Thursday, November 1, 2012

'Best Of' Math 2012...

A quick blurb about "The Best Writing On Mathematics 2012" which I received a review copy of. It is once again edited by Mircea Pitici, and I believe this is the best edition thus far. Upon reading the first edition in 2010, it seemed a wonderful idea, the execution of which would improve in coming years. The 2011 volume was better than 2010, and this year's version has hit its stride even further, especially in containing more pieces that should appeal to a wider audience.
There are several well-known names (Terry Tao, Tim Gowers, Mario Livio, Brian Hayes, John Baez…) in this edition. The Foreword by David Mumford is a wonderful delineation of pure versus applied mathematics (also throwing physics into the mix). And I enjoyed most all the early entries in the volume. It slogged along a bit more in the middle and toward the end (for me), and, like most anthologies, overall, contains a mix for many different tastes. I doubt that anyone will enjoy every single entry, but that is in the nature of such (somewhat disjointed) compilations. At the end of the text, editor Pitici gives a list of other articles considered for inclusion that didn't make the cut. Of course several of them look quite interesting as well, although I don't know how readily available they are for lay readers.

There may be fewer technical pieces in this edition than previous ones, and I'll warn readers there is a lot of material on philosophical and historical underpinnings of mathematics -- topic areas I find rich and enjoyable, but some do not, and will be less enamored than I of certain portions of the book. There is still some fairly technical reading involved as well, so I'll also warn that this remains largely a volume for those already inclined toward mathematics and having some preparation; it is not for the general reader hoping to be newly engaged by the "best writing" to be found on mathematics. Unlike, say the 'best science writing in 2012' which might still appeal to a non-scientist, large chunks of 'the best writing in mathematics' will still only be accessible to math buffs.

The two oddest or quirkiest offerings (to me), came near the end: an essay by Fernando Gouvea on whether or not Cantor was truly surprised (and over what) when he famously wrote (in translation), "I see it, but I don't believe it" (essentially upon proving that a line segment contained as many points as a multi-dimensional geometric form), and the very last piece by Mark Colyvan on mathematics and dating/mating algorithms.

My favorite piece also was toward the end... I only discovered Brit Richard Elwes a couple years ago and he has quickly vaulted forth as one of my favorite math explicators. His essay bringing the subjects of Cantor set theory, infinity, and the Continuum, up-to-date with current ideas of an "ultimate L" logic-world promoted by Hugh Woodin is excellent and mind-bending. I'll be going back to re-read his and several other of the entries more slowly/carefully when time permits, and looking forward to next year's edition as well! For now, this series seems to be Pitici's 'baby,' and I don't wish to take anything away from his efforts, but it would be interesting to see what different editors each year would come up with (as is the practice with the more famous annual "best American writing" series that's been around for awhile).
Despite what the public might think, math is an incredibly diverse field of study, and therefore difficult to anthologize. If you're not already acquainted with Pitici's series I recommend this 2012 volume as a place to start.

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