[Music and mathematics - Wikipedia](https://en.wikipedia.org/wiki/Music_and_mathematics) is there something like "mathematician guide to practically playing piano"? this book on piano practice mentions group theory (mathematical theory of symmetries)! [4. Mozart’s Formula, Beethoven and Group Theory — Fundamentals of Piano Practice](https://fundamentals-of-piano-practice.readthedocs.io/chapter1/ch1_research/IV.4.html) "We all know that Beethoven never really studied advanced mathematics. Yet he incorporates a surprising amount of math in his music, at very high levels. The beginning of his Fifth Symphony is a prime case, but examples such as this are legion. He “used” group theory type concepts to compose this famous symphony. In fact, he used what crystallographers call the Space Group of symmetry transformations! This Group governs many advanced technologies, such as quantum mechanics, nuclear physics, and crystallography that are the foundations of today’s technological revolution. At this level of abstraction, a crystal of diamond and Beethoven’s 5th symphony are one and the same! I will explain this remarkable observation below."