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Discrete thoughts: Essays on mathematics, science, and philosophy
"‘Mathematicians, like Proust and everyone else, are at their best when writing about their first love†… They are among the very best we have; and their best is very good indeed. … One approaches this book with high hopes. Happily, one is not disappointed." "…In paperback it might well have become a best seller. …read it." From The Mathematical Intelligencer "Mathematics is shaped by the consistent concerns and styles of powerful minds —three of which are represented here. Kacâ€s work is marked by deep commitment and breadth of inquiry. "Rota is the easiest of these authors to read…a witty and urbane, with a clear and interesting agenda and an astonishing intellectual range. To read him is to be a part of a pleasant and rewarding conversation. "Jacob T. Schwartz attacks problems in…computer science, mathematical economics, computer and instructional … No matter how slippery the problem, Schwartz manages to capture a substantial chunk of it in his mathematical net." — Mathematics Magazine This is a volume of essays and reviews that delightfully explore mathematics in all its moods — from the light and the witty, and humorous to serious, rational, and cerebral. Topics logic, combinatorics, statistics, economics, artificial intelligence, computer science, and applications of mathematics broadly. You will also find history and philosophy covered, including discussion of the work of Ulam, Kant, Heidegger among others.
264 pages, Paperback
First published January 1, 1985
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Displaying 1 - 4 of 4 reviews
December 22, 2007
The full title of the book is Discrete Thoughts: Essays on Mathematics, Science, and Philosophy. The full author list is Mark Kac, Gian-Carlo Rota, and Jack Schwartz. I bought it after reading Indiscrete Thoughts by Gian-Carlo Rota. While some Schwartz's essays are cogent and pointed (e.g. "The Pernicious Influence of Mathematics on Science"), most of my favorite essays in this collection belong to Rota, who has an elegant and sometimes devastating turn of phrase. The book would be worth buying just for Rota's "discrete thoughts," compiled like bookends at the beginning and the end of the volume. My favorite may be this one, from the end of the first chapter: "Mathematicians, like Proust and everyone else, are at their best when writing about their first love."
August 29, 2019
It's a shame that this book isn't a regular fixture of undergraduate math departments, because it's one of the few books that reads the same way mathematicians speak. Kac and Rota write with such easy whimsy, and erudite doublespeak, that it makes you dizzy.
The book is actually a pretty good litmus test: if you can survive reading their essays, which are remarkably readable, insightful, and even at times educational, you might just have a career in mathematics.
Not only is it a joy to read three authors with a deep and varied passion in mathematics, its past and present, but it's an interesting historical relic. They often speculate, particularly on the infant Computer Science, what the future holds. They predict, with startling accuracy, the glorious danger of blindly applying game theory to economics, and the potential for computers to revolutionize everything.
It does, however, start to feel a little scattershot by the end. Some essays are just book reviews -- frankly a little overly scathing at times (a biography of Hilbert is described "factually impeccable and intellectually a fiasco"). And while Schwartz's essays are included since he clearly has a far better grasp of computers, it is also clear that he isn't nearly as talented a writer. Which is a shame, because they're very interesting, but he lacks Kac and Rota's gleeful, devilish approach to verbal antics.
[I'm also less than wild about Rota's tic in particular of including entire passages in German or French untranslated. I suspect if I was reading the essay by itself, a little work on the reader's part is forgivable and even encouraging. But after a while, it sure feels like I'm intentionally being left out]
Nevertheless, I'd wish more books in mathematics took the same approach as this. A frank, mature attitude leavened with childlike love for a wholly human endeavor.
How much longer will the present folie for precision in philosophy last? Need a concept be precise in order to be meaningful and effective? Or do philosophers wish to commit hari-kiri on the altar of mathematics?
Complete axiomatization, someone has rightly said, is an obituary of an idea, and Hilbert's great feat was, in a way only a magnificent necrology of geometry. Anyway, there are worse things than being wrong, and being dull and pedantic are surely among them.
The book is actually a pretty good litmus test: if you can survive reading their essays, which are remarkably readable, insightful, and even at times educational, you might just have a career in mathematics.
Not only is it a joy to read three authors with a deep and varied passion in mathematics, its past and present, but it's an interesting historical relic. They often speculate, particularly on the infant Computer Science, what the future holds. They predict, with startling accuracy, the glorious danger of blindly applying game theory to economics, and the potential for computers to revolutionize everything.
It does, however, start to feel a little scattershot by the end. Some essays are just book reviews -- frankly a little overly scathing at times (a biography of Hilbert is described "factually impeccable and intellectually a fiasco"). And while Schwartz's essays are included since he clearly has a far better grasp of computers, it is also clear that he isn't nearly as talented a writer. Which is a shame, because they're very interesting, but he lacks Kac and Rota's gleeful, devilish approach to verbal antics.
[I'm also less than wild about Rota's tic in particular of including entire passages in German or French untranslated. I suspect if I was reading the essay by itself, a little work on the reader's part is forgivable and even encouraging. But after a while, it sure feels like I'm intentionally being left out]
Nevertheless, I'd wish more books in mathematics took the same approach as this. A frank, mature attitude leavened with childlike love for a wholly human endeavor.
December 3, 2018
Most enjoyable was Rota's philosophicacl musings. 5/5.
January 1, 2019
I wish more people who are interested in science read this. Pithy, sophisticated, novel, and insightful. Short chapters.
Displaying 1 - 4 of 4 reviews