EP450 – 兩家 AI 公司同時推翻電腦科學的大猜想：這代表什麼？

OpenAI and Anthropic recently published papers that challenge a long-held conjecture in computer science known as the Exponential Time Hypothesis (ETH). This conjecture posits that there is no shortcut to solving certain computational problems, meaning that as the number of variables increases, the time required to solve these problems grows exponentially. The new findings suggest that there may be methods that allow for a slower growth rate in computational workload, although these methods are currently impractical for real-world applications.

The significance of this development lies in the foundational role ETH has played in computer science for over two decades. Many results have been built on the assumption that ETH is true, and the recent papers necessitate a reevaluation of these results. While some may remain valid, others will require new proofs. Notably, a prominent computer scientist believes that most of the foundational results will withstand scrutiny, but the implications of this new evidence are profound.

AI played a crucial role in the discovery of this new approach, with Anthropic's model independently identifying the core of the solution without human prompts. Both companies utilized specialized software to verify the proofs, but independent expert validation is still pending. The ongoing review process highlights the need for careful examination of AI-generated results, as the speed of generating answers does not equate to the speed of verifying their accuracy.

For the general public, this development underscores a shift in how AI can contribute to complex problem-solving. While AI has traditionally been viewed as a tool for enhancing productivity, its ability to propose new solutions to longstanding problems marks a significant evolution. As the verification process continues, it is essential to maintain a balanced perspective on AI's capabilities, recognizing both its potential and the need for rigorous validation.

十月底，OpenAI 和 Anthropic 各自公布一份論文，結論一樣：電腦科學裡一個被相信了二十幾年的猜想（ETH）被推翻了，而且證明是 AI 找出來的。這一集用開關謎題的比喻，講這個猜想在猜什麼、為什麼有人在乎、AI 做了什麼、還有哪些事沒確定，以及這件事對一般人的意義。

📄 一手來源 ・OpenAI｜The Exponential Time Hypothesis is False（論文）：https://github.com/openai/math/blob/main/preprints/The-Exponential-Time-Hypothesis-is-False-October-25-2026/paper.pdf ・OpenAI｜openai/math 更新紀錄（獨立專家小組）：https://github.com/openai/math/blob/main/history.md ・Anthropic｜A 2^o(n) Time Algorithm for 3-SAT（論文）：https://github.com/anthropics/formal-math/tree/main/eth ・Scott Aaronson｜Shtetl-Optimized（10/26 貼文與留言）：https://scottaaronson.blog/?p=10239

🎬 參考影片 ・Wes Roth｜OpenAI just broke physics…：https://www.youtube.com/watch?v=lskEzJ7ixw0 ・TheAIGRID｜OpenAI Just Made a Discovery Nobody Thought Was Possible：https://www.youtube.com/watch?v=3uoStyWxO5M ・Adem B10｜800 Papers Assume This. OpenAI and Claude Say It's False.：https://www.youtube.com/watch?v=r0Vy7OvWh1Y ・Dr. Samuel Allen Alexander｜ETH conjecture disproved by OpenAI AND Anthropic on the same day?!：https://www.youtube.com/watch?v=ZbxC0412cys ・HexaValuation｜OpenAI's 3 Huge Claims, Checked：https://www.youtube.com/watch?v=YHfSZtGXGx0 ・TCS Proofs｜The Exponential Time Hypothesis Is False? OpenAI's Claimed Subexponential #SAT Algorithm, Explained：https://www.youtube.com/watch?v=YmU4XTfCV84

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