# Role of Mathematics in the Rise of Science

Publication Year: 2014

The central theme of these essays is the nature and role of mathematics, its growth and spread, and its involvement with ever-wider areas of knowledge. The author attempts to determine the decisive and creative aspects of the abstractness" of mathematics which have made it the dominant intellectual force that it is. He frequently confronts the mathematics and physics of today with the mathematics and physics of the Greeks, which, however renowned, was not yet capable of this abstractness.

Originally published in 1981.

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Published by: Princeton University Press

Series: Princeton Legacy Library

#### Cover

#### Title page, Copyright

#### Preface

The chapters of this book were originally separate essays for several purposes, and all but one have been published before, beginning in 1961. The essays have now been revised, and linked up; and an Introduction, and a collection of Biographical Sketches in lieu of an Epilogue, have been added. ...

#### Part I. Essays

#### 2. How History of Science Differs from Other History

There are differences of consequence, we contend, between history of science and other history, mainly general (that is, politico-social) history, but also history of literature, and even history of philosophy proper. The differences are differences of degree only, but they are significant. ...

#### 3. Revolutions in Physics and Crises in Mathematics

We will now deal with two topics which, although
separable, are closely connected with each other. The first
and larger part of the chapter is concerned with the
conception of a revolution in physics, as recently blueprinted
in a provocative book by Thomas Kuhn.^{1} ...

#### 4. Aristotle's Physics and Today's Physics

In making some observations on the nature of the physics of the Greeks, especially of the physics of Aristotle, our aim will be to point up similarities and dissimilarities, analogies and discrepancies, between the physics of antiquity and the physics of today. ...

#### 5. The Role of Mathematics in the Rise of Mechanics

Mechanics, as a part of physics, is very mathematical, in imagery, content, and consequences. We will make some observations on the mathematical structure of mechanics during some phases of its development, and we will be concerned with the inward mathematical texture rather than with the outward mathematical setting. ...

#### 6. The Significance of Some Basic Mathematical Conceptions for Physics

The present chapter supplements and continues the preceding one, and we will again make observations on the relations between mathematics and physics on the level of abstractions and conceptualizations; in the preceding chapter we emphasized mechanics, and at present we will be more concerned with physics in general. ...

#### 7. The Essence of Mathematics

Mathematics is frequently encountered in association and interaction with Astronomy, Physics, and other branches of Natural Science, and it also has deep-rooted affinities to what are called Humanities nowadays. Actually, it is a realm of knowledge entirely by itself, and one of considerable scope too; ...

#### 8. The Essence of Analysis

Analysis is one of three main divisions of mathematics, the other two being (i) Geometry and Topology and (ii) Algebra and Arithmetic. In extent, Analysis is the largest; it comprises subdivisions which are nearly autonomous and which are easier to describe than the whole division. ...

#### Part II. Biographical Sketches

Aeschylus (525-456 B.C.), Attic Tragedian, the first, and still one of the greatest, tragedians in the "West" of whom entire plays survive. Aeschylus derived from landed aristocracy, and, although a lifelong poet by avocation, he led, as customary with Athenians of his generation, a crowded citizen's life in the service of the polis. ...

E-ISBN-13: 9781400852826

E-ISBN-10: 140085282X

Page Count: 400

Publication Year: 2014

Edition: Course Book

Series Title: Princeton Legacy Library

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