The 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.

'First Principles' Example: A Lattice is a non-empty set and two binary operations, ∨ ("join"), and ∧ ("meet"), that satisfy the 4 identity-pairs to the left. This simple structural basis applies directly to the {"OR","AND"} of propositional logic, as well as to the {"LCM,"GCD"} of elementary number theory. The further development of this structure includes the vector lattice, with which the Daniell Integral may be defined, as well as the orthomodular lattice, which provides a basis for quantum logic.