Agree with your point. The actual title, "If the Universe Is a Hologram, This Long-Forgotten Math Could Decode It," has another issue: physicists may have "forgotten" operator algebras, but it's certainly been a very active part of mathematics.
Wikipedia calls them by a different name! As for history, Tomita is said to be the most important guy* behind the elucidation of Type III but gets no credit…
Feels like this is a classic case of blind men and elephant
>These were further developed later by Takesaki, and the theory is called the Tomita–Takesaki theory. It has great influence in statistical mechanics too. That was the beginning part, but in Tomita’s papers, he didn’t write proofs.
I: Mathematicians usually like proofs. Is Tomita a mathematician?
A: [Minoru] Tomita is a pure mathematician. There are a lot of algebraists in Japan, including [Masamichi] Takesaki, but Tomita is a completely different kind of person, very “singular”.
An operator can be something like the differentation operator (d/dx), the integral operator, gradient, curl, or other structure. Operators are similar to functions but work more generally, like mapping functions to other functions.
IIUC, Operator algebra is the study of the properties of operators just like real, complex, matrix, and linear algebra are the study of the properties of those objects/constructs. As such, once you have defined an operator for e.g. Schroedinger's wave equation you can manipulate and explore that using the rules and principles of operator algebra. Thus, making them easier to work with.
von Neumann algebras are operator algebras. They are algebras whose elements are operators on some Hilbert space. They also satisfy some other conditions. What I just said is not meant as a definition.
