There was a book called “Godel, Escher, and Bach” some years ago.
Escher of course drew optical illusions.
Bach wrote a piece, that when played over and over, sounded as though it was continually ascending in pitch (or was it descending?) So that one was an “audible” illusion.
Godel proved that you can’t prove everything. In math there would always be unanswerable questions. You could introduce new axioms to make them answerable, but unanswerable questions would always remain.
I’m probably not giving a very good summary, and you raise a good point. I wasn’t that great in music but much better at math, and I’m not seeing how music helps with differential equations.
“I’m not seeing how music helps with differential equations”
Well, when you start learning music it’s mostly simple arithmetic and ratios. Not too much complicated stuff.
The higher mathematical aspect comes in when you actually start learning the harmonic side of it. You are basically dealing with applied wave harmonics, but it is approached not from the mathematical side, by studying wave equations and the laws of harmonics and jiggling around coefficients and variables, but from the practical side, actually creating different combinations of waves and then observing how they interact in the real world, both objectively and subjectively, since there is a psychological aspect to music and not just a mathematical one. So a musician may not be able to look at a set of wave equations and tell you “that’s a c major chord”. But if you converted a set of wave equations into music, the musician could recognize what was going on, and tell the mathematician what is happening from a music theory perspective.
Probably would not help you solve differentials. But maybe it could give you a different perspective on them.