...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

Friday, January 10, 2014

Mathematics In 2013... Read All About It

Another edition of "The Best Writing On Mathematics" (for 2013) is now out, from Mircea Pitici (4th in the series since 2010). It is slimmed down from the last issue, which was slimmed down from the prior one etc. -- don't know if Pitici is becoming more selective in what he chooses, or just doesn't have the time to read as many potential entries as in the beginning (or perhaps it's just an economic publishing decision?). In any event, it is another eclectic collection, that, as I often warn about anthologies, will include some chapters to please most any math-lover... and, some that won't; those two categories will simply vary per person by what interests you bring to the table to begin with.

There are some very big names in this compilation: Roger Penrose writes a wonderful Foreward (a quotation from which I used a few days ago on Math-Frolic), and I much enjoyed the overview of Pitici's own Introduction, which includes this ebullient passage:
"Mathematicians are mavericks -- inventors and explorers of sorts; they create new things and discover novel ways of looking at old things; they believe things hard to believe, and question what seems to be obvious. Mathematicians also disrupt patterns of entrenched thinking; their work concerns vast streams of physical and mental phenomena from which they pick the proportions that make up a customized blend of abstractions, glued by tight reasoning and augmented with clues glanced from the natural universe."
Philip Davis follows with one of the longest pieces of the anthology reviewing the place of mathematics across many cultural aspects of the modern world. Ian Stewart covers one of his favorite topics, symmetry, in chapter 2, and after that, the always-interesting Terence Tao overviews the dual tug of complexity and universality in mathematics. In one fine example he tells the "legendary" story from a 1972 gathering, of mathematician Hugh Montgomery meeting physicist Freeman Dyson for the first time and discovering, in that "chance meeting" (where Montgomery feared they'd have nothing in common to talk about), that remarkably, they had both deduced the same formula, but Montgomery working from the arena of number theory and the zeta function, while Dyson, contrarily, had approached it from "the study of energy levels in the mathematics of matrices."

I thought these first three pieces were a strong beginning to the volume, after which followed a real mixed bag of selections of varying interest (and including a few I wouldn't have included). Charles Seife, Donald Knuth, and John Pavlus are some of the other author-names that might be most familiar to readers (about half the writers included were folks I was unfamiliar with).

 The hot topic of education merited only one entry (from Frank Quinn), which seemed a bit unfair -- that subject almost requires a much wider sampling of opinion if you're going to touch upon it at all (but then an entire anthology on math education perspectives could easily be put together separately if one so chose!). On-the-other-hand there are several entries touching on probability, perhaps a bit overweighting that always-interesting topic.

Appropriately, the volume ends with one of the brief but fascinating updates to one of 2013's math highlights: Shinichi Mochizuki's "proof" of the abc conjecture (which other mathematicians are only very, very slowly coming to dissect).
Anyway, I enjoyed the first and last few chapters of the volume most, with less enthusiasm for some of the middle pieces (…but your mileage may vary ;-)
Worth noting that a few entries involve some significant math background, but most are fairly accessible for a lay reader.
If you've enjoyed the Pitici anthologies from prior years you'll certainly want to add this one to your collection, or if unfamiliar, by all means begin with this one.

In closing, I applaud Pitici for taking on the difficult (even unenviable) task each year of distilling from 12-month's worth of math writings a collection that can appeal to the broad spectrum of varied math enthusiasts that are out there.

(I might just note that Pitici's series is published by Princeton University Press, and is NOT part of the "Best Writing In ______ " series that comes out yearly on several other subjects, and which most readers are likely familiar with.)

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