If physics involves so many assumptions and simplification in the process of calculating, how does the math actually check out?

Question

For example, I’ve seen that an electron is assumed to be a point-particle, i.e, occupies negligible space.

But it obviously has mass, so it’s gotta occupy *some* space!

However, the math seems to add up (pun intended), and the behaviour of the electron can be explained.

How?

(This was inspired by the *assume a spherical cow* thing)

In: Physics

Answer 1

Because we only use assumptions which we can show are valid for the problem we’re working on. For example the spherical cow thing, if you are working on a problem that doesn’t care about the exact geometry of the surface of the cow, only it’s total surface area then it is completely fine to approximate it as a sphere with a radius such that the surface area matches.