Many essays have been written on the definition of number. But most of them contain too many technical expressions, both philosophical and mathematical, to suit the non-mathematician. The clearest idea of what counting and numbers mean may be gained from the observation of children and of nations in the childhood of civilization.   When children count or add, they use either their fingers, or small sticks of wood, or pebbles, or similar things, which they adjoin singly...

Bestselling author and astrophysicist Mario Livio examines the lives and theories of history’s greatest mathematicians to ask how—if mathematics is an abstract construction of the human mind—it can so perfectly explain the physical world.Nobel Laureate Eugene Wigner once wondered about “the unreasonable effectiveness of mathematics” in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ...

This book is a collection of the finest mystical writings of the great physicists of the 20th Century. They are Max Planck, Albert Einstein, Niels Bohr, Werner Heisenberg, Erwin Schrödinger, Wolfgang Pauli, James Jeans, Arthur Eddington, Eugene Wigner, David Bohm, and Freeman Dyson. The essays are written in nontechnical language and will be of absorbing interest to a wide range of readers.The most beautiful thing we can experience is the mysterious. It is the fundamental emotion w...

The Holy Grail of mathematics revealed in a truly 17th-century numerical and geometrical proof as a letter by Fermat to a colleague. This will withstand all challenges.

The ancient Greeks discovered them, but it wasn't until the nineteenth century that irrational numbers were properly understood and rigorously defined, and even today not all their mysteries have been revealed. In The Irrationals, the first popular and comprehensive book on the subject, Julian Havil tells the story of irrational numbers and the mathematicians who have tackled their challenges, from antiquity to the twenty-first century. Along the way, he explains why irrational nu...

Time and again, when studying the history of scientific and philosophical thought in the sixteenth and the seventeenth centuries-they are, indeed, so closely interrelated and linked together that, separated, they become ununderstandable-I have been forced to recognize, as many others have before me, that during this period human, or at least European, minds underwent a deep revolution which changed the very framework and patterns of our thinking and of which modern science and modern philo...

THE ABSTRACT NATURE OF MATHEMATICSThe study of mathematics is apt to commence in disappointment. The important applications of the science, the theoretical interest of its ideas, and the logical rigor of its methods, all generate the expectation of a speedy introduction to processes of interest. We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this great science eludes the efforts...

Geometry defines the world around us, helping us make sense of everything from architecture to military science to fashion. And for over two thousand years, geometry has been equated with Euclid's Elements, arguably the most influential book in the history of mathematics In The King of Infinite Space, renowned mathematics writer David Berlinski provides a concise homage to this elusive mathematician and his staggering achievements. Berlinski shows that, for centuries, sci...

Adrian Bardon's A Brief History of the Philosophy of Time is a short introduction to the history, philosophy, and science of the study of time-from the pre-Socratic philosophers through Einstein and beyond. A Brief History of the Philosophy of Time covers subjects such as time and change, the experience of time, physical and metaphysical approaches to the nature of time, the direction of time, time travel, time and freedom of the will, and scientific and philosophical approaches to eternit...

Though formal logic has in recent times been the object of radical and spirited attacks from many and diverse quarters, it continues, and will probably long continue, to be one of the most frequently given courses in colleges and universities here and abroad. Nor need this be surprising when we reflect that the most serious of the charges against formal logic, those against the syllogism, are as old as Aristotle, who seems to have been fully aware of them. But while the realm of logic seem...

The mystical writings of the world’s great physicists—now in one eye-opening volume that bridges the gap between science and religionQuantum Questions collects the mystical writings of each of the major physicists involved in the discovery of quantum physics and relativity, including Albert Einstein, Werner Heisenberg, and Max Planck. The selections are written in nontechnical language and will be of interest to scientists and nonscientists alike.

A witty, conversational, and accessible tour of math's profoundest mysteries.Mathematical symbols, for mathematicians, store worlds of meaning, leap continents and centuries. But we need not master symbols to grasp the magnificent abstractions they represent, and to which all art aspires. Through language, anyone can come to delight in the works of mathematical art, which are among our kind's greatest glories.Taking the concept of infinity, in its countless...