陶哲轩博客写数学问题时，通常先把对象定义清楚，再给直觉、反例和证明轮廓。把「Mini-polymath2 discussion thread」改写成可阅读的中文笔记，重点是：问题在问什么、已知到哪一步、下一步最容易走偏在哪。原站广告、分享条和导航已去掉。

问题在问什么

I’ve just opened the Mini-polymath2 project over at the polymath blog . I decided to use Q5 from the 2010 IMO in the end, rather than Q6, as it seems to be a little bit more challenging and interesting.

This post will serve as the discussion thread of the project, intended to focus all the non-research aspects of the project such as organisational matters or commentary on the progress of the project. (Is it possible for one blog thread to “live-blog” another?) The third component of the project is the wiki page , which is intended to summarise the progress made so far on the problem.

已知结果和反例

As with mini-polymath1 , I myself will be serving primarily as a moderator, and hope other participants will take the lead in the research and in keeping the wiki up-to-date. (Ideally, once we get all the kinks in the format ironed out, it should be possible for anyone with a blog and an interested pool of participants to start their own mini-polymath project, without being overly dependent on one key contributor.)

证明或构造的主线

先写出对象、假设和失败的例子，再进入证明。没有反例的直觉，很容易把局部技巧当成一般定理。

阅读时建议盯住的点

先写出对象、假设和失败的例子，再进入证明。没有反例的直觉，很容易把局部技巧当成一般定理。

阅读和落地时建议先做的 5 件事

1. 用自己的语言重写定义和结论，不看原文能不能说清对象是什么。
2. 找一个最小反例或边界情形，确认假设少一条会怎样。
3. 把证明拆成可独立检验的引理，每步只保留一个新想法。
4. 若涉及计算或形式化，先写可复现的小例子，再谈一般情形。
5. 记下尚未解决的缺口：缺估计、缺构造，还是缺正确的范畴。

和智能体、形式化工具怎么接

龙虾PRO做 OpenClaw 落地时，数学笔记最有用的部分往往是「可检验的步骤」：定义、反例、引理边界。智能体适合帮忙展开计算和检索，不适合代替你决定哪条假设能扔。

本文侧重全链路风控方法论。落地时请用自身业务单据做回放验证，不要把示例阈值直接当生产策略。 相关：风控体检 · 方案资源