Beauty and explanation in mathematics

I just moved into a new house and haven’t had time to blog much lately.  But I did want to advertise my friend Manya Raman-Sundström’s upcoming Workshop on Beauty and Explanation in Mathematics at Umeå University in Sweden: http://mathbeauty.wordpress.com/wbem/

The list of invited speakers includes Hendrik Lenstra, one of my graduate school teachers.  (If you haven’t see it before, you should check out Lenstra’s lovely short article Profinite Fibonacci Numbers.)

Here’s a blurb from the conference web page:

The purpose of this workshop is to bring together philosophers, mathematicians, and mathematics educators to study a question which is both relevant and timely for all three groups, namely whether mathematical beauty and mathematical explanation are related. Our approach is largely empirical– we will develop a set of examples that will help us make necessary distinctions and connections. The central questions of the workshop fall into three classes. One class concerns relations between beauty and visualization in mathematics; the other class concerns relations between explanation and visualization in mathematics. The third, perhaps most intriguing, class deals with the question whether visualization is an essential link between explanation and beauty and mathematics, that is: When some mathematics is both beautiful and explanatory, does the conjunction depend on the presence of a visual element? In addition to the scientific aims of the workshop, an important goal is to reach across normally rigid disciplinary domains to work on an area of common interest.  We have invited top people from respective fields, some of whom know each other, but others (even within the same field) have never read each other’s work.

More about the philosophy behind the conference can be found in this guest post on mathbabe.

Here is a personal favorite example of a math problem with an unexpectedly beautiful solution.  I heard it as a graduate student at Berkeley from one of Lenstra’s students, and I still remember the feeling of incredible elation when I figured it out.  (You can find this problem, and more like it, in Peter Winkler’s phenomenal book Mathematical Mind Benders.)

Image

You are given four lines in a plane in general position (no two parallel, no three intersecting in a common point). On each line a ghost bug crawls at some constant velocity (possibly different for each bug). Being ghosts, if two bugs happen to cross paths they just continue crawling through each other uninterrupted.  Suppose that five of the possible six meetings actually happen. Prove that the sixth does as well.

A solution will appear in my next blog post.

4 thoughts on “Beauty and explanation in mathematics

  1. I’ve never seen that problem before. Solving it was great fun, and I agree with your assessment — the solution is really striking and beautiful! Thanks for sharing it!

    Reply
  2. Pingback: The Pentagon Problem | Matt Baker's Math Blog

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