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What Is Mathematics?


An Elementary Approach to Ideas and Methods

Second Edition

the late Richard Courant and Herbert Robbins
Revised by Ian Stewart

05 September 1996

ISBN: 9780195105193

592 pages

Price: £15.99


Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics?, Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving.

About the Author(s)

the late Richard Courant, Courant Institute of Mathematical Sciences, New York University, and Herbert Robbins, Professor of Mathematics, Rutgers University

Revised by Ian Stewart, Professor of Math and Gresham Professor of Geometry, University of Warwick

The late Richard Courant, headed the Department of Mathematics at New York University and was Director of the Institute of Mathematical Sciences—which has subsequently renamed the Courant Institute of Mathematical Sciences. His book Mathematical Physics is familiar to every physicist, and his book Differential and Integral Calculus is acknowledged to be one of the best presentations of the subject written in modern times. Herbert Robbins is New Jersey Professor of Mathematical Statistics at Rutgers University. Ian Stewart is Professor of Mathematics at the University of Warwick, and author of Nature's Numbers and Does God Play Dice?. He also writes the "Mathematical Recreations" column in Scientific American.


Can...be read with great profit by anyone desiring general mathematical literacy. - Mathematics Abstracts

A great book. - Ludwig Otto, Paul Quinn College

A lucid representation of the fundamental concepts and methods of the whole field of mathematics. It is an easily understandable introduction for the layman and helps to give the mathematical student a general view of the basic principles and methods. - Albert Einstein

Without doubt, the work will have great influence. It should be in the hands of everyone, professional or otherwise, who is interested in scientific thinking. - The New York Times

A work of extraordinary perfection. - Mathematical Reviews

It contains an excellent selection of material for students who have no desire to develop mathematical skills but who may be willing to look briefly into this field of intellectual activity....For the inquiring student who wishes to know what real mathematics is about, or for the trained engineer or physicist who has some interest in the justification of procedures he uses, it should prove a source of great pleasure and satisfaction. - Journal of Applied Physics

This book is a work of art. - Marston Morse

This is not a book in philosophy; but there are probably few philosophers who can not gain instruction and clarification from it. It succeeds brilliantly in conveying the intellectual excitement of mathematical inquiry and in communicating the essential ideas and methods."Journal of Philosophy -

It is a work of high perfection, whether judged by aesthetic, pedagogical or scientific standards. It is astonishing to what extent What is Mathematics? has succeeded in making clear by means of the simplest examples all the fundamental ideas and methods which we mathematicians consider the life blood of our science. - Herman Weyl

Still a book that all prospective mathematics teachers should read and experience. A rare book that has retained its "freshness" and readability for more than 50 years....Very readable. - Stephen Krulik, Temple University