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 shaped and supported, or not, by convention, subject matter, calculation, and analogy. The cases studied include the central limit theorem of statistics, the sound of the shape of a drum, the connection between algebra and topology, the stability of matter, the Ising model, and the Langlands Program in number theory and representation theory.

Doing Mathematics sheds bright light on some of the main characteristics of the mathematical quest. -- Library of Science, 2003

The book Doing Mathematics by Martin Krieger is truly a masterpiece. -- T T Wu, Gordon Mckay Professor of Applied Physics & Professor of Physics

this book will stimulate and inform, perharps even surprise, the most sophisticated of mathematical readers -- Mathematical Reviews, 2004