Let's pretend that we live in a world where there are invisible pixies running around messing everything up. Let's say you have 3 balls in your left hand and 4 balls in your right hand. Whenever you combine the balls together, one of these invisible pixies secretly throws in another ball, so that whenever you count the balls, you come up with 8 balls. So in this pretend world, it is a known fact that 3+4=8. Anyone who disputes this fact in our pretend world is considered either crazy or stupid.
In our real world, it is a known fact that 3+4=7. But how can we be sure that there are no invisible pixies running around taking balls away from us causing us to think that 3+4=7 when really 3+4=8?
My point is that mathematics is considered a deductive science, in which everything is absolutely certain. But how can mathematics prove that the above scenario cannot be true?