The Mathematical Experience

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Houghton Mifflin Harcourt, 1998 - Mathematics - 440 pages
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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.
 

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Contents

Overture
1
Varieties of Mathematical Experience
31
platonism
52
A Conventionalist
68
Symbols
122
Generalization
134
Mathematical Objects and Structures Exis
140
Proof
147
Pólyas Craft of Discovery
285
Comparative Aesthetics
298
From Certainty to Fallibility
317
matics
339
Lakatos and the Philosophy of Dubita
345
The Riemann Hypothesis
363
it and
369
Mathematical Models Computers
375

The Stretched String
158
The Aesthetic Component
168
Algorithmic vs Dialectic Mathematics
180
The Drive to Generality and Abstraction
187
Mathematics as Enigma
196
Confessions of a Prep School Math
272
Classification of Finite Simple Groups
387
FourDimensional Intuition
400
True Facts About Imaginary Objects
406
Glossary
412
Index
435
Copyright

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About the author (1998)

Phillip J. Davis is professor of applied mathematics at Brown University.

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