{"id":52006,"date":"2026-05-25T13:31:03","date_gmt":"2026-05-25T17:31:03","guid":{"rendered":"https:\/\/mjtsai.com\/blog\/?p=52006"},"modified":"2026-05-25T13:31:03","modified_gmt":"2026-05-25T17:31:03","slug":"openai-models-proof-of-erds-unit-distance-problem","status":"publish","type":"post","link":"https:\/\/mjtsai.com\/blog\/2026\/05\/25\/openai-models-proof-of-erds-unit-distance-problem\/","title":{"rendered":"OpenAI Model&rsquo;s Proof of Erd&#x151;s Unit Distance Problem"},"content":{"rendered":"<p><a href=\"https:\/\/openai.com\/index\/model-disproves-discrete-geometry-conjecture\/\">OpenAI<\/a> (<a href=\"https:\/\/news.ycombinator.com\/item?id=48212493\">Hacker News<\/a>):<\/p>\n<blockquote cite=\"https:\/\/openai.com\/index\/model-disproves-discrete-geometry-conjecture\/\">\n<p>This proof is an important milestone for the math and AI communities. It marks the first time that a prominent open problem, central to a subfield of mathematics, has been solved autonomously by AI. It also demonstrates the depth of reasoning these systems now support.<\/p>\n<p>[&#8230;]<\/p>\n<p>The proof is available <a href=\"https:\/\/cdn.openai.com\/pdf\/74c24085-19b0-4534-9c90-465b8e29ad73\/unit-distance-proof.pdf\">here<\/a>. The companion paper by leading external mathematicians is available <a href=\"https:\/\/cdn.openai.com\/pdf\/74c24085-19b0-4534-9c90-465b8e29ad73\/unit-distance-remarks.pdf\">here<\/a>. You can find an abridged version of the model&rsquo;s chain of thought <a href=\"https:\/\/cdn.openai.com\/pdf\/1625eff6-5ac1-40d8-b1db-5d5cf925de8b\/unit-distance-cot.pdf\">here <\/a>.<\/p>\n<\/blockquote>","protected":false},"excerpt":{"rendered":"<p>OpenAI (Hacker News): This proof is an important milestone for the math and AI communities. It marks the first time that a prominent open problem, central to a subfield of mathematics, has been solved autonomously by AI. It also demonstrates the depth of reasoning these systems now support. [&#8230;] The proof is available here. The [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"apple_news_api_created_at":"2026-05-25T17:31:07Z","apple_news_api_id":"5e9088ee-4f6a-45fa-9ea4-cddfd00b97dc","apple_news_api_modified_at":"2026-05-25T17:31:07Z","apple_news_api_revision":"AAAAAAAAAAD\/\/\/\/\/\/\/\/\/\/w==","apple_news_api_share_url":"https:\/\/apple.news\/AXpCI7k9qRfqepM3f0AuX3A","apple_news_coverimage":0,"apple_news_coverimage_caption":"","apple_news_is_hidden":false,"apple_news_is_paid":false,"apple_news_is_preview":false,"apple_news_is_sponsored":false,"apple_news_maturity_rating":"","apple_news_metadata":"\"\"","apple_news_pullquote":"","apple_news_pullquote_position":"","apple_news_slug":"","apple_news_sections":"\"\"","apple_news_suppress_video_url":false,"apple_news_use_image_component":false,"footnotes":""},"categories":[2],"tags":[1351,259,2361],"class_list":["post-52006","post","type-post","status-publish","format-standard","hentry","category-technology","tag-artificial-intelligence","tag-math","tag-openai"],"apple_news_notices":[],"_links":{"self":[{"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/posts\/52006","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/comments?post=52006"}],"version-history":[{"count":1,"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/posts\/52006\/revisions"}],"predecessor-version":[{"id":52007,"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/posts\/52006\/revisions\/52007"}],"wp:attachment":[{"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/media?parent=52006"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/categories?post=52006"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/tags?post=52006"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}