Induction and Analogy in Mathematics

Mathematics and Plausible Reasoning #1

by George Pólya

A guide to the practical art of plausible reasoning, this book has relevance in every field of intellectual activity. Professor Polya, a world-famous mathematician from Stanford University, uses mathematics to show how hunches and guesses play an important part in even the most rigorously deductive science. He explains how solutions to problems can be guessed at; good guessing is often more important than rigorous deduction in finding correct solutions. Vol. I, on Induction and Analogy in Mathematics , covers a wide variety of mathematical problems, revealing the trains of thought that lead to solutions, pointing out false bypaths, discussing techniques of searching for proofs. Problems and examples challenge curiosity, judgment, and power of invention.

Genres: Mathematics, Science, Nonfiction, Logic, Philosophy, Computer Science

296 pages, Paperback

First published January 1, 1954

Reviews

[Jeff Yoak]

I loved this book, but as it got harder, I lost the time that I had for going through it. I should revisit it.

[Dan]

Not for the general reader (one star). This mostly about induction, mathematical and logical. Useful as an introduction to a limited readership interested in science with a strong leaning toward Mathematics. Valuable mostly in pointing out inductive fallacies. That is worth the third star.

Probably suited best to high school math whizzes and college undergrads majoring or minoring in Mathematics or a closely related field such as Physics.

I have a math degree (48 years ago) and found that the most interesting parts were stuff I already knew, and most of the rest not especially engaging. I did enjoy Euler's discovery of a pattern in the primes, which was new to me. It would seem that has deep implications for group theory, but this was only hinted at and not explored. Also enjoyed some of Archimedes's proofs.

[Alan]

Great stuff, but a little heavy lifting involved.