[nsomaru]

As a layman reading this, it’s funny. Because I do not need gravity proven to me from first principles ;)

[maxnoe]

Proven is the wrong word. You cannot prove a theory.

Deriving a description of gravity from first principles would be more appropriate

[hprotagonist]

*an empirical theory.

I can certainly prove things about, say, addition.

[solarist]

if you mean you can prove 2+2==4, it's actually tautology: | | + | | == | | | |

[hprotagonist]

no like, "addition is closed over the integers" is something you can show to be True (for all members of an infinite set, no less -- so it's not empirical.)

[bsder]

And yet, funnily enough, your phone needs a more thorough understanding of gravity than you do. The GPS system must correct for relativistic effects that cause the atomic clocks to shift relative to ground.

[saagarjha]

Isn’t this corrected by the satellites themselves?

[bsder]

Mostly, but there are still correlations between the satellites that are corrected by the receiver.

The Earth's gravity field is not deterministic.