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「Google Wave」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

As readers of this blog are no doubt aware, I (in conjunction with Tim Gowers and many others) have been working collaboratively on a mathematical project . To do this, we have been jury-rigging together a wide variety of online tools for this, including at least two blogs , a wiki , some online spreadsheets , and good old-fashioned email, together with offline tools such as Maple, LaTeX, C, and other programming languages and packages. (To a lesser extent, I also rely this s

While this has been working reasonably well so far, the mix of all the various tools has been somewhat clunky, to put it charitably, and it would be good to have a more integrated online framework to do all of these things seamlessly; currently there seem to be software that achieves various subsets of what one would need for this, but not all. (This point has also recently been made at the Secret Blogging Seminar.)

已知结果和反例

Yesterday, though, Google Australia unveiled a new collaborative software platform called “ Google Wave ” which incorporates many of these features already, and looks flexible enough to incorporate them all eventually. (Full disclosure: my brother is one of the software engineers for this project.) It’s nowhere near ready for release yet – it’s still in the development phase – but with the right type of support for things like LaTeX, this could be an extremely useful platform

There is a demo for the product below. It’s 80 minutes long, and aimed more at software developers than at end users, but I found it quite interesting, and worth watching through to the end:

证明或构造的主线

[ Update , May 30: Apparently a LaTeX renderer is already being developed as an API extension to Google Wave ; here is a very preliminary screenshot . Also, a shorter explanation of what Google Wave is and does can be found here . ]

[ Update , Jun 7: Another review can be found here. ]

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