Can anyone actually prove this

This might sound like a really dumb question, but can anyone actually prove that 2+2=4? I know in higher levels of math they prove a lot of things. Is this one of things they prove -- and how? Thanks!

Yes, there exists a proof in number theory.

However, in arithmetic it is simply considered part of the definition of "4".

"4" is the name we give to the number that represents the number that follows 3 (in this context, "follows" means that you add one to it).
3 is, of course, defined as the number that follows 2, itself the number that follows 1, the basis of the counting numbers.

(The definition used by Archimedes, around 2000 years ago) went something like this.

1 is a number which represents a single item. It is a "unit".
If n is a number, then n+1 is also a number.

Using these definitions, you could say:

2 + 2 = ?
2 = 1 + 1 (one is a number, therefore 2 is the following number).

we substitute:
2 + (1 + 1) = ?

By associativity, we can change the order of the operations

2 + 2 + 2 + (1+1) = (2 + 1) + 1

(2 + 1) is what defines 3

(2 + 1) + 1 = 3 + 1 = ?

3 + 1 is what defines 4, therefore we can say:
2 + 2 = 4

It is more a construction than a proof.

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The proof in number theory is weird (because it requires building the operations themselves from scratch, for example, what does "+" really mean?)

There's a link below to the answer that usually gets copypasted when this question is asked, and it's even partially correct, but it needs some motivation. The idea is to give more basic definitions for '2', '2', '4', and '+', so we can focus on what's important. Then basic arithmetic facts can be verified without the lazy response of 'This is how it's always been done, don't ask stupid questions'.