mathematics is actually built on a foundation of things we can’t prove but assume are true. We call them “axioms,” and we think they’re safe assumptions, but at the end of the day, they remain beliefs we cannot prove. Axioms include ideas like “2 + 1 gives the same result as 1 + 2” and “if a equals b, and if b equals c, then a equals c.” These assumptions are useful because they match up with reality—and building math on a foundation that matches up with reality has proven reasonably practical—but there is nothing stopping you from building different mathematical systems.
