...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.

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"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

Sunday, February 9, 2014

Still More Beauty.... and Appreciation


The previous MathTango posting touched upon the frequent topic of "beauty" in mathematics, and then lo-and-behold just yesterday Nobel physicist Frank Wilczek posted his own brief take on that very topic:

http://frankwilczek.com/2014/mathematicalBeauty02.pdf

Wilczek links "beauty, prediction and reward" and also "novelty" in a simple and interesting way (though I'm not sure others haven't written similarly before, with different words). Wilczek speculates on why so many people "don't find mathematics beautiful at all, and who in fact fear and hate it," based on his prediction/reward emphasis, and believes his ideas will have "important practical implications for teaching and learning." His piece is very brief but he also mentions having a forthcoming book in-the-works fleshing out the subject more, so something to look forward to!

Slightly relatedly, this weekend I was reading a 1981 essay by R.P. Boas, which included this passage:
"…it was not until I became editor of the [American Mathematical] Monthly that I quite realized how hard it is for mathematicians to write so as to be understood even by other mathematicians (outside of fellow specialists). The number of manuscripts rejected, not for mathematical deficiencies but for general lack of intelligibility, has been shocking. One of my predecessors had much the same experience 35 years earlier.
"To put it another way, why do we speak and write about mathematics in ways that interfere so dramatically with what we ostensibly want to accomplish? I wish I knew."
Knowing and understanding math, has never been a guarantee of ability to effectively communicate mathematical content or beauty to others -- and if it is hard to communicate to one's mathematical peers, how much harder is it to communicate to the wider public. Thus, I think it worthwhile on occasion to salute those who do accomplish that goal, and also acknowledge those who toil away less prominently striving toward such a goal.

So to the Strogatz's and Stewarts, the Devlins and du Sautoys, the Pickovers and Posamentiers, the Hershes and Hofstadters, (and of course to Martin Gardner, who may stand in a class all by himself), and so very many others who do a great job of communicating mathematical material/thinking for a wider audience... and also to those in the blogosphere, and in their personal classrooms, who similarly endeavor to do the same, THANK YOU! Even the titan-likes of Tim Gowers and Terry Tao, when they put their mind to communicating to a broader audience, do so splendidly! It remains astonishing to me, in this culture of such widespread math dread and discomfort, how many wonderful books for a general audience yet appear every year! (thank you also to editors at Princeton University Press and Basic Books, et.al.)  I don't know that there's ever been a better, richer time in history to be a student (or just an interested follower) of mathematics. Enjoy.

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