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「DHJ Polymath paper accepted」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

Ordinarily, I only mention my research papers on this blog when they are first submitted, or if a major update is required. With the paper arising from the DHJ Polymath “Low Dimensions” project , though, the situation is a little different as the collaboration to produce the paper took place on this blog.

Anyway, the good news is that the paper has been accepted for the Szemerédi birthday conference proceedings. The referee was positive and recommended only some minor changes (I include the list of changes below the fold). I have incorporated these changes, and the new version of the paper can be found here . Within a few days I need to return the paper to the editor, so this is the last chance to propose any further corrections or changes (though at this stage any major chang

已知结果和反例

The editor asked a good question: should we have a list of participants for this project somewhere? If so, it seems to make more sense to have this list as a link on the wiki, rather than in the paper itself. But making a list opens the can of worms of deciding what level of participation should be the threshold for inclusion in the list – should someone who only contributed, say, one tangential comment to one of the blog posts be listed alongside a substantially more active

One possibility is that of self-reporting; we could set up a page for participants on the wiki and let anyone who felt like they contributed add their name, and rely on the honour code to keep it accurate. This might be feasible as long as the page is kept unofficial (so, in particular, it will not be used as the formal list of authors for the paper).

证明或构造的主线

A related question is whether to add an explicit link to the timeline for progress on this project and on the sister “New proof” project. If so, this should also be kept unofficial (there was no formal guidelines as to what was included in the timeline and what was not).

These decisions do not necessarily have to be taken quickly; one can simply point to the wiki in the paper (as is already done in the current version), and update the wiki later if we decide to add these sorts of acknowledgments on that site.

阅读时建议盯住的点

Incidentally, if we have another successful Polymath project to write up, I would now strongly recommend using version control software (such as Subversion or git) to organise the writing process, both at the informal notes stage and also at the drafting stage. It is certainly far superior to our improvised solution of putting the raw TeX files on a wiki…

In the referee’s opinion the paper is very well written and there were a few typos find only. I would like to ask you and the contributors to check it again (spell check) and send me the tex file.

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