''What Is Mathematics?'' is the title of a classic book by

Richard Courant Richard Courant (January 8, 1888 – January 27, 1972) was a German-American mathematician. He is best known by the general public for the book '' What is Mathematics?'', co-written with Herbert Robbins. His research focused on the areas of real ...

and

Herbert Robbins Herbert Ellis Robbins (January 12, 1915 – February 12, 2001) was an American mathematician and statistician. He did research in topology, measure theory, statistics, and a variety of other fields. He was the co-author, with Richard Courant ...

, published by

Oxford University Press Oxford University Press (OUP) is the publishing house of the University of Oxford. It is the largest university press in the world. Its first book was printed in Oxford in 1478, with the Press officially granted the legal right to print books ...

. Written in the belief that "the traditional place of mathematics in education is in grave danger," it is an introduction to mathematics, intended to offer "vantage points from which the substance and driving forces of modern mathematics can be surveyed" both by students and by the general public. First published in 1941, it discusses

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

, and

calculus Calculus is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the ...

. A posthumous edition was published in 1996 with an additional chapter on recent progress in mathematics, written by Ian Stewart.

Authorship

The book was based on Courant's course material. Although Robbins assisted in writing a large part of the book, he had to fight for authorship. Courant alone held the copyright for the book. This resulted in Robbins receiving a smaller share of the royalties.Reid, Constance, Courant in Göttingen and New York. The story of an improbable mathematician. Springer-Verlag, New York-Heidelberg, 1976. ii+314 pp.

Title

Michael Katehakis, remembering Robbins's interest in literature, believes that the title of the book is probably due to Robbins, inspired by '' What Is Art?'' by

Leo Tolstoy Count Lev Nikolayevich Tolstoy Tolstoy pronounced his first name as , which corresponds to the romanization ''Lyov''. () (; ,Throughout Tolstoy's whole life, his name was written as using Reforms of Russian orthography#The post-revolution re ...

. Robbins did something similar in ''Great Expectations: The Theory of Optimal Stopping'', which he co-authored with Yuan-Shih Chow and David Siegmund. In this case, literate readers are likely to note that ''

Great Expectations ''Great Expectations'' is the thirteenth novel by English author Charles Dickens and his penultimate completed novel. The novel is a bildungsroman and depicts the education of an orphan nicknamed Pip. It is Dickens' second novel, after ''Dav ...

'' is a well-known novel by

Charles Dickens Charles John Huffam Dickens (; 7 February 1812 – 9 June 1870) was an English novelist, journalist, short story writer and Social criticism, social critic. He created some of literature's best-known fictional characters, and is regarded by ...

. According to

Constance Reid Constance Bowman Reid (January 3, 1918 – October 14, 2010) was the author of several biographies of mathematicians and popular books about mathematics. She received several awards for mathematical exposition. She was not a mathematician ...

, Courant finalized the choice of the title after discussing it with

Thomas Mann Paul Thomas Mann ( , ; ; 6 June 1875 – 12 August 1955) was a German novelist, short story writer, social critic, philanthropist, essayist, and the 1929 Nobel Prize in Literature laureate. His highly symbolic and ironic epic novels and novell ...

Translations

*The first Russian translation ''Что такое математика?'' was published in 1947; there were 5 translations since then, the last one in 2010. *The first Italian translation, ''Che cos'è la matematica?'', was published in 1950. А translation of the second edition was issued in 2000. *The first German translation ''Was ist Mathematik?'' by Iris Runge was published in 1962. *A Spanish translation of the second edition, ''¿Qué Son Las Matemáticas?'', was published in 2002. *The first Bulgarian translation, ''Що е математика?'', was published in 1967. А second translation appeared in 1985. *The first Romanian translation, ''Ce este matematica?'', was published in 1969. *The first Polish translation, ''Co to jest matematyka'', was published in 1959. А second translation appeared in 1967. А translation of the second edition was published in 1998. *The first Hungarian translation, ''Mi a matematika?'', was published in 1966. *The first Serbian translation, ''Šta je matematika?'', was published in 1973. *The first Japanese translation, ', was published in 1966. А translation of the second edition was published in 2001. *A Korean translation of the second edition, ', was published in 2000. *A Portuguese translation of the second edition, ''O que é matemática?'', was published in 2000.

Reviews

What is Mathematics? An Elementary Approach to Ideas and Methods
book review by Brian E. Blank, ''Notices of the American Mathematical Society'' 48, #11 (December 2001), pp. 1325–1330
What is Mathematics?
book review by Leonard Gillman, ''The American Mathematical Monthly'' 105, #5 (May 1998), pp. 485–488.

Editions

* Reprinted several times with a few corrections of minor errors and misprints as a "Second Edition" in 1943, a "Third Edition" in 1945, a "Fourth Edition" in 1947", a "Ninth Printing" in 1958 and a "Tenth Printing" in 1960, and another edition in 1978.Courant, Richard and Robbins, Herbert Ellis, ''What is Mathematics?'', Oxford University Press, London-New York-Toronto, Tenth Printing, 1960. xix+521 pp.Courant, Richard and Robbins, Herbert Ellis, ''What is Mathematics?'', Oxford University Press, London-New York-Toronto, 1978. * (1996) 2nd edition, with additional material by Ian Stewart. New York:

. . * French translation of the second English edition by Marie Anglade and Karine Py. * Spanish translation of the second English edition. * (first Italian translation, from the 1945 English edition) * (based on the previous Eianudi's edition) * (Vietnamese translation by Hàn Liên Hải from the Russian edition) * (Italian translation of the second English edition)

References

{{Authority control Books by Ian Stewart (mathematician) Mathematics textbooks 1941 non-fiction books