{"id":"openai-math/The-irrationality-exponent-of-pi-is-2","pdf":"https://github.com/openai/math/blob/main/preprints/The-irrationality-exponent-of-pi-is-2-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-irrationality-exponent-of-pi-is-2-September-24-2026","tags":["number-theory","diophantine-approximation","irrationality-measure"],"score":0,"title":"The irrationality exponent of pi is 2","domain":"Number theory","family":"017","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.NT","summary":"We prove the conjecture that the irrationality exponent of π is 2. As a consequence, the classical Flint–Hills series $`\\sum_{n\\ge1}1/(n^3\\sin^2 n)`$ converges, with angles in radians.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":2,"published":"2026-09-24","reactions":{},"discussion":[{"url":"https://galoisrepresentations.org/2026/10/08/a-brief-digest-of-some-new-openai-results/#:~:text=the%20close%20similarity%20between%20the%20arguments%20here%20and%20Roth%E2%80%99s%20argument%20for%20algebraic%20irrationals","kind":"web","site":"galoisrepresentations.org","text":"the close similarity between the arguments here and Roth’s argument for algebraic irrationals. Again, this is something that I hope we shall address at our upcoming conference. Broadly speaking, for the problems in the Langlands program that I am interested in, while OpenAI did an amazing job,…","added":"2026-10-24","title":"A Brief Digest of Some New OpenAI Results | Persiflage","author":"Persiflage"},{"url":"https://www.youtube.com/watch?v=QNSbI3mrrhc","kind":"web","site":"youtube.com","text":"Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube.","added":"2026-10-24","title":"OpenAI Claimed 722 Math Breakthroughs. Did Any Hold Up?","author":"Nontrivial"}],"formalized":false,"family_title":"The irrationality exponent of π is 2"}