
Front Matter Front Matter (pp. ivi) 
Table of Contents Table of Contents (pp. viiviii) 
ACKNOWLEDGMENTS ACKNOWLEDGMENTS (pp. ixxii) 
Introduction Introduction (pp. 18)This book, unlike most books on mathematics, is about mathematicians, their extraordinary passion for mathematics and their full complexity of being. We emphasize the social and emotional sides of mathematical life.
In the great and famous works of Euclid and Newton, we find axioms and theorems. The mathematics seems to speak for itself. No first person speaks, no second person is addressed: “Here is Truth, here is Proof, no more need be said.” Going back to the reports of Plato and Descartes, mathematical thinking has been seen as pure reason–a perfect and eternal faculty. The thoughts, feelings, and tribulations...

1 Mathematical Beginnings 1 Mathematical Beginnings (pp. 945)In this chapter, we tell contrasting stories about the childhood, adolescence, and schooling, up through graduate school, of some future mathematicians, both famous and not so famous. We also report the experiences of youngsters in Olympiad competitions, psychologists’ investigations of prodigies, and what the parents of math prodigies are like.
A few famous mathematicians showed their interest and ability before school age. The Hungarian combinatorialist and number theorist Paul Erdős¹(1913–1996) claimed that he independently invented negative numbers at age 4.
Stan Ulam (1909–1984) (sometimes referred to as “the father of the Hbomb”) wrote in 1976: “When I was...

2 Mathematical Culture 2 Mathematical Culture (pp. 4688)Mathematicians constitute a community with a long, rich history. They recognize each other as fellow members of that community.What is the culture of mathematics and of the mathematical community?
This question seems to have been seldom asked and little studied. The American topologist Raymond Wilder was one outstanding contributor to this subject. In this chapter, we attempt to continue his work and highlight some salient features of mathematical culture.
When Paul Halmos was asked, “What is mathematics?” He answered, “It is security. Certainty. Truth. Beauty. Insight. Structure. Architecture.”¹ Most mathematicians agree with Halmos and treat the aesthetic components of...

3 Mathematics as Solace 3 Mathematics as Solace (pp. 89105)When looking at mathematical life, we usually focus on its public face: the institutions in which mathematicians work, their interactions within their communities, their jokes and eccentricities, their prizes and competitions, their breakthrough discoveries. In the following pages we address the more personal consequences of loving mathematics. We ask, “Is mathematics a safe hiding place from the miseries of the world?”
According to GianCarlo Rota, “Of all escapes from reality, mathematics is the most successful ever. It is a fantasy that becomes all the more addictive because it works back to improve the same reality we are trying to evade....

4 Mathematics as an Addiction: Following Logic to the End 4 Mathematics as an Addiction: Following Logic to the End (pp. 106137)The question is sometimes asked, To be a great mathematician, does being crazy help? The simple and straightforward answer is, No, of course not. Working in a university math department, or attending the meetings of the American Mathematical Society, one cannot help observing the pervasive normality. Still, there is something different about mathematicians compared to, say, chemists or geologists or even English professors. It is possible to be “crazy”—that is, conspicuously eccentric, very odd, even antisocial—and still hold a job as a math professor. Even, perhaps, as an industrial mathematician in certain organizations. If you are really good...

5 Friendships and Partnerships 5 Friendships and Partnerships (pp. 138175)Do mathematicians have friends?The popular image of a mathematician is that of a solitary man, alone at his desk or blackboard. In this chapter, we will see how far from the truth this picture is. While the sustained concentration needed for mathematical research does require quiet and a highly focused mindset, an intense and prolonged independent search can come to a dead end. The researcher who listens to colleagues’ insights can break through his private perspective.
One morning early in my (Hersh’s) years as a thesis student of Peter Lax, I entered my mentor’s office to find him glowing...

6 Mathematical Communities 6 Mathematical Communities (pp. 176227)What sorts of communities do mathematicians form? How do their communities shape their lives?We will describe some informal groups, which were formed around specific needs of their participants. Whether inside or outside universities, communities that were fueled by a shared vision have brought about significant change in mathematics.
Stan Ulam has written:
Much of the historical development of mathematics has taken place in specific centers. These centers, large or small, have formed around a single person or a few individuals, and sometimes as a result of the work of a number of people—a group in which mathematical activity...

7 Gender and Age in Mathematics 7 Gender and Age in Mathematics (pp. 228272)By the expression “a young man’s game” Hardy did not mean to exclude women. The famous British analyst Mary Cartwright was his student. In 1941, when Hardy wrote hisApology, normal usage was to write “man” either in the sense of “masculine” or in the sense of “human.” Nowadays, of course, we say “young person” if we mean to include both sexes. Hardy was not only a pacifist and an atheist but can even be counted as an early feminist, as attested by his active support for the EnglishAmerican mathematicianturnedbiophysicist Dorothy Wrinch.¹
Here we will give a brief survey of...

8 The Teaching of Mathematics: Fierce or Friendly? 8 The Teaching of Mathematics: Fierce or Friendly? (pp. 273300)In the previous chapter we wrote about the impact of age and gender on the ways in which mathematicians develop and sustain their lives. We emphasized the importance of balance and social connections as sources of support when researchers face societal stereotypes. Some may even find in mathematics an escape from social challenges, from “everyday life, with its painful harshness and wretched dreariness, and from the fetters of one’s shifting desire.”¹ But more often, one’s mathematical life is intimately entwined with the life and conditions of the larger society. The impact of a mathematician’s early socialization and its attending values...

9 Loving and Hating School Mathematics 9 Loving and Hating School Mathematics (pp. 301333)Mathematical life is an immersion in a world of endlessly varied forms and relations. The mathematician is challenged and tempted to commit all her energy and enthusiasm to learn and to understand. Mathematical thinking is also enjoyed by people working puzzles, playing chess, or doing recreational problem solving. Engagement with and enjoyment of mathematics is the primary topic of this book.
But there’s also another thing called mathematics. It’s the thing people are talking about when they say:
“I hate math! I couldn’t learn it, and I can’t teach it!”
“I’m bad at math. It’s always been my leastliked subject.”...

Conclusions Conclusions (pp. 334338)We have completed our journey, our tour around various aspects of mathematical life. We looked at the beginnings of mathematical life for children and students. Then we studied some of its special features as a unique subculture of modern society. We saw its ability, on the one hand, to provide its devotees with solace and refuge; and we saw, on the other hand, its dangers in permitting them isolation and eccentricity, which have in some rare cases extended to utter madness. We looked next at some of the glue that holds the mathematical community together, in a chapter on friendships,...

Review of the Literature Review of the Literature (pp. 339348) 
Biographies Biographies (pp. 349384) 
Notes Notes (pp. 385402) 
INDEX OF NAMES INDEX OF NAMES (pp. 403409) 
GENERAL INDEX GENERAL INDEX (pp. 410416)