New book on the ontology of mathematics

Springer has published a new collection on the ontology of mathematics, edited by son and father Ernest and Philip Davis. According to the publisher’s website,

The seventeen thought-provoking and engaging essays in this collection present readers with a wide range of diverse perspectives on the ontology of mathematics. The essays address such questions as: What kind of things are mathematical objects? What kinds of assertions do mathematical statements make? How do people think and speak about mathematics? How does society use mathematics? How have our answers to these questions changed over the last two millennia, and how might they change

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The Princeton Companion to Applied Mathematics is out at last

For those readers anxiously awaiting the publication of The Princeton Companion to Applied Mathematics, the day has come. The book can be purchased either from Princeton University Press or Amazon.com. It is a companion to the prize-winning volume Princeton Companion to Mathematics, edited by Timothy Gowers, June Barrow-Green and Imre Leader, which was reviewed by one of us for Siam Review, November 2009.

This book is decidedly not an easy read for a weekend at the cabin. For one thing, at 994 pages and 2.3 kg (5.0 pounds), it is a hefty volume to carry around. It also is not

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Amir Aczel’s Finding Zero

Amir Aczel, mathematician and author of a number of semi-popular books on mathematics and science (see, for example, Fermat’s Last Theorem: Unlocking the Secret of an Ancient Mathematical Problem), has just published Finding Zero: A Mathematician’s Odyssey to Uncover the Origins of Numbers.

Aczel’s Finding Zero addresses a very significant historical question: What is the origin of positional decimal notation with zero, and the associated schemes we learn in grade school for doing basic arithmetic? We concur with Aczel that this discovery is clearly one of the most important scientific discoveries of the ancient world, although his characterization “the

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Max Tegmark’s “Our Mathematical Universe”

Physicist Max Tegmark has just published an interesting new book entitled Our Mathematical Universe: My Quest for the Ultimate Nature of Reality. In this very lucidly written book, Tegmark takes the reader on a tour of modern physics and then introduces his theory of the ultimate nature of the universe.

Tegmark starts out by exploring a list of questions, such as “How big is space?,” “Where did our solar system come from?” and “Where did our big bang come from?.” He then examines some of the difficulties with current theories, including both the successes and failures of the “inflation”

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Number Theory and Related Fields

Number Theory and Related Fields

In Memory of Alf van der Poorten

Series: Springer Proceedings in Mathematics & Statistics, Vol. 43

Borwein, Jonathan M.; Shparlinski, Igor; Zudilin, Wadim (Eds.) 2013, X, 395 p. 8 illus. ISBN 978-1-4614-6642-0

Collects contributions based on the proceedings of “International Number Theory Conference in Memory of Alf van der Poorten” These proceedings present high quality research articles and comprehensive surveys from distinguished mathematicians in order to promote number theory and related topics The subjects of these articles and surveys are inspired by Alf van der Poorten’s wide area of research interests, including number theory,

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Book Review: “Why Beliefs Matter: Reflections on the Nature of Science”

In his book Why Beliefs Matter: Reflections on the Nature of science, noted British mathematician E. Brian Davies surveys the sweeping landscape of modern philosophy of science and mathematics, with considerable skill and numerous thoughtful insights. Its closest analogue would be John Barrow’s 1992 book Pi in the Sky: Counting, Thinking and Being.

Davies is certainly qualified to write this book. He has published works in spectral theory, operator theory, quantum mechanics, and the philosophy of science. He served as the President of the London Mathematical Society from 2008-2009.

Some of Davies’ most intriguing comments relate to the nature of

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Borwein’s book Convex Functions selected as Outstanding Academic Title

The new book Convex Functions by Jonathan M. Borwein and Jon D. Vanderwerff has been selected as one of the “Outstanding Academic Titles” for 2011 by Choice, the American Library Association’s library book review journal.

Here is an excerpt from a review written by John D. Cook and published by the Mathematical Association of America in their Mathematical Sciences Digital Library:

When mathematicians say a function is “nonlinear” they often mean that it is not necessarily linear. In this sense “nonlinear” is not an assumption but rather the absence of an assumption. To make progress in studying a nonlinear problem,

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Review of “Loving and Hating Mathematics”

Loving and Hating Mathematics (Princeton University Press, 2010) is the child of two passionate scholars: a mathematician (Reuben Hersh) and a social scientist (Vera John-Steiner). Reuben Hersh has written for many articles for the Intelligencer, as well as earlier books such as The Mathematical Experience, coauthored with Davis and Marchisotto, and What is Mathematics Really?.

The present book has as its expressed aim the vanquishing of four myths:

Mathematicians are different from other people, lacking emotional complexity. Mathematics is a solitary pursuit. Mathematics is a young man’s game. Mathematics is an effective filter for higher education.

More generally, the book

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Merchants of Doubt

In a previous blog post, we addressed the perplexing phenomenon that whereas the scientific community years ago reached a strong consensus regarding the fact of global warming and the very likely human contribution to global warming, the public continues to believe that there is significant uncertainty and disagreement in the scientific community.

For example, in a recent poll, only 56% of Americans agreed that there is solid evidence of warming, and only 32% agreed that this warming can mostly be attributed to human actions. Similar results were found in 2009. For details, see 2010 Pew poll; 2009 Pew poll. Similarly,

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Are science and mathematics socially constructed?

Richard C. Brown, Are Science and Mathematics Socially Constructed?: A Mathematician Encounters Postmodern Interpretations of Science, World Scientific, 2009.

In this book, Brown recounts the rise of what is now known as the “postmodern interpretations of science” (PIS) or “sociology of scientific knowledge” (SSK) movement. In addition to pioneers Karl Popper and Thomas Kuhn (the latter of whom Brown personally knew), the author describes the contributions of Berkeley philosopher Paul Feyerabend; Harry Collins and Trevor Pinch at Bath University; Steve Woolgar at Brunel; Michel Callon and Bruno Latour in Paris; a group of scholars at the University of Edinburgh; and

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