You are here

Discrete Thoughts: Essays on Mathematics, Science, and Philosophy

Marc Kac, Gian-Carlo Rota, and Jacob T. Schwartz
Publication Date: 
Number of Pages: 
Modern Birkhäuser Classics
BLL Rating: 

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Fernando Q. Gouvêa
, on

It's important not to confuse Discrete Thoughts with its brother in the same reprint series, Indiscrete Thoughts. Both were originally published in the 1990s: Discrete first, in 1985, with a revised edition in 1992, which is the one reprinted here. Then Indiscrete, in 1997. Both are very good books, and very much worth one's time and attention, and I am delighted that Birkhäuser has brought them back in their Modern Classics series.

In his introduction to Discrete Thoughts, Gian-Carlo Rota argues, in his inimitable style, that

Today, as in the last century, what rare glimpses of genuine expression we ever get will be found in offhand remarks hidden within an ephemeral essay we have allowed ourselves to write in a moment of weakness, or as a casual revelation inserted between the lines of some overdue book review.

That is what Kac, Rota, and Schwartz have collected here: occasional essays about mathematics, mathematicians, and surrounding subjects. There are fairly serious essays on the history and philosophy of mathematics (and, as always, we get some phenomenology from Rota), but there are also many essays on mathematics, statistics, and computer science, often focusing on what is going on in the field and arguing for what should be going on. There is even an article on mathematical economics.

The essays are fun to read, light in manner but serious in content. Many of them are provocative. For example, there is an essay here on "The Pernicious Influence of Mathematics on Science" (Schwartz), and one on "Misreading the History of Mathematics" (Rota). As a result, the book would make wonderful fodder for a reading course or seminar.

Discrete Thoughts has come back into print as part of the Modern Birkhäuser Classics series. I'm always a little skeptical about such reprint series; sometimes it seems as if publishers think "classic" means "book we want to keep in print in a cheap edition." But this time the series title is amply justified: Discrete Thoughts is a classic indeed.

Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College; he is the editor of MAA Reviews.


Preface.- Acknowledgements.- Discrete thoughts.- Mathematics: Tensions.- The Pernicious Influence of Mathematics on Science.- Statistics.- Statistics and Its History.- Combinatorics.- Computer Science.- Mathematics: Trends.- The Future of Computer Science.- Economics, Mathematical and Empirical.- Complicating Mathematics.- Mathematics and Its History.- Academic Responsibility.- Husserl and the Reform of Logic.- Husserl.- Artificial Intelligence.- Computing and Its History.- Will Computers Replace Humans?.- Computer-Aided Instruction.- Misreading the History of Mathematics.- The Wonderful World of Uncle Stan.- Ulam.- Kant.- Heidegger.- Doing Away with Science.- More Discrete Thoughts