On Beliefs (Unsourced)

"A man protesting against error is on the way towards uniting himself with all men that believe in truth." (Thomas Carlyle)

"A theory is a supposition which we hope to be true, a hypothesis is a supposition which we expect to be useful; fictions belong to the realm of art; if made to intrude elsewhere, they become either make-believes or mistakes." (G Johnstone Stoney)

"General impressions are never to be trusted. Unfortunately when they are of long standing they become fixed rules of life and assume a prescriptive right not to be questioned. Consequently those who are not accustomed to original inquiry entertain a hatred and horror of statistics. They cannot endure the idea of submitting sacred impressions to cold-blooded verification. But it is the triumph of scientific men to rise superior to such superstitions, to desire tests by which the value of beliefs may be ascertained, and to feel sufficiently masters of themselves to discard contemptuously whatever may be found untrue." (Sir Francis Galton)

"He who searches for truth must not appease his urge by giving himself up to the narcotic of belief." (Hans Reichenbach)

"[…] if one really understood the central point and its necessity in the construction of the world, one ought to be able to state it in one clear, simple sentence. Until we see the quantum principle with this simplicity we can well believe that we do not know the first thing about the universe, about ourselves, and about our place in the universe." (John A Wheeler)

"Logic makes us reject certain arguments but it cannot make us believe any argument." (Henri Lebesgue)

"Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the mind will never penetrate." (Leonhard Euler)

"Much of the best mathematical inspiration comes from experience and that it is hardly possible to believe in the existence of an absolute, immutable concept of mathematical rigor, dissociated from all human experience." (John von Neumann)

"On foundations we believe in the reality of mathematics, but of course, when philosophers attack us with their paradoxes, we rush to hide behind formalism and say 'mathematics is just a combination of meaningless symbols’ […]. Finally we are left in peace to go back to our mathematics and do it as we have always done, with the feeling each mathematician has that he is working with something real. The sensation is probably an illusion, but it is very convenient." (Jean Dieudonné)

"Our experience hitherto justifies us in believing that nature is the realization of the simplest conceivable mathematical ideas." (Albert Einstein)

"Science is the art of creating suitable illusions which the fool believes or argues against, but the wise man enjoys for their beauty or their ingenuity, without being blind to the fact that they are human veils and curtains concealing the abysmal darkness of the unknowable." (Carl G Jung)

"[…] there are those who believe that mathematics can sustain itself and grow without any further contact with anything outside itself, and those who believe that nature is still and always will be one of the main (if not the main) sources of mathematical inspiration. The first group is identified as ‘pure mathematicians’ (though ‘purist’ would be more adequate) while the second is, with equal inadequacy, referred to as ‘applied’." (Mark Kac)

"The essential quality of a proof is to compel belief." (Pierre de Fermat)

 "[…] the mathematician learns early to accept no fact, to believe no statement, however apparently reasonable or obvious or trivial, until it has been proved, rigorously and totally by a series of steps proceeding from universally accepted first principles." (Alfred Adler)

"There exists, among mathematicians, a deep-seated and strong belief which sustains them in their abstract studies, namely that none of their problems can remain without any answer." (Gheorghe Ţiţeica)

"We know that mathematicians care no more for logic than logicians for mathematics. The two eyes of exact science are mathematics and logic: the mathematical sect puts out the logical eye, the logical sect puts out the mathematical eye, each believing that it can see better with one eye that with two." (Augustus De Morgan)