[FOM] New Book: Doing Mathematics: Convention, Subject, Calculation, Analogy

[Martin Krieger]

URL: http://www.wspc.com/books/mathematics/5133.html

    My new book, Doing Mathematics, has just been published by World
Scientific. The publisher's URL is above. I am interested in describing
some of the ways mathematics is done: how conventions are established
(justifying means and variances); how a subject matter is delineated
(topology); why and how long calculations are "philosophical," showing the
meaning of the manipulations and algorithmcs (Ising model, the stability
of matter); and how an analogy, what I call the Dedekind-Langlands
Program, has an analogy in mathematical physics, what I call the Onsager
Program in statistical mechanics. The idea is to analyze mathematics in
terms of what most mathematicians would call real mathematics, and the
focus is less on conventional philosophical problems (the focus of much of
philosophy of math) than on an analytic description of what is actually
going on in the mathematics. One of my themes is that the mathematics
itself, the facts and theorems and proofs, is the foundation for any
philosophy of mathematics, not some external notions.
    I also provide a translation into English of Andre Weil's faous letter
to his sister (1940) describing how he does mathematics and employs
analogy.
    In some ways, the book is a sequel to my Constitutions of Matter:
Mathematically Modeling the Most Everyday of Physical Phenomena (Chcago,
1996).

Martin Krieger
University of Southern California
krieger at usc.edu