The Mind of the Mathematician
Publication Year: 2007
Published by: The Johns Hopkins University Press
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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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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
Chapter 1. Mathematicians and Their World
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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, ...
Chapter 2. Mathematical Ability
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In his best-known book, Hereditary Genius (1869), Francis Galton presents some evidence in favor of the inheritance of scientific ability but then concludes: ââIt 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.ââ Notwithstanding ...
Chapter 3. The Dynamics of Mathematical Creation
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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
Chapter 4. Lagrange, Gauss, Cauchy, and Dirichlet
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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 ...
Chapter 5. Hamilton, Galois, Byron, and Riemann
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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 ...
Chapter 6. Cantor, Kovalevskaya, Poincar
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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 ...
Chapter 7. Hadamard, Hardy, Noether, and Ramanujan
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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. Hadamardâs father taught Latin at the LycÃ©e Charlemagne, and his mother was a noted music teacher who taught her son to play the violin at an early age. In 1871, ...
Chapter 8. Fisher, Wiener, Dirac, and G
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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 fatherâs family were in business, one of his brothers placed high in the Cambridge ...
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Page Count: 196
Publication Year: 2007