OpenAI Astra評測：2000美元解開10道數學懸案 | OpenAI Astra Review: $2K Solves 10 Open Math Problems

8月 24, 2026

By Kit 小克 | AI Tool Observer | 2026-08-25

🇹🇼 OpenAI Astra評測：2000美元解開10道數學懸案

OpenAI Astra評測：這個目前仍未正式發表的內部模型，用大約2000美元的運算成本，解開了10道懸而未決超過十年的數學與理論電腦科學難題，還把每一題的形式化證明公開在GitHub上，任何人都能用Lean 4驗證。這不是又一次「AI寫論文」的公關稿，而是第一次有主流大型語言模型把答案交給機器去逐行驗證真偽。

Astra評測到底解了什麼

這10道題目橫跨群論、von Neumann代數、高維幾何、量子複雜度、格密碼學與極值組合數學，其中最受矚目的是27年來首次構造出非sofic群(non-sofic group)的具體例子——這是理論電腦科學圈子裡長期卡關的經典難題。OpenAI連同結果一起發布了249頁技術手冊與62頁「怎麼想出來的」說明，證明過程不是黑箱。

為什麼Lean證明是關鍵

Lean 4是一套以型別理論為基礎的形式化證明語言，每一步推導都要通過一個很小、經過驗證的核心kernel逐步檢查。結果只有兩種：編譯通過，或編譯失敗，沒有模糊地帶。OpenAI公開的repo裡「sorry」計數是零——代表沒有任何一步是用佔位符蒙混過去的。這直接回答了外界對LLM數學能力最大的質疑：你怎麼知道它不是在唬爛？

誠實看待：這代表AI會做研究了嗎？

還不算發現新數學：這10題都是已知的公開問題，Astra是解題而不是提出問題，跟人類數學家自己找方向仍有差距
模型還沒公開：Astra目前只是OpenAI內部測試版，一般開發者拿不到，實際落地能力未知
成本數字有行銷成分：2000美元只算最終那次成功的運算，不含前期研發與失敗嘗試的隱藏成本
形式化驗證是真本事：把證明轉成Lean可驗證格式，這一步本身就很難，值得肯定

對開發者跟研究者來說，Astra評測比較實際的意義是：AI輔助形式化證明的門檻正在快速下降，未來審核AI生成的數學或程式邏輯，Lean這類可驗證工具會變成標配，而不是選配。

好不好用，試了才知道。

🇺🇸 OpenAI Astra Review: $2K Solves 10 Open Math Problems

OpenAI Astra Review: an internal, not-yet-released model just solved 10 math and theoretical computer science problems that had stayed open for over a decade — for roughly $2,000 in compute — and published machine-checkable Lean 4 proofs for every single one on GitHub. This isn't another AI-writes-a-paper press release; it's the first time a frontier LLMs math claims were handed to a formal verifier instead of a peer-review committee.

What Astra Actually Solved

The 10 results span group theory, von Neumann algebras, high-dimensional geometry, quantum complexity, lattice cryptography, and extremal combinatorics. The headline result is the first explicit construction of a non-sofic group in 27 years — a problem that had stumped the theoretical CS community for decades. OpenAI released a 249-page technical manuscript alongside a 62-page account of how the arguments were assembled, so the process is not a black box.

Why the Lean Proofs Matter More Than the Headline

Lean 4 is a formal proof language built on type theory, where every deduction step is checked line-by-line by a small, trusted kernel. There is no partial credit — a proof either compiles or it fails. The published repository reports a sorry count of zero, meaning no step was left unproven or hand-waved. That directly answers the biggest skeptic question about LLM math claims: how do you know it is not bluffing?

The Honest Take: Is This AI Doing Research Yet?

Not new mathematics, technically — all 10 problems were already known and stated by humans; Astra solved them, it did not discover them
Astra itself is not available — this is an internal preview, not a product; nobody outside OpenAI can test it yet
The $2,000 figure is cherry-picked — it covers only the successful final run, not the R&D and failed attempts behind it
The formalization work is genuinely hard — translating a proof into Lean-verifiable form is itself a real engineering achievement worth crediting

The more practical takeaway for developers and researchers: AI-assisted formal verification just got a lot cheaper, and tools like Lean are about to become standard practice for auditing AI-generated math and logic — not an optional extra.

好不好用，試了才知道。

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