A volume of anecdotes, stories, quips, and ruminations about mathematics and mathematicians.

A companion to Mathematical Apocrypha (published in 2002) this second volume of anecdotes, stories, quips, and ruminations about mathematics and mathematicians is sure to please. It differs from other books of its type in that many of the stories are from the twentieth century and many about currently living mathematicians. A number of the best stories come from the author's first-hand experience. The writing is lively, engaging, and informative. There are stories the reader may wish to share with students and colleagues, friends, and relatives. The purpose of the book is to explore and to celebrate the many facets of mathematical life. The stories reveal mathematicians as intense, human, and sympathetic. They should resonate with readers everywhere. This book will appeal to students from high school through graduate school, to faculty and mathematical scientists of all stripes, and also to physicists, engineer, and anyone interested in mathematics.

An exploration of the hidden human, emotional, and social dimensions of mathematics Mathematics is often thought of as the coldest expression of pure reason. But few subjects provoke hotter emotions—and inspire more love and hatred—than mathematics. And although math is frequently idealized as floating above the messiness of human life, its story is nothing if not human; often, it is all too human. Loving and Hating Mathematics is about the hidden human, emotional, and social forces that shape mathematics and affect the experiences of students and mathematicians. Written in a lively, accessible style, and filled with gripping stories and anecdotes, Loving and Hating Mathematics brings home the intense pleasures and pains of mathematical life. These stories challenge many myths, including the notions that mathematics is a solitary pursuit and a "young man's game," the belief that mathematicians are emotionally different from other people, and even the idea that to be a great mathematician it helps to be a little bit crazy. Reuben Hersh and Vera John-Steiner tell stories of lives in math from their very beginnings through old age, including accounts of teaching and mentoring, friendships and rivalries, love affairs and marriages, and the experiences of women and minorities in a field that has traditionally been unfriendly to both. Included here are also stories of people for whom mathematics has been an immense solace during times of crisis, war, and even imprisonment—as well as of those rare individuals driven to insanity and even murder by an obsession with math. This is a book for anyone who wants to understand why the most rational of human endeavors is at the same time one of the most emotional.

Modular Forms is a graduate student-level introduction to the classical theory of modular forms and computations involving modular forms, including modular functions and the theory of Hecke operators. It also includes applications of modular forms to various subjects, such as the theory of quadratic forms, the proof of Fermat's Last Theorem and the approximation of π. The text gives a balanced overview of both the theoretical and computational sides of its subject, allowing a variety of courses to be taught from it.This second edition has been revised and updated. New material on the future of modular forms as well as a chapter about longer-form projects for students has also been added.

In this follow-up to his popular Science Secrets, Alberto A. Martinez discusses various popular myths from the history of mathematics: that Pythagoras proved the hypotenuse theorem, that Archimedes figured out how to test the purity of a gold crown while he was in a bathtub, that the Golden Ratio is in nature and ancient architecture, that the young Galois created group theory the night before the pistol duel that killed him, and more. Some stories are partly true, others are entirely false, but all show the power of invention in history. Pythagoras emerges as a symbol of the urge to conjecture and "fill in the gaps" of history. He has been credited with fundamental discoveries in mathematics and the sciences, yet there is nearly no evidence that he really contributed anything to such fields at all. This book asks: how does history change when we subtract the many small exaggerations and interpolations that writers have added for over two thousand years? The Cult of Pythagoras is also about invention in a positive sense. Most people view mathematical breakthroughs as "discoveries" rather than invention or creativity, believing that mathematics describes a realm of eternal ideas. But mathematicians have disagreed about what is possible and impossible, about what counts as a proof, and even about the results of certain operations. Was there ever invention in the history of concepts such as zero, negative numbers, imaginary numbers, quaternions, infinity, and infinitesimals? Martinez inspects a wealth of primary sources, in several languages, over a span of many centuries. By exploring disagreements and ambiguities in the history of the elements of mathematics, The Cult of Pythagoras dispels myths that obscure the actual origins of mathematical concepts. Martinez argues that an accurate history that analyzes myths reveals neglected aspects of mathematics that can encourage creativity in students and mathematicians.

This book is a collection of fourteen essays that describe an inspiring journey through the universe and discusses popular science topics that modern physics and cosmology are struggling to deal with. What is our place in the universe and what happens in the magnificent cosmos where we exist for a brief amount of time. In an unique way that incorporates mythological and philosophical perspectives, the essays in this work address the big questions of what the universe is, how it came into being, and where it may be heading. This exciting adventure is a rich scientific history of elegant physics, mathematics, and cosmology as well as a philosophical and spiritual pursuit fueled by the human imagination.