Sunday, January 2, 2011

Liking... "Loving and Hating Mathematics"

 "Loving and Hating Mathematics" by Reuben Hersh & Vera John-Steiner -- a review

I received a review copy of "Loving and Hating Mathematics" from Princeton University Press, a new volume from Reuben Hersh and Vera John-Steiner. Any new volume from Hersh is anxiously anticipated, and for the sake of simplicity I'll simply refer to his name throughout this review (it is also my suspicion, though I don't know for certain, that the parts of the book I liked most were primarily penned by him, and the parts I liked less came from the secondary author, who is listed as a linguist and educator, not a mathematician).
I have liked Hersh's writing in the past, although never quite finding it as engaging as I'd expect for the material he covers. The same is true in this volume which, for me, has a sort of Bell Curve of appeal. It starts off so-so, but quickly builds through some interesting, well-done middle chapters, only to then trail off into some shallowness in the last few chapters. For the right audience I do still recommend the volume, as a likeable, if not necessarily lovable volume.

The book is especially for those interested in mathematical culture, persons, and modern math history. It is about the milieu and nature, the sociology and personalities, of mathematics, more than it is about mathematics itself. Mathematical professionals, or those otherwise focused on doing math, may find less of interest here. The lay person with a side interest in mathematics will find over 300 pages about math in a loose sense, but with no significant amount of applied mathematics to get in the way of the narration.
The writing style is a tad dry, although much of the subject matter is so inherently interesting as to carry the material along without flashy writing. For those well-versed in mathematical history (or Hersh's past writings), the book may not add greatly to your knowledge, but it is nice to have so much of this material brought together in an orderly manner in a single volume.

The subtitle of the book, "challenging the myths of the mathematical life," implies that one purpose of the offering is to counter many of the images/stereotypes that people carry around of mathematicians and math study. While the book certainly contains a lot of diverse examples I'm not so sure but that a surprising number of them don't do more to reinforce, rather than counter, the generalizations people often make of the introspective, eccentric, oddball, isolated, anti-social or loner math-type. There are a lot of quirky stories told herein. One entire chapter on "Mathematics As An Addiction" almost makes the problematic lives led by so many math prodigies and logicians seem to be the norm. But other chapters do communicate the aesthetics, feeling, creativity, and sheer joy, that are (to the surprise of some I s'pose) an underlying aspect of doing math. Still, the subject of recreational mathematics, one of the most 'normal,' social, fun areas in all of math is oddly entirely absent.

You get some sense of the overall subject matter of the book from the middle chapter titles which I most enjoyed, as Hersh builds from more singular aspects of mathematics to its more social context:

Ch.2  -- Mathematical Culture
Ch. 3 -- Mathematics as Solace
Ch. 4 -- Mathematics as an Addiction
Ch. 5 -- Friendships and Partnerships
Ch. 6 -- Mathematical Communities

(The latter two chapters above, dealing with mathematicians in association with others, were for me, the best chapters of the book, but all these chapters were quite good.)

Chapter 7 on "Gender and Age in Mathematics" seemed less engaging, but might perhaps mean more to those most directly affected by these components (of math study when being female or older). I felt the last two chapters ("The Teaching of Mathematics" and "Loving and Hating School Mathematics") were a bit more shallow in their material, causing the volume to end somewhat weakly (though on some very important topics). Had the book's final few chapters been as strong as the middle chapters it would have been a great read; as it is, it is still a very good read. The brief biographic section of mathematicians at the end is nice as well, except that it is hard to decipher just why certain of the individuals were included, while a number of modern popularizers are omitted.

I have just two minor beefs with the volume:

1) I'm not sure the title is all that pertinent to the contents. The title is probably intended to be 'catchy,' but almost seems a bit glib. And just by including the phrase "hating mathematics" it could even turn off a segment of its prospective audience, who may indeed harbor long-ago school memories of hating mathematics. In short, I'm not so sure the title won't chase away more readers than it attracts.

2) A second minor concern is that Hersh puts out almost 400 pages on "math culture," including extensive bibliographic listings and an end-compendium of famous mathematicians, and yet never mentions Martin Gardner at all. Gardner and Hersh feuded across the years over the underlying nature of mathematics (with Gardner harshly reviewing Hersh on occasion), so it may be no surprise that Hersh affords him no recognition here. Moreover, Gardner was never a 'professional' mathematician, and, as mentioned above, Hersh essentially doesn't touch on recreational mathematics in this volume at all.
There are many other modern "popularizers" of math who also are not included here besides Gardner, however none have had the impact of Gardner on the current math community. Gardner's fame, contributions, and influence on many mathematicians, is undeniable, and his absence here almost seems a petty oversight, even detracting from the volume's credibility --- to the degree that this book addresses educating, motivating, and encouraging future mathematicians, Gardner and recreational math ought be mentioned.

With those two criticisms out of the way (and they are minor overall), I do recommend the work to the interested mathematics observer... especially if you already love mathematics; this volume will let you soak up more math-thought without having to work at it. If you 'hate' math, well, I don't think this volume will transform you, though even then, some parts may intrigue.

The book, BTW, has a Facebook page devoted to it here:

Finally, on a side-note, in the course of reading Hersh's book, I discovered that William Byers, author of one of my all-time favorite math books, "How Mathematicians Think," has a new book coming out around May 2011, entitled "The Blind Spot: Science and the Crisis of Uncertainty" --- something definitely to look forward to, especially if you are sympathetic to Hersh's view of mathematics.

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