Doing Mathematics

Doing Mathematics: Convention, Subject, Calculation, Analogy, 2nd Edition, is a book that examines the methods and practices of mathematicians and mathematical physicists and the subject matters they uncover and fashion. The text investigates how practitioners adopt conventions, delimit fields of inquiry, and use calculations and analogies grounded directly in mathematics.

The volume explores diverse mathematical and physical problems through specific case studies. Topics addressed include the central limit theorem of statistics, the sound of the shape of a drum, connections linking algebra and topology, and rigorous proofs establishing the stability of matter.

For this second edition, the text deepens selected examples, analyzes the practical role of mathematical rigor, and explores how an initial derivation can embody essential features that gain recognition only across subsequent proofs.