Classics of Mathematics

Classics of Mathematics, edited by Ronald Calinger, 1995, 816 pages, $50.67, ISBN 0-02-318342-X.  Prentice Hall, Upper Saddle River, NJ 07458http://www.prenhall.com/

I am all for truth in advertising, and Classics of Mathematics is just that.  Calinger has assembled 134 classic mathematical works, covering the time period from ancient Mesopotamia and Egypt to the 20th century.  Calinger also includes a short section with some Arabic, Chinese, Indian, and Mayan works.  For teachers in secondary schools and for instructors of core college mathematics, the highlights are here: Euclid, Archimedes, Apollonius, Ptolemy, Lobachevsky (geometry); al-Khwarizmi, Cardano, Viète, Descartes, Fermat (algebra); Leibniz, Newton, Euler, Lagrange (calculus).  There is much more, of course.  For instructors of analysis there are Fourier, Cauchy, Weierstrass, and Dedekind;  for abstract algebra there are works by Gauss, Abel, and Galois.  There are even readings for “transition to advanced mathematics” courses: Boole, Peano, Cantor.  In summary, the readings in this book cover the usual topics from an undergraduate course on the history of mathematics.  As such this is an excellent anthology for undergraduate mathematics instructors.

Not only is this collection broader in both time frame and subject matter than most other anthologies, but it also has extra material that further sets it apart.  Before each entry is a considerable biography of its author which includes a discussion of the work and its relation to its time frame. 

Each chapter (roughly corresponding to the various time periods) begins with a substantial introduction which contains an overview of the mathematics of the time period and its place in the scientific, political, and cultural history of the era.  This perspective is often missing from history of mathematics courses, to the detriment of our students.  Each introduction ends with a great collection of references for further study, containing both primary and secondary sources.

The book is recommended for a variety of audiences.  For instructors of history of mathematics courses it has original sources of most of the highlights of the course.  Undergraduate mathematics instructors will find foundational papers in the usual core courses.  Undergraduate students could get their money’s worth just from the list of references—no literature search necessary!  Once you have gone through Calinger’s collection, your appetite should be whetted for the more specialized collections of source material of G. Birkhoff, D. E. Smith, D. J. Struik, and J. van Heijenoort.  Once you’ve read the classics, you won’t want to stop!

(Note:  This, the second printing, is noticeably thicker than the first printing.  The only differences appear to be a different page stock and printing that is not as crisp as before.  The page numbers remain the same.)

Gary S. Stoudt, Professor of Mathematics, Indiana University of Pennsylvania

See also the MAA Review by Fernando Q. Gouvêa.