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「A statement on the cost of knowledge declaration」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

It has been a little over two weeks now since the protest site at thecostofknowledge.com was set up to register declarations of non-cooperation with Reed Elsevier in protest of their research publishing practices, inspired by this blog post of Tim Gowers . Awareness of the protest has certainly grown in these two weeks; the number of signatories is now well over four thousand, across a broad array of academic disciplines, and the protest has been covered by many blogs and als

The statement of the protest itself , though, is rather brief, reflecting the improvised manner in which the site was created. A group of mathematicians including myself therefore decided to write and sign a more detailed explanation of why we supported this protest, giving more background and references to support our position. The 34 signatories are Scott Aaronson , Douglas N. Arnold , Artur Avila , John Baez , Folkmar Bornemann , Danny Calegari , Henry Cohn , Ingrid Daubec

已知结果和反例

Of course, the 34 of us do not presume to speak for the remaining four thousand signatories to the protest, but I hope that our statement is somewhat representative of the position of many of its supporters.

Further discussion of this statement can be found at this blog post of Tim Gowers .

证明或构造的主线

EDIT: I think it is appropriate to quote the following excerpt from our statement:

All mathematicians must decide for themselves whether, or to what extent, they wish to participate in the boycott. Senior mathematicians who have signed the boycott bear some responsibility towards junior colleagues who are forgoing the option of publishing in Elsevier journals, and should do their best to help minimize any negative career consequences.

阅读时建议盯住的点

Whether or not you decide to join the boycott, there are some simple actions that everyone can take, which seem to us to be uncontroversial:

值得单独记下的条目

• Make sure that the final versions of all your papers, particularly new ones, are freely available online, ideally both on the arXiv and on your home page.
• If you are submitting a paper and there is a choice between an expensive journal and a cheap (or free) journal of the same standard, then always submit to the cheap one.

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