A modern mathematical proof is not very different from a modern machine, or a modern test setup: the simple fundamental principles are hidden and almost invisible under a mass of technical details. ---- Hermann Weyl
After 3 courses in analysis I have finally reached Banach algebras, I feel exhausted by the climb and yet there's more theory ahead until the true pinnacle: the theory of $C^*$-algebra, for quantum mechanics!
Let's read, what is being promised?
$C^*$-algebras were first considered in quantum mechanics to model algebras of physical observables... began with Heisenberg's matrix mechanics and in a more mathematically developed form with Pascual Jordan around 1933. Subsequently, John von Neumann attempted to establish a general framework for these algebras which culminated in a series of papers on rings of operators. These papers considered a special class of $C^*$-algebras which are now known as von Neumann algebras.So experiments in quantum mechanics → weird behavior of observables in quantum mechanics → Heisenberg matrix mechanics → Jordan purified it into Jordan algebra → von Neumann generalized to rings of operators → von Neumann algebra generalized to $C^*$-algebras.
