The Mathematical Experience
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.
Varieties of Mathematical Experience
From Certainty to Fallibility
The Riemann Hypothesis
Mathematical Models Computers
Classification of Finite Simple Groups
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abstract aesthetic algebra algorithmic analog analysis analytic angle answer application argument arithmetic asserts axiom of choice Bibliography calculus called century circle complex concept conjecture construct continuum hypothesis course definition elements equal Euclid Euclidean geometry Euler example existence fact figure finite formal language formalist formula Fourier series function Further Readings G. H. Hardy given Gödel graph human idea ideal infinite set infinitesimal infinity integers intuition knowledge Lakatos Leibniz logic mathe mathematical objects mathematical proof mathematicians matics means ment method natural numbers non-Euclidean geometry nonstandard notion paradox parallel parallel postulate philosophy of mathematics physical Platonism Platonist postulate prime number prime number theorem problem proof properties proved question real numbers reason restricted set theory rigorous sense solution square standard statement straight line string symbols theorem thing tion triangle true truth universe words zero
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