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Mathematics and Plausible Reasoning, Volume 1: Induction and Analogy in Mathematics (v. 1) Hardcover – October 1, 1954

5 out of 5 stars 4 customer reviews

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Editorial Reviews

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"Polya . . . does a masterful job of showing just how plausible reasoning is used in mathematics. . . . The material in both volumes is fresh and highly original; the presentation is stimulating, informal, and occasionally humorous; examples from science, legal reasoning, and daily life make the arguments clear even to a nonspecialist. Polya's book is a rare event."--Morris Kline, Scientific American

"Professor Polya's beautifully written hook has become a classic."---A. 0. L. Atkin, The Mathematical Gazette

"Professor Polya . . . is interested in problem solving and the psychological aspects of mathematical discovery. . . . [These books] should provide many entertaining hours for anyone who cares to pick up the challenge."--Carl Hammer, Journal of the Franklin Institute

"Professor Polya presents a forceful argument for the teaching of intelligent guessing as well as proving. . . . There are also very readable and enjoyable discussions of such concepts as the isoperimetric problem and 'chance, the ever-present rival of conjecture.' "--Bruce E. Meserve, The Mathematics Teacher

About the Author

G. Polya (1887-1985) was Professor of Mathematics at Stanford University. --This text refers to the Paperback edition.
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Product Details

  • Series: Mathematics and Plausible Reasoning
  • Hardcover: 296 pages
  • Publisher: Princeton University Press; 2d Ed edition (October 1, 1954)
  • Language: English
  • ISBN-10: 0691080054
  • ISBN-13: 978-0691080055
  • Product Dimensions: 0.8 x 6.2 x 9.5 inches
  • Shipping Weight: 1.3 pounds
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (4 customer reviews)
  • Amazon Best Sellers Rank: #504,879 in Books (See Top 100 in Books)

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The author of this work has a special relationship to math. As people were trying to forcefeed me the subject over 50 years ago, what I mostly got was pure math, with no intest in how or whether math had any true real-world connections. There was a heavy emphasis on deductive, Euclidian proof.

Polanyi is a breath of fresh air, because he is the first mathematician I have read who identifies insight and intuition as very important parts of math exploration. He identifies this element as guessing. Flat out.

Math and science do not begin with formalized statements which are then studied and tested. They begin with someone's sense that there is something interesting to look at, poking around some, and THEN seeing if you can come up with a rule which might help predict, or explain an outcome.. sort of. The analytical part-- E = MC squared, for example-- comes after the intuition and the poking.

What his work is about is getting better and the inductive part-- the improvement of guessing.
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Format: Paperback
This is a continuation of the first volume on the same topic. He talks about plausible reasoning and helps researchers very much. I was most interested in problem solving though. I am nevertheless giving 5 stars because he does a good job of explaining plausible reasoning. In the last chapter (no. 16), he talks about the 'Deus ex machina' where a step in the proof of a tough problem appears as if the step was pulled out of a hat the way magicians do. In section 6, he explains it for a specific case but nevertheless the book does not provide ample examples of how such critical steps were pulled out of a hat. I feel that today, the only way to acquire that skill is to obtain proper mentorship from someone like Arthur Engel or Titu Andrescu. If you wish to understand plausible reasoning in math research, this book is very helpful and very well written.
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Format: Hardcover Verified Purchase
Every maths lover most keep this !! It is a book which motivate us do research in a systematic way!! written in a lucid manner!! Interactive also!!
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Format: Paperback Verified Purchase
Wonderful book; gave me tools to understand the process of critical reasoning, so necessary with the flood of today's news. (News?) So many opinions are floated on the TV and internet, it is important to sort out fact from fiction.
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