...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

Sunday, March 2, 2014

Alexander Bogomolny -- "Cut The Knot"

Math-Frolic Interview #21

"A person who abhors reading in general may be suspected of lacking in intelligence, but otherwise, in the absence of further personal data, would likely be judged 'normal.'  A rare person would dislike music as opposed to the one who dislikes a particular kind of music (classic, chamber, pop, country, etc). You would probably be surprised to meet a fellow who feels indiscriminately dizzy at the sight of a painting. Why then has it become an acceptable norm to confess a dislike and misunderstanding of Mathematics as a whole?"
                                 -- Alexander Bogomolny (from his Manifesto to "Cut The Knot")

Well before web surfers knew of James Tanton, or Sal Khan, or Vi Hart, or any number of other digital math impresarios, Alexander Bogomolny was ardently constructing one of the richest, wide-ranging math websites around -- a sort of mini-wikipedia of mathematical delights. You can't surf around math webpages very long without running into his "Cut The Knot" site… and once there you could probably spend several days enjoying it!
The quotation above is drawn from the site and seems to capture the essence of Dr. Bogomolny's motivation for putting so much effort into such an educational resource. Below, the proprietor of "Cut The Knot" (and its companion blog, "CTK Insights"), took time to answer some of my questions:

1) Can you tell us a little about your early biographical journey that brought you to the field of mathematics… and at what point did you know you wanted to do mathematics professionally?

I never thought in such terms. As far as I can remember I simply liked solving problems and was always surprised by what I learned. I began attending math circles and participating in math olympiads in fifth grade. It just never occurred to me that I could do anything else.

2) I don't really know the history of math sites on the Web, but I suspect your "Cut the Knot" site may have been among the early trailblazers? It is one of the most useful, fun, educational sites around. How old is it, and how did the idea for it first come to you? Did you feel from the start that it would be successful, or was it sort of an experiment in the beginning? And finally, where does the name "Cut the Knot" come from?

I started the site in October 1996, the moment I learned of the existence of the Web. I felt there is something I have to share. At the time there were no google, Yahoo, wikipedia, or the notion of SEO. I was happy when people I knew (relatives, coworker, friends) found it necessary to mention that they read this page or that. This was a  success for me, for the site provided a starting point for many interesting discussions.

Until the Fall of 1999 I lived on 1 Alexander Road. Being Alexander myself I could not miss the coincidence. When the time came to naming the site, I sought the way to tag as a collection of math surprises; the story of Alexander the Great cutting the Gordian knot with his sword came to mind...

3) The site is chockfull of interesting, wide-ranging stuff! For a newcomer visiting for the first time it could almost be overwhelming -- which pages might you encourage a first-timer to check out right away? And are there certain elements/pages/aspects of  Cut-the-Knot that you're ESPECIALLY proud of?

There are presently in excess of 5500 pages. I do not even remember writing some of them. A first time user should probably at least glance at the Manifesto where I tried to convey my idea of what mathematics is about and the purpose of the site. But, otherwise, the visitors are on their own. I intentionally put the word "Miscellany" into the title. There are many ways to search the site: separate thematic lists (algebra, arithmetic, etc.), alphabetized index, google's search. It's not very difficult to find whether there is something on a particular topic. Some pages are even available on search engines from outside the site. As to being proud, for a number of years I wrote a column (Cut the Knot) for the MAA online. Some of these I believe may do for a good reading.

4) You're very interested in math education… are there certain other math websites you'd want to single out and recommend for anyone involved in math instruction to be sure to follow?

There are plenty of good sites. I follow people on twitter.com, and, for reading, often depend on their selections. I regularly come across articles by Gary Davis, David Coffey, Fawn Nguyen.

5) Your Masters degree in mathematics comes from Moscow State University in the USSR… Ed Frenkel wrote somewhat extensively about his experience with mathematics education (positive and negative) in the USSR, in his recent volume "Love and Math." I'm wondering if you can relate pretty closely to his experience or was it different for you? And do you ever have occasion to visit Russia these days for mathematics-related affairs?

There is a generation gap between us. While at my time (1966) antisemitism existed (my oral math exam lasted more than 5 hours) but at the end I still got my double 5 - for written and oral math and, as an honors student, was admitted to the Moscow State University without further exams (physics and Russian). When I applied for a visa to leave for Israel, the administration of the institute I worked at sent a virulent letter to the university complaining that it graduated implacable zionists. This was in 1974. In fact many of my classmates moved to Israel and the US starting 1972. Each could tell a similar story. So I guess by the time Edward thought of entering the university there was a sufficient justification to make antisemitism official: why should the state pay for somebody's education when the guy would not make any useful contribution to the Soviet economy? This became an official argument.

The first time I visited Moscow was last year -- after a 39 year gap. I still have friends there, and it was moving to meet with them. No mathematics was involved.

6) Your Ph.D. dissertation was on something called "the stamp problem" (or "postage stamp problem") which I'd never heard of and had to look up… turns out it's one of those lovely, easy-to-state, innocent-sounding math puzzles that's actually very difficult to solve -- could you tell us much at a layperson's level about what you were able to accomplish with your work on the problem?

Depending on the boundary data there are three more or less standard problems in static differential equations: Dirichlet (function is given), Neumann (normal derivative is given), mixed (part of the boundary is Direchlet, part Neumann. My problem was close to the latter, with a complication that the part of the boundary where one of the conditions held was an unknown. Under the stamp, in the domain of contact with a surface, one knew the Dirichlet condition (it was given by the shape of the stamp.) Elsewhere, assuming the stamp and the surface were static, the normal derivative was zero. But the domain of contact was unknown. The probem reduces to a variational inequality with a pseudodifferential (fractional derivatives) operator.

7) I always like to ask interviewees what math books they would especially recommend to a general audience of math-fans; and also what math books/authors were especially influential for you (if different from the more general recommendations)?

I slept with a translation of Hans Rademacher and Otto Toeplitz's "The Enjoyment of Mathematics", John Littlewood's "Mathematical Miscellany", and Hugo Steinhaus' "Mathematical Snapshots". Of the later authors, I read and enjoyed books by Martin Gardner, Ian Stewart, John Allen Paulos, Steven Strogatz, David Gale, Julian Havil, Cliff Pickover, Douglas Hofstadter.

8) When you're not doing mathy things, what are some of your main interests/hobbies/activities?

Photography, biking, scuba diving, traveling, seeing sights.


Thanks for the responses Dr. Bogomolny; your site is a treasure-trove for math enthusiasts of all ages. And your passion for showcasing mathematics to a wider audience shines through!

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