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.
For more than two thousand years a familiarity with mathematics has
been regarded as an indispensable part of the intellectual
equipment of every cultured person. Today, unfortunately, the
traditional place of mathematics in education is in grave danger.
The teaching and learning of mathematics has degenerated into the
realm of rote memorization, the outcome of which leads to
satisfactory formal ability but does not lead to real understanding
or to greater intellectual independence.
This new edition of Richard Courant's and Herbert Robbins's
classic work seeks to address this problem. Its goal is to put the
meaning back into mathematics.
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, from topology
and calculus to matters of principle and the Continuum Hypothesis,
this fascinating survey allows readers to delve into mathematics as
an organic whole rather than an empty drill in problem solving.
With chapters largely independent of one another and sections that
lead upward from basic to more advanced discussions, readers can
easily pick and choose areas of particular interest without
impairing their understanding of subsequent parts. Brought up to
date with a new chapter by Ian Stewart, What is Mathematics?,
Second Edition offers new insights into recent mathematical
developments and describes proofs of the Four-Color Theorem and
Fermat's Last Theorem, problems that were still open when
Courant and Robbins wrote this masterpiece, but ones that have
since been solved.
Formal mathematics is like spelling and grammar - a matter of the
correct application of local rules. Meaningful mathematics is like
journalism - it tells an interesting story. But unlike some
journalism, the story has to be true. The best mathematics is like
literature - it brings a story to life before your eyes and
involves you in it, intellectually and emotionally. What is
Mathematics is like a fine piece of literature - it opens a window
onto the world of mathematics for anyone interested to view.
*Praise for the previous edition: "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 "Should prove a source of great pleasure and satisfaction."--Journal of Applied Physics "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
Richard Courant was born in 1888 in a small town of what is now Poland, and died in New Rochelle, N.Y. in 1972. He received his doctorate from the legendary David Hilbert in Göttingen, where later he founded and directed its famed mathematics Institute, a Mecca for mathematicians in the twenties. In 1933 the Nazi government dismissed Courant for being Jewish, and he emigrated to the United States. He found, in New York, what he called "a reservoir of talent" to be tapped. He built, at New York University, a new mathematical Sciences Institute that shares the philosophy of its illustrious predecessor and rivals it in worldwide influence. For Courant mathematics was an adventure, with applications forming a vital part.
