The Mathematical Experience

Front Cover
Houghton Mifflin Harcourt, 1998 - Mathematics - 440 pages
4 Reviews
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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User Review  - FPdC - LibraryThing

This is the portuguese translation of The Mathematical Experience. An interesting attempt to convey the nature and importance of Mathematics to the lay reader, the text digresses through a variety of ... Read full review

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User Review  - phiroze - LibraryThing

A truly enjoyable read. The author tries to focus on the "experience" of mathematics. However, the depth and breath of the topic makes this an unsurmountable task. To that end, a user looking for an ... Read full review

Contents

Overture
1
Varieties of Mathematical Experience
31
A Conventionalist
68
Symbols
122
Generalization
134
Mathematical Objects and Structures Exis
140
Proof
147
The Stretched String
158
Selected Topics in Mathematics
202
Confessions of a Prep School Math
272
Polyas Craft of Discovery
285
Comparative Aesthetics
298
From Certainty to Fallibility
317
The Riemann Hypothesis
363
TT and 7T
369
Why Should I Believe a Computer?
380

The Aesthetic Component
168
Algorithmic vs Dialectic Mathematics
180
The Drive to Generality and Abstraction
187
Mathematics as Enigma
196
Classification of Finite Simple Groups
387
FourDimensional Intuition
400
True Facts About Imaginary Objects
406
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About the author (1998)

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

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