The Mathematical Experience

Front Cover
Houghton Mifflin Harcourt, 1998 - Mathematics - 440 pages
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.
 

Contents

Overture
1
Varieties of Mathematical Experience
31
Mathematics and
93
Hermetic Geometry
100
Religion
108
Symbols
122
xvii
153
13
174
Comparative Aesthetics
298
From Certainty to Fallibility
317
Unorthodoxies
334
The Riemann Hypothesis
363
π and
369
Mathematical Models Computers
375
Classification of Finite Simple Groups
387
FourDimensional Intuition
400

Mathematics as Enigma
196
R Shafarevitch and the New Neo
202
Confessions of a Prep School Math
272
Pólyas Craft of Discovery
285
True Facts About Imaginary Objects
406
Glossary
412
Index
435
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About the author (1998)

Phillip J. Davis is professor of applied mathematics at Brown University. Rueben Hersh is professor of mathematics at the University of New Mexico in Albuquerque.

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