DOING MATHEMATICS
Convention, Subject, Calculation, Analogy
by Martin H Krieger (University of Southern California, USA)
About the AuthorMartin Krieger has taught at the University of California (Berkeley), the University of Minnesota (Twin Cities), MIT, and the University of Michigan (Ann Arbor). He has been a fellow at the Center for Advanced Study in the Behavioral Sciences and at the National Humanities Center. He is professor of planning at the University of Southern California. Professor Krieger was trained as physicist.Professor Krieger's earlier books include Marginalism and Discontinuity, Tools for the Crafts of Knowledge and Decision (1989), Doing Physics, How Physicists Take Hold of the World (1992), and Constitutions of Matter, Mathematically Modeling the Most Everyday of Physical Phenomena (1996).
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.
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