As simple as one, two, three....
Of the math books I've been perusing/reading lately, the only one grabbing and holding my attention much (and oddly a volume I wasn't expecting to like), is David Berlinski's 2011 volume, "One, Two, Three." Indeed, I've enjoyed the book quite a bit, but must throw in my frequent precaution that it won't suit everyone's taste… or, to put it more bluntly, I suspect MOST readers (even math readers) may NOT relish it.
Leonard Mlodinow, in reviewing the volume, called it, "candy for the intellectually curious"… but I'd feel more comfortable deeming it 'candy for the epistemologically curious' -- some 'intellectuals' (and mathematicians for that matter) don't have the patience for philosophy that this volume requires. The book deals with matters at such an elementary level, where ideas tend to be ingrained and taken-for-granted, that many readers simply may fail to appreciate the significance of what is expounded.
Berlinski calls his subject matter "absolutely elementary mathematics" (which is also the sub-title of the book) or AEM for short -- it's not clear to me if that is his own concocted term or comes from somewhere else (and one Web commenter mistakenly bought the volume thinking it would be a nice introduction to math for her youngster... this it definitely is NOT!). At any rate, the subject matter includes the very most rudimentary foundations of math, logic, arithmetic. You either like this sort of thing… or, you don't. The author romps through a playground of ideas regarding numbers, algebra, axioms, sets, integers, fractions, rings, polynomials, proof, and clearly enjoys himself while doing so (even if it isn't always such a merry-go-round for the reader!). Parts of it will read quite pedantically to many readers, but this kind of elementary and obvious-sounding subject matter can't help but be pedantic at times… and it is FAR less so, in Berlinski's deft hands/voice, than it would be within some other textbook relating the same notions.
Berlinski's style is terse and economic, and yet with such careful, and even interesting, word choice that I'd be tempted to call it breezy; at times surprisingly engaging; even witty and humorous (though still with interspersed and inevitable dryness at points). His rhetoric can often be fun, even when it is challenging.
There are also interesting brief sidebars about various historical mathematicians throughout the volume, though it wasn't always clear to me just why some of these were included… yet they did make a nice interlude between some of the more tedious sections. The penetrating focus though is always on pulling back the curtain on the fundamental logical and axiomatic thought processes/assumptions that underlie mathematics. I do recommend the book, but not to the mathematically-nervous nor philosophically-naive, nor to readers who read for pleasure and not to be challenged. Whereas a Keith Devlin or Ian Stewart book might connect with a large audience of the mathematically curious, this volume may only resonate with a narrow slice of the popular-math crowd.
I'll admit that I find it hard to objectively read Berlinski's math writings because I find some of his other philosophical/science/political writings rather distasteful (…and yet having said that, there are elements of his "radical skepticism," as some call it, that I'm in sympathy with). He remains a highly controversial figure. Worth noting though, I did also enjoy one of his earlier math works, "Infinite Ascent," a nice historical look at major ideas in mathematics.
The Wikipedia entry on Berlinski is here:
http://en.wikipedia.org/wiki/David_Berlinski
and here are a few more Web entries that lend some sense of the controversy surrounding the man:
http://tinyurl.com/7sdcuj9
http://www.observer.com/1998/06/is-the-big-bang-just-a-big-hoax-david-berlinski-challenges-everyone/
http://recursed.blogspot.com/2008/04/david-berlinski-king-of-poseurs.html
(…of course googling his name will lead you to many more references on him, including clips on YouTube)
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