Most helpful positive review
209 of 216 people found the following review helpful
Excellent Book. Belongs on Your Bookshelf.
on August 3, 2003
Courant's 500-page text is not entirely suitable for the layman. Its target audience includes those who enjoy reading and studying mathematics and have a good background through precalculus or higher. "What is Mathematics?" is a mathematics book, not a book about mathematics.
"What is Mathematics?" is not a new book. It was first published by Oxford University Press in 1941 with later editions in 1943, 1945, and 1947. Good quality soft cover copies are still in print as Oxford Paperbacks.
The authors indicate that it is no means necessary to "plow through it page by page, chapter by chapter". I fully agree. I have skipped around, jumping to chapters of particular interest, but I have now read nearly every chapter.
I initially skipped to page 165 and delved directly into projective geometry (chapter IV), proceeded to topology (chapter V), and then jumped backwards to the beginning to explore the theory of numbers. After moving to geometry, I finally returned to the later chapters on functions and limits, maxima and minima, and the calculus.
Courant engages the reader in discussions on mathematical concepts rather than focusing on applications and problem solving. "What is Mathematics?" is a great textbook for students that have completed a year or more of calculus and wish to pull all of their mathematical learning together before moving on to more advanced studies. I suspect that it would even be welcomed by students that have completed an undergraduate degree in mathematics.
I cannot resist quoting Albert Einstein's comment on What is Mathematics? - "A lucid representation of the fundamental concepts and methods of the whole field of mathematics...Easily understandable."
Richard Courant was a highly respected mathematician. He taught in Germany and in Cambridge and was director of the Institute of Mathematical Sciences at New York University (now renamed the Courant Institute of Mathematical Sciences). Courant has authored other widely acclaimed mathematical texts including Methods of Mathematical Physics (co-authored with David Hilbert) and his popular Differential and Integral Calculus.