[小资料] 阿诺德原理、复杂的模型几乎毫无用处：出自 1998年《On teaching mathematics》

图1  阿诺德，Владимир Игоревич Арнольд, Vladimir I Arnol'd,  Vladimir Igorevich Arnold, 1937-06-12 ~ 2010-06-03

https://rs.resalliance.org/wp-content/uploads/2010/06/Vladimir_Arnold-1.jpg

一、复杂的模型几乎毫无用处

   In exactly the same way a small change in axioms (of which we cannot be completely sure) is capable, generally speaking, of leading to completely different conclusions than those that are obtained from theorems which have been deduced from the accepted axioms. The longer and fancier is the chain of deductions ("proofs"), the less reliable is the final result.

   Complex models are rarely useful (unless for those writing their dissertations).

   与此完全一样的是，公理（那些我们不能完全确定的）的一个小小的改变虽是容许的，一般来说，由那些被接受的公理推出的定理却将导出完全不同的结论。推导的链（即所谓的“证明”）越长越复杂，最后得到的结论可靠性越低。

   复杂的模型几乎毫无用处（除了对那些无聊的专写论文的人）。

图2  截取自 Arnold, 1998, On teaching mathematics 第232页

二、 Arnold 原理

   Prof. M. Berry once formulated the following two principles:

   The Arnold Principle. If a notion bears a personal name, then this name is not the name of the discoverer.

   The Berry Principle. The Arnold Principle is applicable to itself.

   M. Berry 教授曾经提出过如下两个原理：

   Arnold 原理：如果某个理念中出现了某个人名，则这个人名必非发现此理念者的名字。

   Berry 原理：Arnold 原理适用于自身。

图3  截取自 Arnold, 1998, On teaching mathematics 第230页

参考资料：

[1] Vladimir I Arnol'd ((Arnold). On teaching mathematics [J]. Russian Mathematical Surveys, 1998, 53(1): 229-234.  Number 1, February 1998

doi:  10.1070/RM1998v053n01ABEH000005

https://iopscience.iop.org/article/10.1070/RM1998v053n01ABEH000005

[2] S. H. Lui, An Interview with Vladimir Arnol'd [J], NOTICES OF THE AMS, 1997, 44(4): 432-438

https://www.ams.org/journals/notices/199704/arnold.pdf

https://www.ams.org/journals/notices/199704/index.html

[3] 豆瓣，2018-01-06，阿诺德 谈数学教育

https://www.douban.com/note/652185910/?type=rec&_i=5741715NW4Iu2n

相关链接：

[1] 2020-03-20，破除论文“SCI至上”：弗拉基米尔·阿诺德1995年的几句话

https://blog.sciencenet.cn/blog-107667-1224424.html

[2] 2022-10-13，[求助] 关于“量子纠缠”的科普级答疑

https://blog.sciencenet.cn/blog-107667-1359275.html

[3] 2017-01-09，复杂方法在实际中往往用途不大（在有噪声的情况下）

https://blog.sciencenet.cn/blog-107667-1026473.html

感谢您的指教！

感谢您指正以上任何错误！

感谢您提供更多的相关资料！