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.

• Journey through Genius: The Great Theorems of Mathematics
• A Concise History of Mathematics: Fourth Revised Edition (Dover Books on Mathematics)
• History Mathematics 3e
• How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library)
• The History of Mathematics: A Very Short Introduction
• A Book of Abstract Algebra: Second Edition (Dover Books on Mathematics)
• Proofs and Refutations: The Logic of Mathematical Discovery (Cambridge Philosophy Classics)
• How To Solve It: A New Aspect of Mathematical Method
• What Is Mathematics, Really?
• Mathematics: Its Content, Methods and Meaning (3 Volumes in One)