Proof and the Art of Mathematics

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.

Joel David Hamkins is Professor of Logic at Oxford University and Sir Peter Strawson Fellow in Philosophy at University College, Oxford. The author of Proof and the Art of Mathematics (MIT Press), he is the creator of the popular blog Mathematics and Philosophy of the Infinite. He is a prominent contributor to MathOverflow, where he has posted more than 1,000 mathematical arguments.

1 A Classical Beginning
2 Multiple Proofs
3 Number Theory
4 Mathematical Induction
5 Discrete Mathematics
6 Proofs Without Words
7 Theory of Games
8 Pick's Theorem
9 Lattice-Point Polygons
10 Polygonal Dissection Congruence Theorem
11 Functions and Relations
12 Graph Theory
13 Infinity
14 Order Theory
15 Real Analysis