The Mathematical ExperienceThis is the classic introduction for the educated lay reader to the richly diverse world of mathematics: its history, philosophy, principles, and personalities. 
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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 
Common terms and phrases
abstract aesthetic algebra algorithm analysis analytic angle answer applications argument arithmetic asserts axiom of choice Bibliography calculus called century circle complex concept conjecture construct continuum hypothesis course definition elements ematics Euclid Euclidean geometry Euler example existence experience fact figure finite formal language formalist formula Fourier Fourier series function Further Readings G. H. Hardy given Hilbert human hypercube idea ideal infinite set infinitesimal infinity integers intuition knowledge Lakatos logic mathe mathematical objects mathematical proof mathematicians matics means ment method natural numbers nonEuclidean geometry nonstandard notion paradox parallel postulate philosophy of mathematics physical Platonism Platonist possible postulate prime number prime number theorem problem proof Proofs and Refutations properties proved question real numbers reason restricted set theory result rigorous sense solution square statement straight line string symbols theorem thing tion triangle true truth universe words zero