Doing Mathematics: Convention, Subject, Calculation, Analogy

This book discusses some ways of doing mathematical work and the subject matter that is being worked upon and created. It argues that the conventions we adopt, the subject areas we delimit, what we can prove and calculate about the physical world, and the analogies that work for mathematicians — all depend on mathematics, what will work out and what won''t. And the mathematics, as it is done, is s...