The Unreasonable Elegance of Mathematics

This book offers an introduction to the nature of mathematics, its history, and some of the curious individuals who have shaped it. It explores a range of fundamental ideas that can be appreciated without prior mathematical training.
 
Highlighting the human side of mathematics and its shared lineage with philosophy, the book embraces the subject’s colorful history, incorporating original source material in the main text. Based on a course taught to non-science majors, it is intended for anyone with an interest in mathematics—including those whose last experience with algebra was less than enjoyable.

1 What is Mathematics?.- 2 Pascal’s Triangle, Number Magic and the Apocalypse.- 3 Some Simple Number Mysteries.- 4 Cellular Automata.- 5 Axioms: the Rules of the Game.- 6 Direct and Indirect Proofs.- 7 Dirichlet’s Box Principle.- 8 Adding Infinitely Many Things.- 9 Incorrectly Adding Infinitely Many Things.- 10 The Other Side of the Story (Plato vs. Wittgenstein).- 11 Different Infinities.- 12 The Monte Carlo Method.- 13 Chaos Theory.- 14 Mathematics as a Tool for Dishonesty.- 15 Able Amateurs and Colorful Crackpots.- 16 The House Always Wins.- 17 Matching Things.- 18 Conflict and Cooperation.- 19 The End of Knowledge.

Stefan Steinerberger is a Professor of Mathematics at the University of Washington, Seattle. He is broadly interested in the area of analysis and its applicability to problems in applied mathematics. His research has been supported by the Austrian Science Fund, the National Science Foundation, the Institute for New Economic Thinking and the Alfred P. Sloan Foundation.