Though I have gone further in my mathematical career, my past is also filled with music.
Violin performance in multiple orchestras and chamber groups, together with with several concerto competitions and intense practice this required, had a large impact in my life. There is also the fact that my father was a musician, that our family was immersed in a musical environment.
I recently listened to a concerto while watching the notes scroll by. The complexity of the notes on the page were, somehow, not matched by the experience of music in that innermost place — that place from which you play when you perform. I found this experience very similar to the experience of creating new mathematics and then writing it down to communicate what I see.
Because I believe musical notes on paper and detailed proofs in a book or published paper are both misleading.
The music and the mathematics are, somehow, much simpler in their pure, newly created form. The complication evident in the written form comes from the unnatural way we have to communicate music and mathematics.
When I slowly recall or relive the creation of a proof, whose written form is non-trivial and may even seem imposing, I find the natural state of the proof in the imagination to be simpler, even minimalistic. Yet when written, expanding to something that looks imposing, it is often hard to read or imagine.
In the natural language of the soul, both mathematical proofs and musical compositions sing and flow. But in the language of things written down, we usually lose this living simplicity and beauty.
When we do harmonize the imagining and the telling, it is through the action of a whole person, in real time, speaking, writing, drawing, adapting, listening, responding … finding the music that, for us, connects the inner and outer universe.
For it is the human being integrates the universe, speaking the language that cannot be spoken.