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「On time management」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

Prodded by several comments, I have finally decided to write up some my thoughts on time management here. I actually have been drafting something about this subject for a while, but I soon realised that my own experience with time management is still very much a work in progress (you should see my backlog of papers that need writing up) and I don’t yet have a coherent or definitive philosophy on this topic (other than my advice on writing papers , for instance my page on rapi

I can maybe make some unorganised comments, though. Firstly, I am very lucky to have some excellent collaborators who put a lot of effort into our joint papers; many of the papers appearing recently on this blog, for instance, were to a large extent handled by co-authors. Generally, I find that papers written in collaboration take longer than singly-authored papers, but the net effort expended per author is significantly less (and the quality of writing higher). Also, I find

已知结果和反例

[For reasons having to do with the academic calendar, many more of these papers get finished during the summer than any other time of year, but many of these projects have actually been gestating for quite some time. (There should be a joint paper appearing shortly which we have been working on for about three or four years, for instance; and I have been thinking about the global regularity problem for wave maps problem on and off (mostly off) since about 2000.) So a paper be

Another thing is that my ability to do any serious mathematics fluctuates greatly from day to day; sometimes I can think hard on a problem for an hour, other times I feel ready to type up the full details of a sketch that I or my coauthors already wrote, and other times I only feel qualified to respond to email and do errands, or just to take a walk or even a nap. I find it very helpful to organise my time to match this fluctuation: for instance, if I have a free afternoon, a

证明或构造的主线

It helps a lot here to be able to honestly and accurately evaluate your work potential (a function of your location, your current level of motivation and energy, your upcoming duties and commitments, availability of resources, and the expected level of distraction) for a given period of time into the future (e.g. the rest of the day): being either overconfident or underconfident about what you can achieve leads to taking on either more or less than you can properly handle, bo

While I have a large number of things on my “to do” list, at various levels of complexity, difficulty, and length, when it comes to any task requiring dedicated thought, I try to focus on it exclusively, postponing or shutting out everything else; I find that multitasking only works for me when none of the tasks requires more than a fraction of my attention (in particular, it seems to work best when I am not inspired to do any one particular task). Quite often, these tasks ta

阅读时建议盯住的点

More generally, tasks that require little concentration seem to be best done in batches if possible, while tasks that require a lot of concentration seem to be best done individually, with as few distractions as one can manage.

Related to the point about “closure” is the desirability of being able to chop up an extremely long task into smaller, self-contained ones, ideally each with its own immediate “payoff”. To give one example: I doubt I would ever attempt to write (let alone finish) the equivalent of my 19 or so lectures on the Poincaré conjecture if I had decided to write one enormous article or monograph rather than 19 reasonably manageable and self-supporting shorter pieces. (It helped also t

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