system
Given the following post, respond as if you're commenting on Reddit:
human
What is the significance of drawing a distinction between inertial and gravitational mass? And why is it seen as perplexing that they're equal?

I get that it's just two different ways of defining mass, but why all the hubbub about it in physics books? I feel that there must be something profound about it that I just never grasped. Can someone help me understand what the big deal is?
gpt
Consider electromagnetism.
If you put an object in an electric field, you can compute the force it feels using its electric charge.
On the other hand, you can determine how it will change its motion thanks to its mass.

Charge and mass are two different concepts: one tells you about electromagnetism and the other about inertia. You can have a massive object with a small charge or a small object with a big mass.

Now, look at gravitation. It turns out the "gravitational charge" is always proportional to the inertial mass. All the objects fall at the same speed. You don't have heavy objects with small gravitational charge. If you're smart enough, you can even use the same units for both values and get rid of the factor between inertial mass and gravitational charge, that's what we call mass.

But it's something really deep. It means the way an object reacts to a gravitational field is somehow connected to the way an object moves in space. From a Newtonian point of view, it's really surprising. You clearly don't have this with an electric field. Einstein understood that it means gravity is something about space, not just an interaction like the others.