OpenAI的Astra模型花约2000美元解出10个数学难题，证明还带Lean验证，硬核得让人服气。
OpenAI下一代模型Astra的内部版本解决了10个数学与理论计算机科学问题，总成本约2000美元。官方发布了10个Astra证明，每个都附带Lean证书和思维链走查。成果包括反驳Connes刚性猜想、改进高维球堆积界限、给出电路复杂度新界限，并确认nonsofic群存在。另外还改进了多色图中单色三角形的界限。
ten significant advances in mathematics and theoretical computer science. solved using an internal ...
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: Sebastien Bubeck @SebastienBubeck 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 algebras (disproof of Connes' Rigidity Conjecture) to better bounds for high dimensional sphere packing, for circuit complexity, for monochromatic triangles in multicolored graphs, and more. More thoughts here: openai.com/index/ten-adva… 🔗 View Quoted Tweet 💬 32 🔄 16 ❤️ 113 👀 6860 📊 31 ⚡