This collection of essays and reviews on mathematics covers topics including logic, combinatorics, statistics, economics, artificial intelligence, computer science and other applications of maths. History and philosophy are also covered, including discussion of the work of Ulam, Kant, Heidegger and others.
From the reviews of the second edition:
"...These papers reflect on mathematics and its influence on human society. They can help the specialist to notice what is going on around him, and they may lead educated people from other domains to a better understanding of mathematics. Many of these papers can advise educators how to form a modern mathematics education, which develops approved ideas and institutions...I admire the stimulating perspectives of the authors"
--American Mathematical Society
"Kac, Rota, and Schwartz have collected here: occasional essays about mathematics, mathematicians, and surrounding subjects. ... The essays are fun to read, light in manner but serious in content. Many of them are provocative. ... As a result, the book would make wonderful fodder for a reading course or seminar. ... Discrete Thoughts is a classic indeed." (Fernando Q. Gouvêa, MathDL, January, 2008)