Doing Mathematics: Convention, Subject, Calculation, Analogy [Paperback]

Martin H. Krieger (Author)

Book Description

ISBN-10: 9812382062 | ISBN-13: 978-9812382061 | Publication Date: January 1, 2003

A discussion of 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.

Editorial Reviews

Review

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 --This text refers to the Hardcover edition.

Product Details

• Paperback: 472 pages
• Publisher: World Scientific Pub Co Inc (January 1, 2003)
• Language: English
• ISBN-10: 9812382062
• ISBN-13: 978-9812382061
• Product Dimensions: 8.6 x 6 x 1 inches
• Shipping Weight: 1.4 pounds (View shipping rates and policies)
• Average Customer Review: 3.0 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #3,211,703 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

8 of 10 people found the following review helpful:

1.0 out of 5 stars The Value of Clear Expository Writing, April 2, 2004

By 

Richard Bentley (Tucson, AZ United States) - See all my reviews

This review is from: Doing Mathematics: Convention, Subject, Calculation, Analogy (Hardcover)

When one attempts to write an expository presentation, one should try to write clearly, directly, and in the simplest language possible. This book does not succeed in that endeavor. Rather, the author is to me a model of obfuscation, arcane language, wandering threads of reference, obscure relationships, and opaque explanation.

Perhaps a philospher who likes to couch his writings in such wrapping would relate to this style of presentation, but certainly not a reader interested in how mathematicians actually do mathematics. I would assume that rules out professional mathematicians by default. In some ways this could have been a good book, if the author had been less interested in showing us how much obscura he knows and more in explaining in a truly understandable fashion how people do mathematics .

A reader who is looking for insights into mathematicians and their methods would not go far wrong reading Hardy's A Mathematician's Apology, or Littlewoood's Miscellany.

5 of 6 people found the following review helpful:

3.0 out of 5 stars Mathematical Association of America review, November 3, 2003

By A Customer

This review is from: Doing Mathematics: Convention, Subject, Calculation, Analogy (Paperback)

For potential readers of this book, I would suggest that they read the Mathematical Association of America's review of this book (you can search for it; urls aren't allowed on Amazon reviews). It is less positive than the review by the author.

7 of 13 people found the following review helpful:

5.0 out of 5 stars What do mathematicians really do-- From the Author, May 25, 2003

By 

Los Angeles Professor - See all my reviews

This review is from: Doing Mathematics: Convention, Subject, Calculation, Analogy (Paperback)

I am the author of this book, and I thought it would be useful to say a bit more about the book. First of all, it is a a sequel to another book of mine, Constitutions of Matter (1996) published by Chicago, a study of the models mathematical physicists employ. And that is a sequel to Doing Physics (1992) published by Indiana, a description of some of the models physicists have in their toolkit.
Second, the book can be read at various levels, and that may be why it was chosen as a Library of Science selection. I have a friend who is a Hollywood director (originally trained as an attorney), and he understood it exactly, even though he knows little technical physics or mathematics. He read across that material and got the point. On the other hand, if you have an advanced degree in mathematics, as did another readers or two, you can read it for the technical details as well as the more general features. I have chosen movie stars of mathematics (C. Fefferman, R. Langlands) for much of the work. I also include a rather wonderful letter of Andre Weil (the mathematician) written to his sister (Simone Weil) about how he does mathematics. It appears in French in his collected papers, and it is here translated into English. I suspect that someone like Gian-Carlo Rota would have found congenial what I done here, although he would say that I have been insufficiently phenomenological.
My goal is to say something that mathematicians would find unexpectionable, for they might say--sure, this is what we do. But it is said in such a way that others gain access to that, and to that in terms of classy examples.
Third, I have deliberately not gotten into philosophy of mathematics arguments. I suspect that my materials would be useful for such, but those arguments do not much affect what I say in my descriptions.
Finally, I want to provide a way into what mathematicians do that suggests that it is not so strange compared to what other thinkers do--albeit it is mathematics, not poetry, not rhetoric, not sociology. It is mathematics.

Martin Krieger