HN 提问：组织数学研究的新方法
1 分•作者: youoy•13 天前
大家好，
鉴于近期关于人工智能辅助证明的各种公告以及数学界的反应，我们显然需要新的数学研究组织方式。
目前将论文提交到 arXiv，然后等待社区评审的模式，将无法适应人工智能研究的发展。很可能出现的情况是，数学命题的证明变得（相比过去）异常容易，导致 arXiv 被人工智能生成的“垃圾”解释及其相关的 Lean 代码淹没。届时，寻找“经典”数学证明将变得异常困难。
一方面，社区倾向于认为数学不仅仅是形式系统（甚至有人认为哥德尔很久以前就解决了这个问题）。因此，我们不应允许人工智能数学等同于数学本身。
另一方面，用人工智能工具（例如 NS）证明一个长期存在的猜想，即使社区需要时间来消化，也具有明确的数学价值。
然而，我认为将姓名/公司与这些证明挂钩会对社区造成很大损害。例如，当某人/公司没有付出努力时，很少有人愿意为他人清理人工智能生成的“垃圾”证明。
似乎有必要在人工智能生成的“垃圾”证明和经典数学知识之间建立明确的区分。为此，一个可能的解决方案是构建一个与 arXiv 平行的平台，专门针对人工智能，包含主要由人工智能生成但尚未被完全消化的手稿和 Lean 代码。
该网站的投稿应匿名。这样，如果一位数学家需要消化一个人工智能生成的“垃圾”证明并将其纳入更广泛的完成作品中，他们将是为了社区而做，而不是为了最初提交的个人。即使投稿是匿名的，也可以提取匿名的个人影响力因子指标（这超越了投稿数量），并将其作为人工智能数学贡献的指标纳入求职申请中。这样，我们也能激励人工智能方面的工作。
该网站还应作为数学人工智能工具的上下文层。这将进一步加快数学研究的进程。
我知道这并不是一个完全成熟的想法。我分享出来是为了我们能够开始公开讨论，以完善它并作为社区共同构建它。
期待听到您的想法。提前非常感谢。
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Hi all,<p>After all of the recent announcements of AI assisted proofs and the reaction of the mathematical community, it is clear the we need new ways of organizing mathematical research.<p>The current paradigm of submitting a paper to arxiv, and waiting for the review of the community will not scale with AI research. There is a probable outcome where mathematical statements are so easy to proof (compared to some years ago) that arxiv will be floded with AI slop explanations and their associated lean code. It will then be very difficult to find "classical" mathematical proofs.<p>On the one hand, the community tends to cluster around the impression that mathematics is more than the formal system (one could even argue that Godel settled this question a long time ago). So we should not allow AI mathematics to be synonymous to mathematics.<p>On the other hand, there is clear mathematical value in proving a longstanding conjecture with AI tools (for example NS), even if it will take time for the community to digest it.
However, i think attaching names/corporations to these staments will do a lot of harm to the community. For example there will be very few people willing to clean AI slop for someone else when that person/corporation did not put the effort.<p>There seems to be a need for a clear separation between AI slop proofs and classical mathematical knowledge. For this, a possible solution is to build a parallel platform from archive, adapted to AI, with manuscripts + lean code generated mainly by AI, that have not been fully digested.<p>Submissions to this site should be anonymous. That way, if a mathematitian needs to digest an AI slop proof to include it in a wider finished work, they would be doing it for the community, not for the original person thay submitted it. Even if submission are anonymous, one could extract anonymous metrics about personal impact factor (which goes beyond number of submissions) that could be included for job application as a metric of AI mathematical contributions. That way we also incentivice AI work.<p>The site should also serve as a context layer for mathematical AI harnesses. This would further speed up mathematical research.<p>I am aware this is not a fully landed idea. I am sharing it so that we can start an open discussion to perfect it and build it as a community.<p>I am looking forward to hearing your thoughts. Thank you very much in advance.