violin has taught me much about Mathematics. The only way to
master the complexities and difficulties of the violin is to work from the
simplest first principles. In my experience, the same is true for
mathematics. In the mid-1970's I relearned the fundamentals of violin
playing following the method of Yehudi Menuhin, where the symmetry of the
human body is transformed to create a dynamic asymmetry between the violin
and the bow. This experience impressed upon me the power of simplicity.
Similarly, in the application of mathematics I
have learned to work back to first principles, which then become the focus
of the structured development of solutions. If and when flashes of insight
occur, they occur within the context of this process.
Another lesson learned from music is the value
of a global appreciation of human achievement and endeavor in a given field.
Having learned from Menuhin how to draw the bow across an open violin
string, it is revelatory to hear Menuhin perform the Bach "D minor
Chaconne." Then, one may also follow Menuhin a step further into the
music of India, and beyond to the music of the entire planet.
In mathematics too, first principles and global
appreciation are together the basis for sustained motivation and
inspiration. My personal and professional experience has validated this approach through
successful application in fields as diverse as algorithm/software development,
network troubleshooting, musical performance and composition, and education
for the gifted.