Mathematical truth ultimately depends on an irreducible set of assumptions, which are adopted without demonstration. But to qualify as true knowledge, the assumptions require a warrant for their assertion. There is no valid warrant for mathematical knowledge other than demonstration or proof. Therefore the assumptions are beliefs, not knowledge, and remain open to doubt.
Paul Ernest The Philosophy of Mathematics Education (Falmer, Basingstoke 1991) p. 14.
One would normally define a ‘religion’ as a system of ideas that contains statements that cannot be logically or observationally demonstrated. Rather, it rests either wholly or partially upon some articles of faith. Such a definition has the amusing consequence of including all the sciences and systems of thought that we know; Gödel's theorem not only demonstrates that mathematics is a religion, but shows that mathematics is the only religion that can prove itself to be one!
John Barrow The World Within the World (Oxford University Press, Oxford, 1988) p. 257.