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Mathematics and the Historian's Craft: The Kenneth O. May Lectures

Glen Van Brummelen ; Michael Kinyon (eds.)

Resumen/Descripción – provisto por la editorial

No disponible.

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Institución detectada Año de publicación Navegá Descargá Solicitá
No detectada 2005 SpringerLink

Información

Tipo de recurso:

libros

ISBN impreso

978-0-387-25284-1

ISBN electrónico

978-0-387-28272-5

Editor responsable

Springer Nature

País de edición

Reino Unido

Fecha de publicación

Información sobre derechos de publicación

© Springer Science+Business Media, Inc. 2005

Cobertura temática

Tabla de contenidos

Introduction: The Birth and Growth of a Community

Amy Shell-Gellasch

Retinitis pigmentosa (RP) is a general term used to refer to a group of related inherited diseases typically characterized by poor vision in dim light, constricted visual fields, bone spicule-like pigmentation of the fundus, and electroretinographic evidence of photoreceptor cell dysfunction. These diseases can be inherited as an autosomal dominant, autosomal recessive, or X-linked recessive trait. Mitochondrial inheritance has also been described, often as part of a syndrome. It has been estimated that RP affects approximately 1 in 3700 people in the United States. Inherited retinopathies affect approximately 1 in 2000 individuals worldwide. Approximately 20% of these cases are autosomal dominant,and 6%to 9% are X-linked. The remaining 71% to 84% are either autosomal recessive or isolated “simplex” cases. The latter may represent autosomal recessive disease, a new autosomal dominant mutation,or an environmental phenocopy. In the United Kingdom, X-linked RP appears to be more common than in the United States.

Pp. 3-6

History or Heritage? An Important Distinction in Mathematics and for Mathematics Education

Ivor Grattan-Guinness

My goal here clearly has not been the presentation of a definitive account or a polished treatise. It was my intention to throw out food for thought, to illustrate some of the curiosities and ironies inherent in women’s position in mathematics historically and across cultures. The interactions of gender and culture are never simple or straightforward. The history of women in mathematics has not been some Whiggish triumphal passage from darkness into light, but neither has it been a chronicle exclusively of discrimination and marginalization. The history and present status of women in mathematics are complicated, and often the picture has elements of contradiction. One conclusion seems obvious, however. The complex and multifaceted interactions of gender and mathematics can be understood only if one takes into account historical and cross-cultural perspectives.

Pp. 7-21

Ptolemy’s Mathematical Models and their Meaning

Alexander Jones

My goal here clearly has not been the presentation of a definitive account or a polished treatise. It was my intention to throw out food for thought, to illustrate some of the curiosities and ironies inherent in women’s position in mathematics historically and across cultures. The interactions of gender and culture are never simple or straightforward. The history of women in mathematics has not been some Whiggish triumphal passage from darkness into light, but neither has it been a chronicle exclusively of discrimination and marginalization. The history and present status of women in mathematics are complicated, and often the picture has elements of contradiction. One conclusion seems obvious, however. The complex and multifaceted interactions of gender and mathematics can be understood only if one takes into account historical and cross-cultural perspectives.

Pp. 23-42

Mathematics, Instruments and Navigation, 1600–1800

Jim Bennett

In the years 1935–1945 there are distinct signs of research mathematics beginning to come to Canada. Synge returned to Toronto in 1930 as the head of a new Department of Applied Mathematics, which later included Alexander Weinstein and Leopold Infeld. In addition, the Nuremberg Laws brought the first refugee mathematician of what would later be a large and productive group: Richard Brauer came to Toronto in 1935. Brauer’s appointment was apparently made at the suggestion of Emmy Noether, as Robinson reports. However, Robinson also reports that “Our chairman was anxious to build up the department, and the suggestion was immediately accepted”, while Morawetz notes “It is hard to imagine today the struggle to make that appointment”. This is just one example of history that this brief article has not been able to unravel. In addition to the refugee influx-in part unwilling, as enemy aliens arrested in Britain and transported-we see a general growth in interest in both pure and applied mathematics across the country after the war. Young mathematicians began to leave the country for mathematical study. Their return to teaching posts, their research activity, and the founding of the Canadian Mathematical Society/Société mathématique du Canada brought new perspectives to mathematics in Canada. Mathematics began to develop in an independent fashion, with new contacts with the world mathematics community.

Pp. 43-55

Was Newton’s Calculus a Dead End? The Continental Influence of Maclaurin’s

Judith V. Grabiner

My goal here clearly has not been the presentation of a definitive account or a polished treatise. It was my intention to throw out food for thought, to illustrate some of the curiosities and ironies inherent in women’s position in mathematics historically and across cultures. The interactions of gender and culture are never simple or straightforward. The history of women in mathematics has not been some Whiggish triumphal passage from darkness into light, but neither has it been a chronicle exclusively of discrimination and marginalization. The history and present status of women in mathematics are complicated, and often the picture has elements of contradiction. One conclusion seems obvious, however. The complex and multifaceted interactions of gender and mathematics can be understood only if one takes into account historical and cross-cultural perspectives.

Pp. 57-79

The Mathematics and Science of Leonhard Euler (1707–1783)

Rüdiger Thiele

My goal here clearly has not been the presentation of a definitive account or a polished treatise. It was my intention to throw out food for thought, to illustrate some of the curiosities and ironies inherent in women’s position in mathematics historically and across cultures. The interactions of gender and culture are never simple or straightforward. The history of women in mathematics has not been some Whiggish triumphal passage from darkness into light, but neither has it been a chronicle exclusively of discrimination and marginalization. The history and present status of women in mathematics are complicated, and often the picture has elements of contradiction. One conclusion seems obvious, however. The complex and multifaceted interactions of gender and mathematics can be understood only if one takes into account historical and cross-cultural perspectives.

Pp. 81-140

Mathematics in Canada before 1945: A Preliminary Survey

Thomas Archibald; Louis Charbonneau

In the years 1935–1945 there are distinct signs of research mathematics beginning to come to Canada. Synge returned to Toronto in 1930 as the head of a new Department of Applied Mathematics, which later included Alexander Weinstein and Leopold Infeld. In addition, the Nuremberg Laws brought the first refugee mathematician of what would later be a large and productive group: Richard Brauer came to Toronto in 1935. Brauer’s appointment was apparently made at the suggestion of Emmy Noether, as Robinson reports. However, Robinson also reports that “Our chairman was anxious to build up the department, and the suggestion was immediately accepted”, while Morawetz notes “It is hard to imagine today the struggle to make that appointment”. This is just one example of history that this brief article has not been able to unravel. In addition to the refugee influx-in part unwilling, as enemy aliens arrested in Britain and transported-we see a general growth in interest in both pure and applied mathematics across the country after the war. Young mathematicians began to leave the country for mathematical study. Their return to teaching posts, their research activity, and the founding of the Canadian Mathematical Society/Société mathématique du Canada brought new perspectives to mathematics in Canada. Mathematics began to develop in an independent fashion, with new contacts with the world mathematics community.

Pp. 141-182

The Emergence of the American Mathematical Research Community

Karen Hunger Parshall

My goal here clearly has not been the presentation of a definitive account or a polished treatise. It was my intention to throw out food for thought, to illustrate some of the curiosities and ironies inherent in women’s position in mathematics historically and across cultures. The interactions of gender and culture are never simple or straightforward. The history of women in mathematics has not been some Whiggish triumphal passage from darkness into light, but neither has it been a chronicle exclusively of discrimination and marginalization. The history and present status of women in mathematics are complicated, and often the picture has elements of contradiction. One conclusion seems obvious, however. The complex and multifaceted interactions of gender and mathematics can be understood only if one takes into account historical and cross-cultural perspectives.

Pp. 183-202

19th Century Logic Between Philosophy and Mathematics

Volker Peckhaus

The history of modern logic is usually written as the history of mathematical or, more general, symbolic logic. As such it was created by mathematicians. Not regarding its anticipations in Scholastic logic and in the rationalistic era, its continuous development began with George Boole’s of 1847, and it became a mathematical subdiscipline in the early 20th century. This style of presentation cuts off one eminent line of development, the philosophical development of logic, although logic is evidently one of the basic disciplines of philosophy. One needs only to recall some of the standard 19th century definitions of logic as, e.g., the art and science of reasoning (Whateley) or as giving the normative rules of correct reasoning (Herbart). In the paper the relationship between the philosophical and the mathematical development of logic will be discussed. Answers to the following questions will be provided:

Pp. 203-220

The Battle for Cantorian Set Theory

Joseph W. Dauben

My goal here clearly has not been the presentation of a definitive account or a polished treatise. It was my intention to throw out food for thought, to illustrate some of the curiosities and ironies inherent in women’s position in mathematics historically and across cultures. The interactions of gender and culture are never simple or straightforward. The history of women in mathematics has not been some Whiggish triumphal passage from darkness into light, but neither has it been a chronicle exclusively of discrimination and marginalization. The history and present status of women in mathematics are complicated, and often the picture has elements of contradiction. One conclusion seems obvious, however. The complex and multifaceted interactions of gender and mathematics can be understood only if one takes into account historical and cross-cultural perspectives.

Pp. 221-241