Published online by Cambridge University Press: 22 September 2009
To speak informatively about bakery you have got to have put your hands in the dough.
(Diderot, Oeuvres Politiques)The history of mathematics, lacking the guidance of philosophy, has become blind, while the philosophy of mathematics, turning its back on the most intriguing phenomena in the history of mathematics, has become empty.
(Lakatos, Proofs and Refutations)REAL MATHEMATICS
To allay any concerns for my mental health which the reader may be feeling if they have come to understand from the book's title that I believe mathematics based on the real numbers deserves singling out for philosophical treatment, let me reassure them that I mean no such thing. Indeed, the glorious construction of complex analysis in the nineteenth century is a paradigmatic example of what ‘real mathematics’ refers to.
The quickest way to approach what I do intend by such a title is to explain how I happened upon it. Several years ago I had been invited to talk to a philosophy of physics group in Cambridge and was looking for a striking title for my paper where I was arguing that philosophers of mathematics should pay much closer attention to the way mathematicians do their research. Earlier, as an impecunious doctoral student, I had been employed by a tutorial college to teach eighteen-year-olds the art of jumping through the hoops of the mathematics ‘A’ level examination.
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