Right, the math is the same. We face this in physics all the time. You drop a ball and it accelerates downward. Should the distance it covers be a negative number? Well, it seems linear distance should be positive, but if it is, then does down become positive? Shouldn't up be positive? Or do we reverse from end-minus-start and make it start-minus-end?
It doesn't matter. The math is all the same with just different labeling conventions.
For the general physics of electric charges, the convention that a proton is +1 and electron is -1 is somewhat useful as a reminder of the larger range of phenomena: protons carry charge, too, and a movement of positively charged molecules makes the charge carriers and current move in the same direction.
But as soon as you start working with practical, artificial electrical circuits (as opposed to, say, neurons), the electron-is-negative is a nuisance, because the charge carriers are almost always simple electrons. To visualize "stuff" moving one way, you have to visualize "other stuff" moving the opposite direction. You have to keep thinking that when you add more you get less. Visualization of electric/electronic technology would have been a lot more convenient if the convention had been that electrons were positive, protons negative.