Here 2 + 2 does not equal 4; it does not even surprise with 5.

On the other hand, if math is invented, then why can't a mathematician legitimately invent that 2 + 2 = 5?

When we say that 2 + 2 = 4 or 2 + 3 = 5, we're saying something about numbers that our mind is able to grasp.