This Element aims to present an outline of mathematics and its
history, with particular emphasis on events that shook up its
philosophy. It ranges from the discovery of irrational numbers in
ancient Greece to the nineteenth- and twentieth-century discoveries
on the nature of infinity and proof. Recurring themes are intuition
and logic, meaning and existence, and the discrete and the
continuous. These themes have evolved under the influence of new
mathematical discoveries and the story of their evolution is, to a
large extent, the story of philosophy of mathematics.
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