Proof and the Art of Mathematics

by Joel David Hamkins

An introduction to writing proofs, presented through compelling mathematical statements with interesting elementary proofs.

This book offers an introduction to the art and craft of proof-writing. The author, a leading research mathematician, presents a series of engaging and compelling mathematical statements with interesting elementary proofs. These proofs capture a wide range of topics, including number theory, combinatorics, graph theory, the theory of games, geometry, infinity, order theory, and real analysis. The goal is to show students and aspiring mathematicians how to write proofs with elegance and precision.

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

240 pages, Paperback

Published September 29, 2020

Reviews

[Joel · Rating 3 out of 5]

Despite showing up in a few lists of popular math books (that's how I came across it), be warned that Proof and the Art of Mathematics is, at its core, much more serious and less friendly to anyone who is simply looking for an entertaining read.
The content, especially concerning the proofs, is presented rigorously (as it should, of course!) and assumes, in most chapters, that readers have an intermediate knowledge of mathematics and certain skills in terms of abstract reasoning.
Nevertheless, Joel Hamkins does an excellent job covering a wide range of topics and providing historical contextualization. His remarks/suggestions on Mathematical Habits are also quite poignant.

[Paul O'Malley · Rating 5 out of 5]

Now I've finished it, I can and do recommend it if you like mathematics.
There are a couple of things that were new to me, the extensions to Hilbert's hotel. I've done them differently previously and I really enjoyed the expansion.
Overall I've no complaints about the book, it helped me understand more methods and clear instructions on how to be better at this kind of thing.

[Devin]

Pg rec: “Joel Hamkins's Proof and the Art of Mathematics is a beautiful book in both senses. It's both beautifully written, but also physically beautiful, thanks to its many illustrations, which I was surprised to hear were made by the author himself. It's hard to imagine a better book to buy for a teenager with a nascent interest in math. This book shows how much more interesting it can be than the stuff they have to learn in school to pass exams.”

[Andrea Valente · Rating 4 out of 5]

Very nice book. A great way to refresh most of the math I had in university. Clever examples and great variety of proofs and techniques, including visual proofs.

[Shannon Heaton · Rating 3 out of 5]

It's a very niche book. If that was mathematics as art, I'd hate to see mathematics as science.