The skeptic doubts one set of propositions because he believes another. None of us live with absolute, unassailable certainly about anything; we all live by faith. What someone thinks or feels absolutely certain of is really relative certainty. It’s certainty based on faith that they are right. The fact that they are certain is proof that they possess great faith. Likewise, one who doubts yet believes also demonstrates that some degree of faith is inescapable and runs through all that we claim to know.
Albert Einstein once said that there is no knowing without believing.
As far as the propositions of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.
The supreme task of the physicist is the search for those highly universal laws from which a picture of the world can be obtained by pure deduction. There is no logical path leading to these laws. They are only to be reached by intuition, based upon something like an intellectual love.
The mechanics of discovery are neither logical nor intellectual. It’s a sudden illumination, almost a rapture. Later, to be sure, intelligence and analysis and experiment confirm (or invalidate) the intuition. But initially there is a great leap of the imagination.
— Albert Einstein