December 21, 2006

17: The Princeton math connection

Mail on 17 as the exemplary random number takes me to mathematicians, especially those at Princeton.  As it happens, I have an A.B. in mathematics from Princeton (before I was wooed away by the siren charms of linguistics), so it's entirely possible I picked up the idea there.

(One of the oddities of blogging is that you can post on some topic, get an assortment of responses, post a follow-up, and then get a fresh set of responses going off in some new direction.  No doubt my habit of not getting around to posting follow-ups for months or even years -- hey, some topics are evergreen -- means that I'm getting a new audience each time.)

In any case, Douglas Davidson writes to say: "Mathematicians are particularly fond of 17 (going back to Gauss, at least) and are likely to use it as an example."  He points me to the wonderfully silly Yellow Pigs page on 17, noting that Hampshire College math professor David C. Kelly gives, or at least used to give, an annual lecture on the number; to further Yellow Pig information on another site about 17s, where it is noted that mathematicians Kelly and Mike Spivak were graduate students together at Princeton in the 1960s and "reportedly got the yellow pig 17 idea in a bar"; and to the Wikipedia page on 17, where the Princeton connection is solidified:

17 is known as the Feller number, after the famous mathematician William Feller who taught at Princeton University for many years. Feller would say, when discussing an unsolved mathematical problem, that if it could be proved for the case n = 17 then it could be proved for all positive integers n. He would also say in lectures, "Let's try this for an arbitrary value of n, say n=17."

Then comes Lance Knobel, reporting that

Thirty years ago I roomed for a year at university with the best mathematician I've ever known. He and some fellow math whizzes, who had all been on the US team for the international math Olympiad, created a club, whose principal tenet was that 17 was the most random number.

What university?  Princeton, of course.  And the extraordinarily talented roommate? Eric Lander, biology professor at both MIT and Harvard Medical School, founding director of the Broad Institute, and many many other things.  Bachelor's in math from Princeton in 1978.

When I was an undergraduate at Princeton (1958-62, omigod), I didn't take any courses from Feller, but there were three professors who might have introduced me to the fabled randomness of 17: Bob Gunning, Paul Benacerraf, and Ray Smullyan, all three of them people with delightful senses of humor (and all three of them wonderful teachers).

Bob Gunning taught the honors calculus course I took in my first semester, thereby leading me to expect, unrealistically, that the rest of the math faculty would be as extraordinary in the classroom (and outside of it) as he was.  Here's a piece of a Princeton Alumni Weekly story about his receiving the distinguished teaching award from Princeton three years ago:

Colleagues and students alike praised his skills at explaining difficult mathematical concepts and his devotion to students. "He has a truly unusual ability for exposition of mathematics at any level," according to one colleague. "He has a clear insight into the subject matter and in the capacity of his students to absorb the material. His classes are superbly organized and his lectures have just the right mix of theory, examples and humor."

Gunning's humor was mentioned many times in his nomination letters for the award. "What sets [Professor] Gunning apart are the intangibles," wrote one student. "He is always smiling. He tells horrendously nerdy math jokes that never fail to make everyone laugh."

The philosopher (of mathematics, among other things) Paul Benacerraf was the adviser for my senior thesis in mathematics.  A wryly funny man then as now.  There's a Wikipedia page.

Mathematician, logician, philosopher, and magician Ray Smullyan is, of course, famous for the good humor of his books on recreational mathematics and logic.  He too has a Wikipedia page.

Any one of these three might have planted the random-17 seed.  Or I could have gotten it from another student.  So hard to tell at this distance in time.

zwicky at-sign csli period stanford period edu

Posted by Arnold Zwicky at December 21, 2006 08:46 PM