SponsoredAI 会员在线充值
Visit sponsor Chatgpt/Claude/Grok 会员24h在线自助充值 安全快速 稳定保障
奥创(Ultra)商城会员充值中心Loading…
SponsoredChatgpt/Claude/Grok 会员24h在线自助充值 安全快速 稳定保障
奥创(Ultra)商城会员充值中心
Sponsored本页公开展示实时样本、模型覆盖与响应时间。先用 5 元按量跑自己的 Claude Code/Codex 任务，成功后再决定是否长期使用。
ACS Gateway
Sponsored【腾讯云】WorkBuddy 全场景 AI 办公工作台，团队旗舰版低至198元/月
腾讯云
Sponsored人人可用的AI应用创作平台 自然语言交互，全栈应用搭建，伟大创意快速实现;个人版新用户注册送5000积分
阿里云OpenAI researchers say an internal version of its upcoming Astra model generated new results on 10 long-standing problems in mathematics and theoretical computer science, with machine-checkable Lean certificates. The claims remain dependent on primary publication and independent review.
OpenAI researchers have described an internal version of Astra, the company’s next major model, as producing 10 new results in mathematics and theoretical computer science. The areas mentioned include non-sofic groups, von Neumann algebras, high-dimensional sphere packing, cryptography, circuit complexity, and monochromatic triangles in multicolored graphs.
Posts attributed to OpenAI staff say that each result will be accompanied by a formal Lean certificate that can be checked by software. An OpenAI executive also estimated the total compute cost at about $2,000 using Sol API prices.
The available record is still largely made up of employee posts and secondary coverage. Until the underlying manuscript, repository, and detailed proofs are independently examined, the claims should be treated as an announced research result rather than a broadly verified set of breakthroughs.
Source review does not guarantee permanent accuracy. Consider the original source, observation time, and later corrections.
OpenAI says an internal version of its next major model, called Astra, has produced ten new results in mathematics and theoretical computer science. Each of the problems had been open for at least a decade. The company published a 249-page manuscript alongside machine-checkable Lean 4 certificates for every result on GitHub. The headline result is the first-ever explicit construction of a non-sofic group, resolving a central question in group theory that has stood since Mikhail Gromov introduced the concept of soficity in 1999. No mathematician had managed to prove or disprove whether non-sofic groups exist in the 27 years since. [...] OpenAI’s head of mathematics research, Sebastien Bubeck, confirmed the results on X, calling them “beautiful” and noting that each ships with a Lean certificate and a chain-of-thought walkthrough. The total compute cost for all ten solutions was roughly $2,000 at Sol API rates, according to OpenAI. The announcement lands against a backdrop of escalatin
Non-sofic groups exist A group is sofic if finite pieces of its multiplication table can be approximated (in a precise sense) by permutations of finite sets. This notion, introduced by Gromov around 1999 (with the name coined by Weiss), generalizes both amenable and residually finite groups. Gromov asked whether every countable discrete group is sofic. The question remained open for ~27 years. > yes, nonsofic groups exist: this statement is one of many new beautiful results proved by Astra, our next major model. > > We're releasing 10 such Astra proofs, complete with lean certificates and CoT walkthroughs for each of them. The results are wide-ranging, from von Neumann… > > — Sebastien Bubeck (@SebastienBubeck) August 1, 2026 Connes rigidity [...] Skip to content NextBigFuture.com # OpenAI Next Major Model Astra Solves Major Math Problems by Brian Wang Sebastien Bubeck of OpenAI says “yes, nonsofic groups exist”—as an example of “many new beautiful results” from Astra, nex
Dr Singularity / @dr\_singularity: What insane times we live in. I said a few days ago that the math Singularity is here. Now we have even more proof that it's really happening. OpenAI's upcoming Astra model family cracked 10 major unsolved problems across mathematics, quantum complexity, and theoretical computer science. Dean W. Ball / @deanwball: Everyone in the world will soon be able to use the model that made these breakthroughs for every problem they face in life, no matter how mundane, at a cost that will fall dramatically in a matter of months. I still struggle to get my head around this fact. Tibo / @thsottiaux: The week was for efficiency. The weekend is for 10 major breakthroughs in science. There will be signs. [...] Sebastien Bubeck / @sebastienbubeck: yes, nonsofic groups exist: this statement is one of many new beautiful results proved by Astra, our next major model. … Derya Unutmaz / @deryatr\_: Another major historical milestone in the age of AI has been a
Log inSign up ## Post user avatar Greg Brockman OpenAI @gdb ten significant advances in mathematics and theoretical computer science. solved using an internal version of Astra, our next major model, for a total cost of about $2000 at Sol API prices: user avatar Sebastien Bubeck @SebastienBubeck 23h yes, nonsofic groups exist: this statement is one of many new beautiful results proved by Astra, our next major model. We're releasing 10 such Astra proofs, complete with lean certificates and CoT walkthroughs for each of them. The results are wide-ranging, from von Neumann 7:39 AM · Aug 1, 2026707KViews user avatar 🚨 AI News | TestingCatalog @testingcatalog 22h Will it be a GPT-6 tier? 👀👀👀 7.3K user avatar 🩵BlueBeba🩵 @Blue\_Beba\_ 23h
Log inSign up Sebastien Bubeck user avatar Sebastien Bubeck I work on AI at OpenAI. Former VP AI and Distinguished Scientist at Microsoft. Seattle, WA sbubeck.com Joined January 2012 1,483 Following78.8K Followers RepliesRepliesArticlesArticlesMediaMedia Don't miss what's happening People on X are the first to know. Log inSign up Pinned user avatar Sebastien Bubeck @SebastienBubeck Aug 20, 2025 Claim: gpt-5-pro can prove new interesting mathematics. Proof: I took a convex optimization paper with a clean open problem in it and asked gpt-5-pro to work on it. It proved a better bound than what is in the paper, and I checked the proof it's correct. Details below. 7.3M user avatar Sebastien Bubeck @SebastienBubeck Jul 25 [...] 23K user avatar Sebastien Bubeck @SebastienBubeck Jul 21 True story. Very good safety work being done to enable the release of the unit distance model! user avatar Andrew Curran Jul 20 OpenAI h
Log inSign up ## Post user avatar Tibo @thsottiaux The week was for efficiency. The weekend is for 10 major breakthroughs in science. There will be signs. user avatar Sebastien Bubeck @SebastienBubeck 23h yes, nonsofic groups exist: this statement is one of many new beautiful results proved by Astra, our next major model. We're releasing 10 such Astra proofs, complete with lean certificates and CoT walkthroughs for each of them. The results are wide-ranging, from von Neumann 2:13 PM · Aug 1, 2026417.3KViews user avatar Abro @br\_huni 15h I know it was a reset only a few hours ago, but I already miss it😭😭 10K user avatar Bren @BrenBuilds 16h Tibo my wife said NO more resets this weekend plz 9.7K user avatar Lisan al Gaib [...] 9.7K user avatar Lisan al Gaib @scaling01 16h and what about next week? 3.8K # Join the conversation Read 336 more replies