数学与猜想

Hacker News 上怎么说

• jonnybgood · 2017 年

  我不会这么轻易忽视类比的作用。George Polya 让我见识到了类比在数学中的强大威力。他那本《Mathematics and Plausible Reasoning》，我怎么推荐都不为过。

  I wouldn’t dismiss analogy so easily. George Polya opened my eyes to the power of analogy in math. I can’t recommend his “Mathematics and Plausible Reasoning” enough.

• jacobolus · 2018 年

  ……解决问题，并且想把自己现有的方法给形式化/体系化。在我看来，即便是高年级数学本科生读了这本书也不会完全理解；我会推荐 Pólya 的其他书（《Mathematics and Plausible Reasoning》、《Mathematical Discovery》），或者也可以从更温和的书入手，比如 Mason、Burton 和 Stacey 的《Mathematical Thinking》。

  …problem solving, and wants to codify their existing methods. Even advanced undergraduate math students who read it aren’t going to fully understand the book IMO; I would recommend Pólya’s other books (Mathematics and Plausible Reasoning, Mathematical Discovery), or maybe start with a gentler book like Mason, Burton, & Stacey, Mathematical Thinking.

• linus_torvalds · 2020 年

  大多数竞赛程序员都会推荐 Polya 的《How to Solve It》。他的《Mathematics and Plausible Reasoning》也很棒，但篇幅更长、内容也更艰深。

  Most competitive programmers suggest Polya's "How to Solve It". His "Mathematics and Plausible Reasoning" is also good, but longer and more dense.

• sverona · 2023 年

  同样由 Polya 所著的两卷本《Mathematics and Plausible Reasoning》，是我找到的对一个职业数学家日常是如何开展工作解释得最透彻的书了。书中还有练习题。我本科的时候读这个觉得好玩极了。

  Mathematics and Plausible Reasoning, in two volumes also by Polya, is the closest thing I've ever found to an explanation of how a working mathematician goes about her business. It has exercises, too. Great fun when I was in undergrad.

• phllip · 2008 年

  Steinhaus 的《Mathematical Snapshots》 Polya 的《Mathematics and Plausible Reasoning》 Pappas 的《The Joy of Mathematics》 Gardner 的《The Colossal Book of Short Puzzles and Problems》 Winkler 的《Mathematical Puzzles: A Connoisseur's Collection》 Andrews 的《Number Theory》（Dover Books on Advanced Mathematics 系列）……

  Steinhaus, Mathematical Snapshots Polya, Mathematics and Plausible Reasoning Pappas, The Joy of Mathematics Gardner, The Colossal Book of Short Puzzles and Problems Winkler, Mathematical Puzzles: A Connoisseur's Collection Andrews, Number Theory (Dover Books on Advanced Mathematics)…

• jacobolus · 2018 年

  在我看来，作为第一步，更有用的做法是去思考“解决问题”本身。例如可以参考：Mason, Burton, & Stacey 的《Thinking Mathematically》；Pólya 的《How to Solve It》、《Mathematics and Plausible Reasoning》（共2卷）、《Mathematical Discovery》（共2卷）；Schoenfeld 的《Mathematical Problem Solving》；Larson 的《Problem-Solving Through Problems》。

  Even more useful as a first step in my opinion is to think about problem solving per se. E.g. see: Mason, Burton, & Stacey, Thinking Mathematically Pólya, How to Solve It; Mathematics and Plausible Reasoning (2 vols); Mathematical Discovery (2 vols) Schoenfeld, Mathematical Problem Solving Larson, Problem-Solving Through Problems

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