Subject: Sunrise Problem: V. Arnold's first eureka! experience
Vladimir Arnol'd mentioned the following problem in a recent Notices
interview. Can you solve this problem as elegantly as did the budding
great mathematician?
The first real mathematical experience I had was when our schoolteacher
I. V. Morozkin gave us the following problem: Two old women started at
sunrise and each walked at a constant velocity. One went from A to B
and the other from B to A. They met at noon and, continuing with no stop,
arrived respectively at B at 4 p.m. and at A at 9 p.m. At what time was
the sunrise on this day?
I spent a whole day thinking on this oldie, and the solution (based on
what is now called scaling arguments, dimensional analysis, or toric
variety theory, depending on your taste) came as a revelation. The
feeling of discovery that I had then (1949) was exactly the same as
in all the subsequent much more serious problems--be it the discovery
of the relation between algebraic geometry of real plane curves and
four-dimensional topology (1970) or between singularities of caustics
and of wave fronts and simple Lie algebra and Coxeter groups (1972).
It is the greed to experience such a wonderful feeling more and more
times that was, and still is, my main motivation in mathematics.
-Vladimir Arnol'd, in http://www.ams.org/notices/199704/arnold.html
-Bill Dubuque