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

By Kit 小克 | AI Tool Observer | 2026-08-11

🇹🇼 Astra評測：OpenAI花2000美元解開10道數學懸案

Astra 是 OpenAI 尚未正式發表的下一代模型，8 月初它做了一件過去 AI 少見的事：用大約 2000 美元的運算成本，產出 10 道數學與理論電腦科學界懸而未決超過十年的難題解答，還附上 249 頁手稿與可機器驗證的 Lean 4 形式化證明。這不是又一次「跑分刷新高」，而是 LLM 第一次被主流數學家認真討論「這算不算原創研究」。

Astra 解開了哪些數學難題？

根據 OpenAI 公布的資料，Astra 這次交出的成績單包括：

首次明確構造出「非 sofic 群」（non-sofic group），解決自 1999 年 Gromov 提出 sofic 群概念以來、懸而未決近 27 年的問題
推翻 Connes 剛性猜想（von Neumann 代數領域的重要猜想）
證明 Ehrhart 體積猜想
解出 Erdős 問題集中 3 道題目，包括第 183 號多色 Ramsey 數問題

所有證明都上傳到 GitHub 的 openai/ten-proofs 倉庫，採 Apache 2.0 授權，Lean 4 的「sorry count」是 0——代表每一步推導都經過形式化系統逐行驗證，任何數學家都能自己下載檢查，不用相信 OpenAI 的一面之詞。

2000 美元的意義：便宜不代表灌水

過去用 AI 輔助證明數學定理的案例不少，但通常需要龐大算力或人工介入很深。Astra 這次用 GPT-5.6 Sol API 定價換算，10 道題目加起來只花 2000 美元，這個數字重點不在便宜，而在於證明「原創數學推理」正在變得可規模化、可複製。

爭議：Astra 有「抄」前人論文嗎？

Astra 的評測不能只看正面消息。菲爾茲獎得主 Timothy Gowers 公開表示，其中一項結果他會毫不猶豫推薦投稿頂級期刊，Erdős 問題集維護者 Thomas Bloom 也稱這是「大新聞」。但 Yeshiva University 數學家 Steven Miller 指出，Astra 的球體堆積證明疑似沿用他 2016 年論文的論證邏輯，卻沒有標註來源；劍橋大學的 Fournier-Facio 也在非 sofic 群證明中發現類似未標註引用的情形。

這揭露了形式化驗證的盲點：Lean 4 能保證「推導邏輯無誤」，但不能保證「問題的形式化敘述忠實呈現原本的懸案」，更不能保證有沒有沿用前人未公開致謝的思路。這是目前完全靠 OpenAI 自己把關的灰色地帶。

對開發者跟一般用戶代表什麼？

目前 Astra 沒有公開發布日期、沒有模型卡、沒有定價，純粹是研究預告，一般用戶還摸不到。但這次事件說明 LLM 正在跨過「解已知題型」邁向「原創研究貢獻」的門檻——同時也提醒我們，AI 產出的東西再漂亮，還是需要人類專家把關引用跟原創性，別急著神化。

好不好用，試了才知道。

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

Astra is OpenAI's unreleased next-generation model, and in early August it did something rare in AI: for roughly $2,000 in compute, it produced solutions to 10 problems in mathematics and theoretical computer science that had been open for over a decade, complete with a 249-page manuscript and machine-checkable Lean 4 proofs. This isn't another benchmark score — it's the first time mainstream mathematicians are seriously debating whether an LLM has done original research.

What Math Problems Did Astra Actually Solve?

According to OpenAI's release, Astra's results include:

The first explicit construction of a non-sofic group, settling a question open since Gromov introduced sofic groups in 1999 — nearly 27 years
Disproving Connes's rigidity conjecture on von Neumann algebras
Proving Ehrhart's volume conjecture
Resolving 3 problems from the Erdős problems catalogue, including problem 183 on multicolor Ramsey numbers

All proofs were published to the openai/ten-proofs GitHub repository under an Apache 2.0 license. The Lean 4 "sorry count" is zero — meaning every step is formally verified, and any mathematician can download and check the certificates independently rather than taking OpenAI's word for it.

Why $2,000 Matters More Than It Sounds

AI-assisted proofs aren't new, but they've usually required massive compute or heavy human intervention. At GPT-5.6 Sol API pricing, all 10 Astra proofs together cost about $2,000. The number isn't about being cheap — it's evidence that original mathematical reasoning is starting to scale.

The Controversy: Did Astra Copy Prior Work?

A fair Astra review can't just repeat the good news. Fields Medalist Timothy Gowers said he'd recommend one result for a top journal without hesitation, and Erdős catalogue curator Thomas Bloom called it "big news." But Yeshiva University mathematician Steven Miller says Astra's sphere-packing proof reused an argument from his own 2016 paper without attribution, and Cambridge's Fournier-Facio flagged a similar unattributed-prior-work pattern in the non-sofic groups result.

This exposes a real blind spot: formal verification guarantees the logic is correct, but it doesn't guarantee the formalized statement faithfully represents the original open problem, and it certainly doesn't guarantee proper credit to earlier work. Right now, that's a judgment call OpenAI is making about its own output — with no independent gatekeeper.

What This Means for Developers and Everyday Users

Astra has no public release date, no model card, and no pricing — this is a research preview, not a product you can touch yet. But it signals LLMs crossing from "solving known problem types" toward "original research contribution." It's also a reminder that no matter how polished AI output looks, human experts still need to check attribution and originality before we crown anything a breakthrough.

好不好用，試了才知道。 (You won't know until you try it.)

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