Mathematics and the pursuit of knowledge

Author: M. Klein
Publisher:
Publication Date: 2005-05-01
Features: This book aims to demonstrate that (these) scientific discoveries are primarily—and in some fields, entirely—dependent on mathematics. Morris Klein is a rare scientist capable of conveying the complex and rich knowledge of his field in language accessible to the general reader. In this book, Klein examines the development of mathematics, the powerful tool the authors explored to understand the world. Since the time of ancient Greece, scientists have increasingly moved away from perception and toward observing phenomena such as gravity, electromagnetic waves, and the cosmic fabric of space-time in a mathematical way. Starting with the mathematics of ancient Greece, followed by early modern scientists like Galileo and Newton, and then the 20th-century theories of relativity and quantum mechanics, Klein traces the rise of mathematics as a scientific tool. He explores our existing mathematical world and explains how it works: a science that enables us to penetrate the secrets of natural phenomena. Surprisingly insightful. [Mathematics and physics] are not mysterious, but often obscure, confusing, and bewildering, and [Klein] elucidates the extraordinary insights and discoveries in both exploration fields with remarkable clarity. Highly enlightening. Dr. Klein is enthusiastic about the progress achieved with the help of mathematics, and he writes with passion. His success lies particularly in explaining to non-professionals the indispensable power and insight of mathematical analysis in exploring our own nature. – The Washington Times Magazine For decades, Klein has been not only a creative mathematician but also an exceptionally gifted mathematical explainer. His characteristic of being erudite yet accessible is evident in Mathematics and the Search for Knowledge. This book splendidly narrates the relentless collaboration of mathematics, physics, and philosophy in the struggle to explore what is real, a partnership that sometimes borders on familial intimacy. – The New York Review of Books With the wisdom of a mathematician, this book explores the role of mathematics in the evolution of modern natural sciences since ancient Greece, particularly since Galileo. The first chapter uses modern psychological illusions to demonstrate the unreliability of sensory perception. In fact, the ancient Greeks had already realized this, and thus turned to mathematics to study natural phenomena, which became a tradition in ancient Greece and also the reason for the rise of ancient Greek astronomy (Chapters 2 and 3). Whether it was Ptolemy’s geocentric theory or the heliocentric theories of Copernicus and Kepler, the pursuit of mathematical simplicity and perfection became the driving force in the quest for natural knowledge (Chapter 4). Descartes established a rigorous mathematical methodology for science, while Galileo, the father of modern science, based his scientific research program on the premise that the book of nature is written in the language of mathematics (Chapter 5). Newton, himself a great mathematician, titled his scientific masterpiece Principia Mathematica (Chapter 6). The Maxwell equations revealed the electromagnetic world beyond human perception, fully demonstrating the penetrating power of mathematics (Chapter 7). The two major scientific discoveries of the 20th century—relativity and quantum theory—show a remarkable correspondence between their fundamental physical ideas and mathematical tools (Chapters 8–10). This raises the question: where does mathematical knowledge itself come from? What is the relationship between mathematics and physical reality (Chapters 11 and 12)?
The book does not elaborate on mathematical knowledge; mathematics is merely present like a queen behind a curtain, subtly yet profoundly. Therefore, students of the humanities and social sciences who wish to gain insights into the history of natural philosophy or scientific methodology can find inspiration in this book, while students of natural sciences may reflect on their own field. And this is precisely what the author strives for: to build a bridge between natural sciences and the humanities and social sciences.