Can’t we view it as new notation creates new mathematics? A placeholder symbol vs an actual number doing the same thing and more (discovery of zero as a number).
The new mathematics at least could be initially tiny, and then the notation provides the leg work for huge forthcoming discoveries.
Can new notation also create new physics, not just mathematics?
Thinking about Feynman diagrams.
I am neither physicist nor mathematician, so I don't know if this makes sense.
Wondering if Feynman diagrams were not just a crisp articulation of existing concepts, but did they also pave the way for new ideas in physics?
People had been doing derivatives (at least sort of) before Newton and Leibniz, Cardano (sort of) used complex numbers before Euler, algebra before Galois, categories before Mac Lane.
But these people "connected the dots", as it were. It's not merely a trick -- it's a fundamental contribution.