I mean, it was rather physics that was worse in this regard.
Mathematicians do define their variable quite rigorously. Everything is so abstract, at some point you do just need to write down “this thing is a number”. Problem with maths folks is rather that they get more creative with their other symbols. So, “this thing is a number” is actually written as “∃x, x ∈ ℝ”.
But yeah, in the school/university physics I experienced, it was assumed that you knew that U is voltage, ρ (rho) is density, ω (omega) is angular velocity etc…
At one point, I had to memorize six pages of formulas and it felt like every letter (Latin, Greek, uppercase, lowercase, some Fraktur for good measure) was a shorthand for something.