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The Mind of the Mathematician

Michael Fitzgerald and Ioan James

Publication Year: 2007

What makes mathematicians tick? How do their minds process formulas and concepts that, for most of the rest of the world’s population, remain mysterious and beyond comprehension? Is there a connection between mathematical creativity and mental illness? In The Mind of the Mathematician, internationally famous mathematician Ioan James and accomplished psychiatrist Michael Fitzgerald look at the complex world of mathematics and the mind. Together they explore the behavior and personality traits that tend to fit the profile of a mathematician. They discuss mathematics and the arts, savants, gender and mathematical ability, and the impact of autism, personality disorders, and mood disorders. These topics, together with a succinct analysis of some of the great mathematical personalities of the past three centuries, combine to form an eclectic and fascinating blend of story and scientific inquiry.

Published by: The Johns Hopkins University Press

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Preface

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pp. vii-viii

Psychologists have long been fascinated by mathematicians and their world. In this book we start with a tour of the extensive literature on the psychology of mathematicians and related matters, such as the source of mathematical creativity. By limiting both mathematical and psychological technicalities, or explaining them when necessary, we seek to make our review of ...

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Introduction

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pp. ix-xiii

Mathematics, according to the Marquis de Condorcet, is the science that yields the most opportunity to observe the workings of the mind. Its study, he wrote, is the best training for our abilities, as it develops both the power and the precision of our thinking. Henri Poincar

PART I: TOUR OF THE LITERATURE

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Chapter 1. Mathematicians and Their World

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pp. 3-23

A mathematician, according to the Oxford English Dictionary, is someone who is skilled in mathematics. Such a person may be involved in teaching or research, or in applications of the discipline. He or she may use mathematics to make a living, or enjoy it more as a form of recreation. Until relatively recently, mathematics embraced much of what we now call natural science, ...

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Chapter 2. Mathematical Ability

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pp. 24-41

In his best-known book, Hereditary Genius (1869), Francis Galton presents some evidence in favor of the inheritance of scientific ability but then concludes: ‘‘It is I believe owing to the favourable conditions of their early training that an unusually large proportion of the sons of the most gifted men of science become distinguished in the same career.’’ Notwithstanding ...

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Chapter 3. The Dynamics of Mathematical Creation

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pp. 42-64

Cognitive activities are the active processes through which knowledge is acquired, such as perception, attention, memory, and learning. Interest in these activities has a long history, stretching back to classical times; today there is a vast literature on the subject. We cannot possibly cover this here, but fortunately a handbook of mathematical cognition has recently been ...

PART II: TWENTY MATHEMATICAL PERSONALITIES

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Chapter 4. Lagrange, Gauss, Cauchy, and Dirichlet

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pp. 67-87

On 25 January 1736, Joseph-Louis Lagrange was born in a small town near the city of Turin, at that time capital of the Piedmont and the seat of the Savoyard kings of Sardinia. He was one of eleven children, only two of whom reached maturity. Their father held the office of treasurer of constructions and fortifications in Turin but had lost most of his money ...

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Chapter 5. Hamilton, Galois, Byron, and Riemann

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pp. 88-104

Archibald Hamilton, a lawyer who acted for the ardent Irish nationalist Archibald Hamilton Rowan, lived in Dublin. Like his wife, Sarah Hutton, he was of Scottish ancestry. At the stroke of midnight on 4 August 1805, their only son William, the future mathematician, was born. Possibly because his father was short on money, the boy was sent at the age of 3 to live with his ...

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Chapter 6. Cantor, Kovalevskaya, Poincar

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pp. 105-130

Georg Woldemar Cantor, the father of the mathematician, was a native of Copenhagen who in his youth moved to St. Petersburg. There he became a successful stockbroker and married Maria Anna Bohm Meyer, who came from a musical family. Their son Georg Ferdinand Ludwig Philipp was born on 3 March 1845, the first of four children. He was raised in an intensely ...

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Chapter 7. Hadamard, Hardy, Noether, and Ramanujan

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pp. 131-148

Jacques Hadamard was born in Versailles, southwest of Paris, on 8 December 1865. Most of his forebears on both sides were intellectuals of Jewish extraction, and had been based in Paris since 1808. Hadamard’s father taught Latin at the Lycée Charlemagne, and his mother was a noted music teacher who taught her son to play the violin at an early age. In 1871, ...

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Chapter 8. Fisher, Wiener, Dirac, and G

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pp. 149-162

Ronald Aylmer Fisher was born in the Finchley district of north London on 17 February 1890. He and his twin brother, who died in infancy, were the youngest of eight children. His father was a member of a well-known London firm of auctioneers. Although most of the members of his father’s family were in business, one of his brothers placed high in the Cambridge ...

References

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pp. 163-174

Index

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pp. 175-181


E-ISBN-13: 9780801896897
E-ISBN-10: 0801896894
Print-ISBN-13: 9780801885877
Print-ISBN-10: 0801885876

Page Count: 196
Publication Year: 2007

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Subject Headings

  • Mathematicians -- Psychology.
  • Mathematical ability.
  • Mathematical ability -- Sex differences.
  • Mathematics -- Psychological aspects.
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