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.