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[笔记，科普，数学] 波利亚 George Pólya, Pólya György 名言之一

已有 249 次阅读 2026-3-29 20:37 |个人分类:资料与科普|系统分类:科普集锦

[笔记，科普，数学] 波利亚 George Pólya, Pólya György 名言之一

希尔伯特－波利亚猜想： Hilbert–Pólya conjecture

素数： prime number

算术基本定理： fundamental theorem of arithmetic

素数计数函数： prime counting function

素数定理： prime number theorem

对数积分： logarithmic integral

唯一分解定理： unique factorization theorem

希尔伯特： David Hilbert, 1862-01-23 ~ 1943-02-14, 81

波利亚： George Pólya, Pólya György, 1887-12-13 ~ 1985-09-07, 98

图1 波利亚 George Pólya, Pólya György, 1887-12-13 ~ 1985-09-07, 98

Polya-BW.jpg

https://matematicaastercas.campus.ciencias.ulisboa.pt/wp-content/uploads/sites/56/2018/03/Polya-BW.jpg

一、波利亚及其《如何解决这个问题 How to Solve It: A New Aspect of Mathematical Method》

Pólya worked in probability, analysis, number theory, geometry, combinatorics and mathematical physics.

波利亚在概率论、分析、数论、几何、组合学和数学物理方面工作。

Pólya was arguably the most influential mathematician of the 20th century. His basic research contributions span complex analysis, mathematical physics, probability theory, geometry, and combinatorics. He was a teacher par excellence who maintained a strong interest in pedagogical matters throughout his long career.

波利亚可以说是20世纪最有影响力的数学家。他的基础研究贡献涵盖了复杂分析、数学物理、概率论、几何和组合学。他是一位杰出的教师，在其漫长的职业生涯中一直对教学问题保持着浓厚的兴趣。

1945年在“Princeton University Press 普林斯顿大学出版社”出版了名著《如何解决问题 How to Solve It: A New Aspect of Mathematical Method》：

“In an age that all solutions should be provided with the least possible effort, this book brings a very important message: mathematics and problem solving in general needs a lot of practice and experience obtained by challenging creative thinking, and certainly not by copying predefined recipes provided by others. Let’s hope this classic will remain a source of inspiration for several generations to come.”—A. Bultheel, European Mathematical Society

“在一个所有解决方案都应该以最少的努力提供的时代，这本书带来了一个非常重要的信息：数学和问题解决通常需要大量的实践和经验，这些实践和经验是通过挑战创造性思维获得的，当然不是通过复制别人提供的预先定义的食谱获得的。让我们希望这本经典著作能在未来几代人中继续成为灵感的源泉。”——A. Bultheel, 欧洲数学学会

二、名言

A GREAT discovery solves a great problem, but there is a grain of discovery in the solution of any problem. Your problem may be modest, but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery.

一个伟大的发现可以解决一个大问题，但在解决任何问题的过程中都有一点发现。你的问题可能不大，但如果它挑战了你的好奇心，发挥了你的创造力，如果你用自己的方式解决了它，你可能会体验到紧张，并享受发现的胜利。

The first rule of discovery is to have brains and good luck. The second rule of discovery is to sit tight and wait till you get a bright idea.

做出发现的第一条规则是要有头脑和好运。做出发现的第二条规则是紧紧等待，等到你有了一个好主意。

If you have to prove a theorem, do not rush. First of all, understand fully what the theorem says, try to see clearly what it means. Then check the theorem; it could be false. Examine the consequences, verify as many particular instances as are needed to convince yourself of the truth. When you have satisfied yourself that the theorem is true, you can start proving it.

如果你必须证明一个定理，不要着急。首先，充分理解定理的意思，试着清楚地看到它的意思。然后检查定理；这可能是假的。检查后果，核实尽可能多的特定情况，以说服自己相信真相。当你确信定理是真的时，你就可以开始证明它了。

Mathematics consists of proving the most obvious thing in the least obvious way.

Quoted in N Rose Mathematical Maxims and Minims (Raleigh N C 1988).

数学就是用最不明显的方式证明最明显的事情。

Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment. All one needs for mathematics is a pencil and paper.

Quoted in D J Albers, G L Alexanderson and C Reid, Mathematical People (Boston 1985).

数学是最廉价的科学。与物理或化学不同，它不需要任何昂贵的设备。数学所需要的只是一支铅笔和一张纸。

There are many questions which fools can ask that wise men cannot answer.

Quoted in H Eves Return to Mathematical Circles (Boston 1988).

有许多问题，愚者可以问，智者却无法回答。

When introduced at the wrong time or place, good logic may be the worst enemy of good teaching.

The American Mathematical Monthly 100 (3).

当在错误的时间或地点引入时，好的逻辑可能是好教学的最大敌人。

The apex and culmination of modern mathematics is a theorem so perfectly general that no particular application of it is feasible.

现代数学的最高度和最终结果是一个极为全面的定理,以至于无法将其具体应用。

The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the theorem and inversely proportional to the effort it takes to see them.

数学定理的优雅程度与人们在定理中可以看到的独立思想的数量成正比，与看到它们所需的努力成反比。

参考资料：

[1] 澎湃，2024-08-20 14:21，波利亚的数学思想：解题是人类的最富有特征的活动

https://www.thepaper.cn/newsDetail_forward_28448679

以前的《科学网》相关博文链接：

[1] 2026-03-28 20:36，[笔记，科普，数学] 素数（20）：希尔伯特－波利亚猜想 Hilbert–Pólya conjecture

https://blog.sciencenet.cn/blog-107667-1527807.html

[2] 2026-03-25 14:50，[笔记，科普，数学] 素数（17）：庞加莱 Poincaré 几乎不研究素数？

https://blog.sciencenet.cn/blog-107667-1527296.html

[3] 2026-03-24 19:25，[笔记，科普，数学] 素数（16）：高斯，除了算术基本定理、素数定理之外，对素数还有哪些看法？

https://blog.sciencenet.cn/blog-107667-1527201.html

[4] 2025-09-18 16:55，[讨论，科普] 什么是数学证明？（关联：演绎、归纳、完全归纳、合情推理）