201d proven true, with researchers initially using ChatGPT for help. Getty Images<\/p>\n

In 1995, renowned French mathematician Michel Talagrand, 74, made a sweeping statement, claiming that in a seemingly endless and scattered plane littered with points across innumerable dimensions, simple, orderly shapes will appear.<\/p>\n

But what Talagrand believed would be a herculean task to prove or disprove his so-called \u201cconvexity conjecture\u201d came to an abrupt end last week after mathematicians at the California Institute of Technology<\/a> used OpenAI\u2019s ChatGPT to play out his theory.<\/p>\n

\u201cThis is the most extraordinary result of my entire life,\u201d Talagrand told Scientific America about seeing the answer. \u201cThe proper word is \u2018sensational.\u2019\u201d<\/p>\n

ChatGPT and OpenAI\u2019s models have been repeatedly used to try and prove or disprove large-scale math problem. REUTERS<\/p>\n

At the heart of Talagrand\u2019s conjecture was the idea that even when facing a billion dimensions, one could draw a simple shape that manages to encircle an enumerable number of points scattered throughout them.<\/p>\n

The French mathematician himself was the first to pour cold water on his own theory, describing it as a \u201cshot in the dark\u201d and saying that, if true, it would amount to nothing less than a \u201ctotal miracle.\u201d<\/p>\n

Talagrand had even put up a $2,000 reward for years for anyone who could take on the challenge, but a collector never came.<\/p>\n

That is, until Antoine Song and his student, Dongming (Merrick) Hu, used ChatGPT to translate Talagrand\u2019s problem and demonstrate that he was right.<\/p>\n

The duo eventually worked with Stefan Tudose, a Princeton mathematician, on the final proof, choosing to exclude ChatGPT due to uncertainties in the language models\u2019 \u201cthought process.\u201d\u00a0\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"OpenAI claims its model solved a famous geometry problem that has eluded the world\u2019s greatest mathematicians for 80…\n","protected":false},"author":2,"featured_media":47410,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[580,1785,157,1246],"class_list":["post-47409","post","type-post","status-publish","format-standard","has-post-thumbnail","category-openai","tag-chatgpt","tag-math","tag-openai","tag-world-news"],"_links":{"self":[{"href":"https:\/\/www.europesays.com\/ai\/wp-json\/wp\/v2\/posts\/47409","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=47409"}],"version-history":[{"count":0,"href":"https:\/\/www.europesays.com\/ai\/wp-json\/wp\/v2\/posts\/47409\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.europesays.com\/ai\/wp-json\/wp\/v2\/media\/47410"}],"wp:attachment":[{"href":"https:\/\/www.europesays.com\/ai\/wp-json\/wp\/v2\/media?parent=47409"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.europesays.com\/ai\/wp-json\/wp\/v2\/categories?post=47409"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.europesays.com\/ai\/wp-json\/wp\/v2\/tags?post=47409"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}