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What do pure mathematicians do, and why do they do it? Looking beyond the conventional answers-for the sake of truth, beauty, and practical applications-this book offers an eclectic panorama of the lives and values and hopes and fears of mathematicians in the twenty-first century, assembling material from a startlingly diverse assortment of scholarly, journalistic, and pop culture sources.
Drawing on his personal experiences and obsessions as well as the thoughts and opinions of mathematicians from Archimedes and Omar Khayyám to such contemporary giants as Alexander Grothendieck and Robert Langlands, Michael Harris reveals the charisma and romance of mathematics as well as its darker side. In this portrait of mathematics as a community united around a set of common intellectual, ethical, and existential challenges, he touches on a wide variety of questions, such as: Are mathematicians to blame for the 2008 financial crisis? How can we talk about the ideas we were born too soon to understand? And how should you react if you are asked to explain number theory at a dinner party?
Disarmingly candid, relentlessly intelligent, and richly entertaining, Mathematics without Apologies takes readers on an unapologetic guided tour of the mathematical life, from the philosophy and sociology of mathematics to its reflections in film and popular music, with detours through the mathematical and mystical traditions of Russia, India, medieval Islam, the Bronx, and beyond.
Michael Harris is professor of mathematics at the Université Paris Diderot and Columbia University. He is the author or coauthor of more than eighty mathematical books and articles, and has received a number of prizes, including the Clay Research Award, which he shared in 2007 with Richard Taylor.
Table of Contents
Chapter 1. Introduction: The Veil 3
Chapter 2. How I Acquired Charisma 7
Chapter a. How to Explain Number Theory at a Dinner Party 41
(First Session: Primes) 43
Chapter 3. Not Merely Good, True, and Beautiful 54
Chapter 4. Megaloprepeia 80
Chapter ß. How to Explain Number Theory at a Dinner Party 109
(Second Session: Equations) 109
Bonus Chapter 5. An Automorphic Reading of Thomas Pynchon's Against the Day (Interrupted by Elliptical Reflections on Mason & Dixon) 128
Part II 139
Chapter 6. Further Investigations of the Mind-Body Problem 141
Chapter ß.5. How to Explain Number Theory at a Dinner Party 175
(Impromptu Minisession: Transcendental Numbers) 175
Chapter 7. The Habit of Clinging to an Ultimate Ground 181
Chapter 8. The Science of Tricks 222
Part III 257
Chapter ?. How to Explain Number Theory at a Dinner Party 259
(Third Session: Congruences) 259
Chapter 9. A Mathematical Dream and Its Interpretation 265
Chapter 10. No Apologies 279
Chapter d. How to Explain Number Theory at a Dinner Party 311
(Fourth Session: Order and Randomness) 311
Afterword: The Veil of Maya 321
Index of Mathematicians 423
Subject Index 427