- Paperback: 440 pages
- Publisher: Houghton Mifflin Company (May 1982)
- Language: English
- ISBN-10: 039532131X
- ISBN-13: 978-0395321317
- Product Dimensions: 1 x 6.5 x 9.2 inches
- Shipping Weight: 1.6 pounds
- Average Customer Review: 27 customer reviews
- Amazon Best Sellers Rank: #2,170,763 in Books (See Top 100 in Books)
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The Mathematical Experience
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We tend to think of mathematics as uniquely rigorous, and of mathematicians as supremely smart. In his introduction to The Mathematical Experience, Gian-Carlo Rota notes that instead, "a mathematician's work is mostly a tangle of guesswork, analogy, wishful thinking and frustration, and proof ... is more often than not a way of making sure that our minds are not playing tricks." Philip Davis and Reuben Hersh discuss everything from the nature of proof to the Euclid myth, and mathematical aesthetics to non-Cantorian set theory. They make a convincing case for the idea that mathematics is not about eternal reality, but comprises "true facts about imaginary objects" and belongs among the human sciences.
"This beautifully written book can be recommended to any cultivated person with a certain sophistication of thought, and also to the practicing mathematician who will find here a vantage point from which to make a tour d'horizon of his science."
--Publ. Math. Debrecen
"This is an unusual book, being more a book about mathematics than a mathematics book. It includes mathematical issues, but also questions from the philosophy of mathematics, the psychology of mathematical discovery, the history of mathematics, and biographies of mathematicians, in short, a book about the mathematical experience broadly considered… The book found its way into "Much for liberal arts students" courses and into education courses directed at future teachers. Term paper topics, essay assignments, problems, computer applications, and suggested readings are included. This new material should greatly enhance the usefulness of this very creative book. The range of topics covered is immense and the contents cannot easily be summarized. The book makes excellent casual reading, would make a good textbook, or could easily be used as a supplement to nearly any course concerned with mathematics."
"This is a people-centered book about mathematics, and as such it provides an opportunity to explore fundamental issues that are typically absent from the experience of most college and university students (as well as their teachers). This new edition provides an excellent initiation of students into some of the more challenging aspects of mathematics…The study edition of The Mathematical Experience will help its readers acquire a real understanding of mathematics."
-Notices of the AMS
"Two distinguished mathematicians...have written a perfectly marvelous book about the Queen of Sciences, from which one will get a real feeling for what mathematicians do and who they are. The exposition is clear and full of wit and humor..."
--The New Yorker (1984 American Book Award Edition)--This text refers to an out of print or unavailable edition of this title.
Top customer reviews
Wherever one stands on this this particular philosophy, the book can be read on multiple levels without agreeing with the philosophy. The short vignettes can be read as enjoyable interesting mathematical and historical snippets, each independent of the other. It can be read as an exposition of the human activity which comprises mathematical investigations and discoveries (or are they creations?). Finally, it can be read as probes into the philosophy and foundations of mathematics.
A fair bit of mathematical knowledge (undergrad/grad-level) and some history of mathematics is recommended, and an understanding of philosophy of mathematics and FOM would be helpful if one wants to get the most out of this book. However, anyone with a motivated interest in mathematics should find this book worthwhile.
After I read this book, I have been trying to be a little more Platonist than I used to.