...a companion blog to "Math-Frolic," specifically for interviews, book reviews, weekly-linkfests, and longer posts or commentary than usually found at the Math-Frolic site.

"Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show." ---Bertrand Russell (1907) Rob Gluck

"I have come to believe, though very reluctantly, that it [mathematics] consists of tautologies. I fear that, to a mind of sufficient intellectual power, the whole of mathematics would appear trivial, as trivial as the statement that a four-legged animal is an animal." ---Bertrand Russell (1957)

******************************************************************** Rob Gluck

Monday, September 7, 2015

Do You Believe In Magic?

Overview of "The Magic of Math" by Arthur Benjamin

I've never read an Amir Aczel book that I didn't more-or-less enjoy, BUT I've also never read an Aczel book that left me wanting to rush out and recommend it to others. I enjoy Aczel's books in a kind of ho-hum sort of way, but not an enthralling sort of way.

I say all that because I had the same reaction reading Arthur Benjamin's new popular math volume, "The Magic of Math." It's certainly an okay book, and indeed arrived with a long set of glittering endorsements from very reputable folks... but I almost felt like they'd read a different book than I had when they use words like dazzling, playful, joyful, fun, delightful, magical, etc. to describe it over and over. Many, perhaps most, readers know Benjamin from his online presences, where I think those words might more aptly apply, but this volume didn't seem that much above-average in such qualities.

There is SO MUCH popular math available these days in book form that it is difficult to write ANYthing very original or exciting anymore (and yet people do -- for example, Jordan Ellenberg's injection of wit, creativity, and humor into his 2014 "How Not To Be Wrong" volume elevated that book well above the crowd, and Alex Bellos regularly manages to approach well-worn topics in clever, engaging ways).

The first five chapters of Benjamin's offering, with discussion of some basic math, patterns, algebra, some combinatorics, and a whole chapter on the Fibonacci sequence, slightly bored me, though if you're unfamiliar with that content or Benjamin's video work, it may well be more interesting for you. It isn't that the material is covered badly, but simply that the material has been covered so many times before by others, and I didn't find Benjamin's treatment that superior to prior efforts. In parts of the book, Benjamin drops his hints/tricks for mentally computing faster or more easily. This is perhaps what some will view as "fun," though I find it a bit formulaic or dryly recipe-like.

The volume picked up (for me) with chapter 6 on "the magic of proofs" followed by chapters on geometry, pi, trig, i and e (perhaps my favorite chapter), calculus, and infinity; a progression of deeper, weightier topics, although again there wasn't that much in Benjamin's presentation setting it above others.  The chapter on calculus is a nice, straightforward textbook-like introduction to basics of differential calculus. It all makes for fine (if slightly pedantic) adjunct reading for a middle or high school student already inclined toward math; I'm just leery of how enlightening or fun this volume will be for the greater mass audience it claims to be targeting.

The book also contains numerous "Asides" in gray boxes where the author sidetracks to briefly highlight some matter tangentially-related to the main discussion -- in the Intro to the book Benjamin writes that the reader may skip these 'Asides' (if s/he so chooses), as being unnecessary to the main text. That may be true, but I actually found the 'Asides' to be the most interesting parts of the volume, so I recommend the reader NOT skip them!

Also on a positive note, the visual presentation, layout, illustrations, and organization of the book are excellent, and if the text had had a bit more pizzazz I'd rate it higher. As it is, I enjoyed the book, and for the right reader it will serve well, but for the broader reading public there are more scintillating math picks.  It will easily merit an honorable mention in my year-end favorites-list, but probably won't crack the 'top 10' for the year.

Worth noting, for those seeking more of a challenge, that Benjamin (as co-author) has another volume already out this year, "The Fascinating World of Graph Theory" that is likely quite good on that particular topic, though I haven't read it.

Anyway, do I believe in magic?... you betcha, and will shamelessly use any excuse I can to play some '60s pop music ;-) (combining it with Harry Potter making it all the sweeter):

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