there is a debate between the intuitionists, formalists, and the symbolists nicely captured in the intro chapter of Heyting's Intuitionism.

constructive mathematics is close to computation and programming. and many including myself have a natural feel or intuition for it. A majority of euclids elements, and galois's original proof are constructive in nature.

lol yea.

bayesian thinking doesnt come to me naturally.. i have no intuition for it. seems forced. believe me - i have tried. but there are those who are swearing by it.