I’ve been spending a few hours a month tutoring high-school-level maths, and being reminded of exactly how janky our standard notation is. Putting two numbers next to each other means “multiply these together” unless they’re parts of a mixed fraction; raising something to the power of −1 can mean “invert this function” or “take the reciprocal of this”[1]; all our variable names have implicit meanings almost no-one bothers to spell out.
I’ve been spending a few hours a month tutoring high-school-level maths, and being reminded of exactly how janky our standard notation is. Putting two numbers next to each other means “multiply these together” unless they’re parts of a mixed fraction; raising something to the power of −1 can mean “invert this function” or “take the reciprocal of this”[1]; all our variable names have implicit meanings almost no-one bothers to spell out.
This is especially egregious w.r.t. trig functions: cos^-1 of x multiplied by cos^3 of x is NOT cos^2 of x!