Kline M. Mathematics in Western Culture

Oxford: Oxford University Press, 1964. — 512 p.The object of this book is to advance the thesis that mathematics has been a major cultural force in Western civilization. Almost everyone knoivs that mathematics serves the very practical purpose of dictating engineering design. Fewer people seem to be aware that mathematics carries the main burden of scientific reasoning and is the core of the major theories of physical science. It is even less widely known that mathematics has determined the direction and content of much philosophic thought, has destroyed and rebuilt religious doctrines, has supplied substance to economic and political theories, has fashioned major painting, musical, architectural, and literary styles, has fathered our logic, and has furnished the best answers we have to fundamental questions about the nature of man and his universe. As the embodiment and most powerful advocate of the rational spirit, mathematics has invaded domains ruled by authority, custom, and habit, and supplanted them as the arbiter of thought and action. Finally, as an incomparably fine human achievement mathematics offers satisfactions and aesthetic values at least equal to those offered by any other branch of our culture. In this book we shall survey mathematics primarily to show how its ideas have helped to mold twentieth-century life and thought. The ideas will be in historical order so that our material will range from the beginnings in Babylonia and Egypt to the modern theory of relativity. Some people may question the pertinence of material belonging to earlier historical periods. Modern culture, however, is the accumulation and synthesis of contributions made by many preceding civilizations. The Greeks, who first appreciated the power of mathematical reasoning, graciously allowing the gods to use it in designing the universe, and then urging man to uncover the pattern of this design, not only gave mathematics a major place in their civilization but initiated patterns of thought that are basic in our own. As succeeding civilizations passed on their gifts to modern times, they handed on new and increasingly more significant roles for mathematics. Many of these functions and influences of mathematics are now deeply imbedded in our culture. Even the modern contributions of mathematics are best appreciated in the light of what existed previously.Introduction. True and False Conceptions
The Rule of Thumb in Mathematics
The Birth of the Mathematical Spirit
The Elements of Euclid
Placing a Yardstick to the Stars
Nature Acquires Reason
Interlude
Renewal of the Mathematical Spirit
The Harmony of the World
Painting arid Perspective
Science Born of Art: Projective Geometry
A Discourse on Method
The Quantitative Approach to Nature
The Deduction of Universal Laws
Grasping the Fleeting Instant: The Calculus
The Newtonian Influence: Science and Philosophy
The Newtonian Influence: Religion
The Newtonian Influence: Literature and Aesthetics
The Sine of G Major
Mastery of the Ether Waves
The Science of Human Nature
The Mathematical Theory of Ignorance: The Statistical Approach to the Study of Man
Prediction and Probability
Our Disorderly Universe: The Statistical View of Nature
The Paradoxes of the Infinite
New Geometries, New Worlds
The Theory of Relativity
Mathematics: Method and Art
Selected references