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「(Timothy Chow) Out-of-print math books」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

I recently had a frustrating experience with a certain out-of-print mathematics text that I was interested in. A couple of used copies were listed at over $150 a pop on Bookfinder.com , but that was more than I was willing to pay. I wrote to the American Mathematical Society asking if they were interested in bringing the book back into print. To their credit, they took my request seriously, and solicited the opinions of some other mathematicians.

Unfortunately, these referees all said that the field in question was not active, and in any case there was a more recent text that was a better reference. So the AMS rejected my proposal. I have to say that I was surprised, because the referees did not back up their opinions with any facts, and I knew that in addition to the high price that the book commanded on the used-book market, there was some circumstantial evidence that it was in demand. A MathSciNet search confirmed

已知结果和反例

A colleague then suggested that maybe I should instead contact the author directly, asking him to regain the copyright from the publisher. The author could then make the book available on his website or pursue print-on-demand options, if conventional publishers were not interested. I tried this, but was again surprised to discover that the author thought it was not worth the trouble to get the copyright back, let alone to make the text available. Again the argument was that,

In both cases I was frustrated because I did not know how to find other people who were interested in the same book, to prove to the AMS or the author that there were in fact many of us who wanted to see the book back in print.

证明或构造的主线

Now for the good news. After hearing my story, Klaus Schmid promptly set up a prototype website at

Anyone can go to this site and suggest a book, or vote for books that others have suggested. This is precisely the kind of information that I believe would have greatly helped me argue my case. Of course, the site works only if people know about it, so if you like the idea, please spread the word to your friends and colleagues.

阅读时建议盯住的点

It might be that a better long-term solution than Schmid’s site is to convince a bookselling website to tally votes of this sort, because such a site will catch users “red-handed” searching for an out-of-print book. I have tried to contact some sites with this suggestion; so far, Booksprice.com and Fetchbook.info have said that they like the idea and may eventually implement it. In the meantime, hopefully Schmid’s site will become a useful tool in its own right.

Let me conclude with a question. What else can we be doing to increase the availability of out-of-print books, especially those that are still copyrighted? Several people have told me that the solution is for authors to regain the copyrights to their out-of-print books and make their books available themselves, but authors are often too busy (if they are not deceased!). What can we do to help in such situations?

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