Mathematics is the only science with a methodology based upon deductive logic, whereas physics is a quantitative science based upon experiment and observation in which trial and error are inherent. Physics uses the most relevant mathematics, for example using group theory to explain the theoretical basis for the crystalline structure of solids, an illustration of how, time and time again, a mathematical theorem perhaps developed by a Greek philosopher is relevant to today's newly developed physics proof.
On the Shoulders of Giants investigates the relationship between the disciplines of physics and mathematics and shows how many of the most significant advances of 20th-century physics rely on mathematics developed, sometimes much earlier, with no particular physics application in mind. Quoting from mathematicians such as Poincaré and Euclid and physicists such as Newton and Feynman, the links between the two disciplines are explored in the author's entertaining style, providing a fascinating account of the twists and turns in scientific progress through the ages.
Challenging, stimulating, and questioning, the book explains how the uncanny ability of formal and abstract mathematics can interpret the properties of the physical world. Using a wide ranging set of examples, it illustrates the manner in which mathematics has been applied to physics and even points to directions for future research. The book discusses how to fill space without leaving gaps; Euclidean geometry, its limitations, and the bending of space; the laws of musical harmony, sound vibrations, and the confinement of electrons in solids; how to tile a floor efficiently; Newton's Laws of Motion, chaos, and the weather; group theory and garlic; the laws of chance; route-planning in Konigsberg with Euler; the rules that turn bath bubbles into suds; the shape of soot; and the Schrödinger equation and why a pendulum can never stop.
Requiring some prior knowledge of physics and mathematics, this well-illustrated book will be of interest to all readers with an interest in physics and mathematics, in learning more about the role of mathematics as the formal language of physics, and in how physics and mathematics have influenced scientific research.
Table of Contents
From Aristotle to the Structure of Glass
From Euclid to General Relativity
From Plucking Strings to Electrons in Solids
The Perception of Number: From Integers to Quaternions
From Tiling Floors to Quasicrystals
Determinism: From Newton to Quantum Chaos
Symmetry: From Galois to Superstrings
From Coin Tossing to Entropy
Topology: From the Bridges of Konigsberg to Polymers
From Parabolas to Fractons
Motion: From Zeno to Schrödinger
"…very readable… On more than one occasion, I found myself saying 'Oh, yes', as Lines brought together historical strands of a familiar derivation. Of course I knew how it was done and where it came from-after Lines had pointed it out."
"This book sets new standards in the popularization of both mathematics and physics. … cross-referencing gives the book a satisfying unity."
"…a very interesting popular science book…"
-Australian and New Zealand Physicist
"His aim has been to demonstrate the value of mathematics in science. The value is undoubted, but few have established it so clearly and with such fresh examples. A large audience of people with some acquaintance with either of those subjects could read this book with profit."
"…a beautifully written and highly entertaining book."
-Zentralblatt fur Mathematik