OpenAI Astra評測：AI解開10道數學懸案僅花2000美元 | OpenAI Astra Review: AI Solves 10 Math Problems for $2K
By Kit 小克 | AI Tool Observer | 2026-08-18
🇹🇼 OpenAI Astra評測：AI解開10道數學懸案僅花2000美元
OpenAI Astra是OpenAI尚未正式發布的下一代模型，最近它做了一件比任何跑分都更硬核的事：解開10道數學與理論電腦科學的懸案難題，每題平均只花約200美元運算成本，10題加總不到2000美元。這不是又一次「刷榜」，而是AI第一次被拿去做真正的原創研究，而且結果全部附上可機器驗證的證明。
OpenAI Astra是什麼？為什麼會引爆討論？
Astra是OpenAI內部代號的下一代模型，尚未決定要叫GPT-5.7還是GPT-6，也還沒有公開發布時程。這次OpenAI破例先公布Astra解出的10道數學研究成果，等於是用「解決人類十年沒人解得出的問題」來當作模型能力的證明，而不是常見的Benchmark分數。
Astra解開了哪些數學難題？
這10道題目大多停滯十年以上，涵蓋純數學到密碼學的多個領域，包括：
- 非sofic群的明確構造：解決自1999年Gromov提出sofic概念以來一直懸而未決的問題
- 高維球體堆積密度的上界，是1978年以來首次改進
- 3道題目來自Erdős數學問題集，包括Erdős問題183（多色Ramsey數）
- permanent計算的電路複雜度下界，理論電腦科學核心難題之一
- 雙人量子遊戲的平行重複定理
- 後量子格密碼學相關進展
為什麼10道題只花2000美元？可信嗎？
關鍵在於Lean 4形式化驗證：Astra產出的每個證明都附上Lean證明證書，OpenAI在GitHub上公開了249頁手稿與程式碼，整個代碼庫的「sorry」（未完成證明的佔位符）計數為零，代表每一步都經過機器嚴格驗證，不是模型自己說了算。運算成本則是以GPT-5.6 Sol的API定價計算，平均每題約200美元。
Astra什麼時候會正式推出？
OpenAI目前尚未決定Astra會以GPT-5.7還是GPT-6的名義發布，也沒有公開時間表，這次等於是「劇透」研究能力，正式產品可能還要一段時間。
Kit小克怎麼看：這對一般用戶和開發者有什麼意義？
老實說，這個消息很驚艷，但也要保持清醒。OpenAI公布的是「精選後成功的10題」，沒有人知道Astra嘗試了多少題失敗、失敗率多高——這是典型的倖存者偏差展示法，跟拿模型去解一整批隨機數學題的真實研究情境不一樣。另外，這些題目雖然懸而未決十年，但未必是數學界公認最難、最重要的問題，媒體標題容易把「十年沒進展」直接等同於「極度困難」，實際上兩者不完全劃等號。
真正有意義的訊號是：形式化驗證+AI推理的組合開始能產出人類專家認可、機器可驗證的原創數學成果，這對數學研究、密碼學、形式化證明社群是實質利多，值得追蹤Astra正式發布後開放給一般用戶測試的表現。目前它還不是一個你我能直接用的工具，先別急著期待它能幫你解作業或寫論文。
好不好用，試了才知道。
🇺🇸 OpenAI Astra Review: AI Solves 10 Math Problems for $2K
OpenAI Astra, OpenAI's not-yet-released next-generation model, just did something more impressive than another benchmark score: it solved 10 open problems in mathematics and theoretical computer science, each stuck for a decade or more, at a total inference cost of roughly $2,000 — about $200 per problem. This isn't leaderboard chasing; it's AI producing original research with machine-checkable proofs attached.
What Is OpenAI Astra, and Why the Buzz?
Astra is OpenAI's internal codename for its next major model — it hasn't been decided whether it ships as GPT-5.7 or GPT-6, and there's no public release date. Instead of a benchmark chart, OpenAI chose to prove Astra's capability by publishing 10 real math results that human experts hadn't cracked in years.
Which Math Problems Did Astra Solve?
Most of these problems saw zero progress for at least a decade, spanning pure math to cryptography:
- An explicit construction of a non-sofic group, settling a question open since Gromov introduced soficity in 1999
- The first improvement to the upper bound on high-dimensional sphere-packing density since 1978
- Three results from the Erdős problem catalogue, including Erdős problem 183 on multicolored Ramsey numbers
- New lower bounds on the circuit complexity of computing the permanent
- A parallel repetition theorem for two-player quantum games
- Advances in post-quantum lattice-based cryptography
How Can 10 Problems Cost Just $2,000?
The trick is Lean 4 formal verification. Every Astra proof shipped with a Lean certificate, and OpenAI published a 249-page manuscript plus proof code on GitHub with zero "sorry" placeholders — meaning every step across all 10 proofs is machine-verified, not just self-reported. The $2,000 figure is compute cost at GPT-5.6 Sol API pricing, averaging about $200 per problem.
When Will Astra Actually Launch?
OpenAI hasn't settled on whether Astra becomes GPT-5.7 or GPT-6, and no release date has been announced — this drop is a capability preview, not a product launch.
Kit's Take: What Does This Mean for You?
This is genuinely impressive, but stay grounded. OpenAI published the 10 problems that succeeded — nobody knows how many attempts failed or what the success rate actually was. That's a curated showcase, not the same as turning a model loose on a random batch of open problems. Also, "no progress for a decade" doesn't automatically mean "the hardest problems in math" — headlines tend to blur that distinction.
The real signal here is that formal verification combined with AI reasoning can now produce original math results that experts accept and machines can verify — genuinely useful for math research, cryptography, and the formal-proof community. It's worth watching how Astra performs once it's actually released to the public. For now, it's not a tool you or I can use — don't expect it to do your homework yet.
好不好用，試了才知道 — Good or not, you won't know until you try it.
Sources / 資料來源
- OpenAI: Ten advances in mathematics and theoretical computer science
- The Decoder: OpenAI announces its next major model Astra by dropping ten previously unsolved math solutions
- Tech Times: OpenAI's Astra Solves Ten Decade-Old Math Problems With Machine-Checkable Lean Proofs
常見問題 FAQ
OpenAI Astra是什麼模型？
Astra是OpenAI尚未正式發布的下一代模型代號，未來可能命名為GPT-5.7或GPT-6，目前無公開發布時間表。
Astra解開的數學問題真的有被驗證嗎？
有，每個證明都附上Lean 4形式化證明證書，GitHub上公開的代碼庫「sorry」佔位符計數為零，代表每一步都經機器嚴格驗證。
解開10道題目為什麼只花2000美元？
這是以GPT-5.6 Sol的API定價計算的運算成本，平均每題約200美元，屬於推理運算成本而非研發總成本。
一般人現在可以用Astra嗎？
不行，Astra目前僅是OpenAI內部研究模型，尚未對外開放，這次公布的是能力預告而非產品發布。
這代表AI已經能取代數學家做研究了嗎？
還不到那個程度。OpenAI公布的是精選後成功的10題，實際嘗試失敗率未知，且這些問題未必是數學界最重要的難題，但形式化驗證+AI推理的組合確實是實質進展。
延伸閱讀 / Related Articles
- Claude Code資安漏洞評測：GitHub留言偷走CI密鑰 | Claude Code Flaw Review: GitHub Comment Steals CI Keys
- MCP Server安全漏洞評測：8000台曝光公網零驗證 | MCP Server Security Review: 8,000 Servers Exposed
- Claude Opus 5評測：追平Fable 5效能砍半價格 | Claude Opus 5 Review: Near-Flagship Power at Half the Price
AI 工具觀察站 — 每日精選 AI Agent 與工具趨勢
AI Tool Observer — Daily curated AI Agent & tool trends
留言
張貼留言