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「Polymath 8b, XI: Finishing up the paper」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

This is the eleventh thread for the Polymath8b project to obtain new bounds for the quantity

The main focus is now on writing up the results, with a draft paper close to completion here (with the directory of source files here ). Most of the sections are now written up more or less completely, with the exception of the appendix on narrow admissible tuples, which was awaiting the bounds on such tuples to stabilise. There is now also an acknowledgments section (linking to the corresponding page on the wiki , which participants should check to see if their affiliations

已知结果和反例

Regarding the numerics in Section 7 of the paper, one thing which is missing at present is some links to code in case future readers wish to verify the results; alternatively one could include such code and data into the arXiv submission.

It’s about time to discuss possible journals to submit the paper to. Ken Ono has invited us to submit to his new journal, “ Research in the Mathematical Sciences “. Another option would be to submit to the same journal “ Algebra & Number Theory ” that is currently handling our Polymath8a paper (no news on the submission there, but it is a very long paper), although I think the papers are independent enough that it is not absolutely necessary to place them in the same journal.

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