OpenAI Astra評測：砸2000美元解開10道數學懸案 | OpenAI Astra Review: AI Solves 10 Unsolved Math Problems

8月 07, 2026

By Kit 小克 | AI Tool Observer | 2026-08-08

🇹🇼 OpenAI Astra評測：砸2000美元解開10道數學懸案

OpenAI Astra是OpenAI下一代旗艦模型的內部代號，8月初一次丟出震撼彈：用它解開了10道懸而未決超過10年的數學與理論電腦科學難題，總運算成本只花了約2000美元（以GPT-5.6 Sol API計費）。這則消息在Hacker News、X和數學圈同步發燒，因為過去AI「解數學題」通常是套用已知方法算得快，這次不一樣——是產出人類還沒證出來的新結果。

Astra到底解出了什麼

OpenAI公布的10個成果橫跨高維幾何、編碼理論、群論、量子複雜度、格密碼學、算子代數與極端組合數學。其中最受矚目的三項：

非可及群（non-sofic group）的顯式構造——這是Mikhail Gromov在1999年提出可及性概念以來懸而未解的問題
推翻Connes剛性猜想，這是馮紐曼代數領域的重要猜想
高維球堆積密度的新上界，把1978年就沒進展的紀錄往前推進到Cohn-Elkies門檻

此外還解出了Erdős問題183（多色Ramsey數）等三道Erdős問題目錄裡的題目。

怎麼確定不是幻覺出來的假證明

這才是Astra這次公告真正值得注意的地方：OpenAI沒有只丟一份249頁的手稿，而是同步釋出Lean 4形式化證明，放在GitHub上以Apache 2.0授權公開，整個repo的「sorry」計數是零——代表所有10道證明的每一步都經過機器驗證，不是模型自己說了算，也不需要數學家肉眼一步步覆核每個推導。這對「LLM會一本正經編造證明」的長期質疑，算是給了一個可驗證的回應。

誠實看待：這代表什麼、不代表什麼

先講清楚：Astra還沒有公開發布，一般人現在用不到。這次公告更像是OpenAI在為下一代模型的正式上市鋪路，挑的10題也是精心挑選過、已知「有機會被推進」的方向，不是隨機出一道題目給AI解。換句話說，這不等於AI已經能像數學家一樣「自主研究」，比較接近在特定、範圍明確的形式化系統裡，高效率地搜索與組合已知技巧。但形式化驗證這一步做得紮實，值得數學圈認真看待，而不是又一次「AI又要取代誰」的行銷話術。

好不好用，試了才知道

🇺🇸 OpenAI Astra Review: AI Solves 10 Unsolved Math Problems

OpenAI Astra, the internal codename for OpenAI's next flagship model, dropped a genuine surprise in early August: it produced solutions to 10 open problems in mathematics and theoretical computer science that had sat unsolved for over a decade — for a total compute cost of roughly $2,000 at GPT-5.6 Sol API rates. The story lit up Hacker News, X, and math circles fast, because this isn't AI applying known techniques faster — it's new results humans hadn't proven yet.

What Astra Actually Solved

The 10 results span high-dimensional geometry, coding theory, group theory, quantum complexity, lattice cryptography, operator algebras, and extremal combinatorics. Three stand out:

An explicit construction of a non-sofic group, settling a question open since Mikhail Gromov defined soficity in 1999
Disproving Connes rigidity conjecture, a major open question in von Neumann algebra theory
A new upper bound on high-dimensional sphere-packing density, pushing past a record that had stood since 1978, down to the Cohn-Elkies threshold

Astra also cracked three problems from Paul Erdos catalog, including Problem 183 on multicolor Ramsey numbers.

How We Know It Is Not Hallucinated Proofs

This is the part worth paying attention to: instead of just publishing a 249-page manuscript and asking the world to trust it, OpenAI released Lean 4 formal proof certificates on GitHub under Apache 2.0. The repos sorry count is zero — meaning every step of all 10 proofs is machine-verified, not just model-asserted. That is a real, checkable answer to the standing complaint that LLMs confidently fabricate mathematical arguments.

The Honest Take

Astra itself is not publicly available yet — this is a preview, not a product launch. The 10 problems were also handpicked as ones OpenAI researchers believed were within reach, not a random sample of open math. So this is not proof that AI can now do autonomous mathematical research the way a human mathematician does; it is closer to highly efficient search-and-recombination of known techniques inside a well-defined formal system. Still, the rigor of the verification step is real and worth taking seriously — this is a step above the usual AI will replace X marketing cycle.

The only way to know if it is good — try it yourself.

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