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「“Density Hales-Jewett and Moser numbers” – nearing the final draft」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

After a hiatus of several months, I’ve made an effort to advance the writing of the second Polymath1 paper, entitled “ Density Hales-Jewett and Moser numbers “. This is in part due to a request from the Szemeredi 60th 70th birthday conference proceedings (which solicited the paper) to move the submission date up from April to February. (Also, the recent launch of Polymath5 on Tim Gowers blog reminds me that I should get this older project out of the way.)

The current draft of the paper is here , with source files here . I have been trimming the paper, in particular replacing some of the auxiliary or incomplete material in the paper with references to pages on the polymath wiki instead. Nevertheless this is still a large paper, at 51 pages. It is now focused primarily on the computation of the Density Hales-Jewett numbers and the Moser numbers for all n up to 6, with the latter requiring a significant amount of computer assista

已知结果和反例

There are a number of minor issues remaining with the paper:

Finally, the text probably needs to be proofread one or two more times before it is ready to go, hopefully by early February. There is still also one last opportunity to propose non-trivial restructuring of the paper (in particular, if there are other ways to trim the size of the paper, this may be worth looking into).

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。

值得单独记下的条目

• A picture of a Fujimura set for the introduction would be nice.
• Reference [15] (which is Komlos’s lower bound on the Moser numbers) is missing a volume number. The reference is currently given as J. Komlos, solution to problem P.170 by Leo Moser, Canad. Math.. Bull. vol ??? (1972), 312-313, 1970.

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