...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, March 6, 2017

The Best Picks From Mircea Pitici

"The main message of this series is that there is a lot more to mathematics than formulas and learning by rote -- a lot more than the stringency of proof and the rigor usually associated with mathematics (and held so dear by mathematicians). Mathematics has interpretative sides with endless possibilities, many made manifest by writing in natural language."

-- Mircea Pitici in the book's Introduction

When I began math-blogging almost 7 years ago I worried whether I could possibly find enough popular math material to blog about for more than a few months. In addition to the Web itself, Mircea Pitici’s yearly “Best Writing on Mathematics” volume is a great reminder of just how much accessible math there is! Popular math not only doesn’t get old or constraining, it seems to be growing in leaps and bounds.

Every year I end up saying ‘this year’s edition [of Pitici's effort] seems like the best one yet.’ And so it does (this is the 7th in the series). It is beautifully-produced (from Princeton University Press), on high-grade paper, with excellent illustrations, layout, and production values, in addition to a fine, varied selection of contributions. 
The downside is, you pay for all that: I’m afraid the retail price of $32.95 (for a paperback) may hurt sales compared to prior years… time will tell (and of course depending where you get it, many/most won’t pay the full retail price).

It's nice to see how many entries this year come from pieces either on the internet or at least from folks with a solid presence on the Web; an indication of how much GREAT math content is now freely available to millions of people via their computers. So if you follow the math blogosphere or Twitterverse several of these contributors will be very familiar to you:

Andrew Gelman
Erica Klarreich
Kevin Hartnett
David Castelvecchi
Brian Hayes
Tanya Khovanova
David Richeson
Steven Strogatz
Australian mathematician Burkard Polster ("Mathologer" on YouTube) gains the distinction of having 2 selections in this volume!

…and the volume ends with Ian Stewart somewhat recursively writing about how to write a popular math book.
…Just some of the 30 authors in this year’s edition.

As usual, the anthology is a mix of pure and applied math, and philosophy and history, as well as some pieces for more serious mathematicians beyond a general audience. Big data, education, statistics/probability, art, physics, are included along the way.
Also, as usual, I’ll warn the reader that due to publication lag time, these pieces are actually from 2015, so if you're disappointed to find some favorite 2016 article missing, wait for NEXT year’s edition and check again.

As always, Pitici is impressive with the eclectic diversity of his choices for inclusion. Any other mathematician taking on the task would likely come up with a very different volume than Pitici has… but that’s simply a testament to how much good material is available to choose from. Also, one of the best aspects of the volume is Pitici’s extensive listing of notable books from the prior year, as well as articles that were not chosen for inclusion, but nonetheless worthy of mention... i.e., this volume can lead to a whole lot further reading if one so chooses.

Last year’s edition had somewhat of an emphasis on recreational math (unlike prior editions), while Pitici notes that thematically many of this year’s picks “refer to the dynamic tension between the object and the practice of ‘pure’ versus ‘applied’ mathematics.”

A few favorite pieces are Erica Klarreich’s on “the Monster Group,” Davide Castelvecchi’s on Mochizuki’s confounding “proof” of the ABC conjecture, and Jorge Almeida’s on “Lottery Perception.” Jennifer Quinn’s entry on combinatorics is an especially fun, creative read. There are several historical pieces, with John Stillwell’s wide-ranging offering, “What Does Depth Mean In Mathematics” perhaps being the most interesting. Also, two back-to-back entries offer very different views (pro and con) of the reforms of Common Core. 
The anthology does not have to be read from beginning to end; the reader can jump around, but several successive pieces do hang together around a topic, and may be best read together.
I thought Derek Abbott’s “The Reasonable Ineffectiveness of Mathematics,” which appears fourth in the book’s lineup, might have been a more effective lead-off piece, as a somewhat contrary, thought-provoking read, arguing against Platonism and against the effectiveness of mathematics... a stand not often seen (I didn't find him convincing, but at least interesting and provocative). I also quite enjoyed Pitici's Introduction to this year's volume, so don't just skip over that.
Other entries cover wide-ranging, unpredictable topics, very clearly written, and each reader will find their own favorites.
Congratulations to Dr. Pitici on another job well-done, and to Princeton University Press for a very handsome edition that will please most anyone with a strong interest in 'the queen of the sciences.' Meanwhile, I saw so many fantastic math pieces last year I'm already anxious for Mircea's 2017 edition!

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