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“Plenty of mathematicians, Hardy knew, could follow a step-by-step discursus unflaggingly—yet counted for nothing beside Ramanujan. Years later, he would contrive an informal scale of natural mathematical ability on which he assigned himself a 25 and Littlewood a 30. To David Hilbert, the most eminent mathematician of the day, he assigned an 80. To Ramanujan he gave 100.”
― Robert Kanigel, The Man Who Knew Infinity: A Life of the Genius Ramanujan

“Quantum phenomena do not occur in a Hilbert space. They occur in a laboratory.”
― Asher Peres, Quantum Theory: Concepts and Methods

“When {Born and Heisenberg and the Göttingen theoretical physicists} first discovered matrix mechanics they were having, of course, the same kind of trouble that everybody else had in trying to solve problems and to manipulate and to really do things with matrices. So they had gone to Hilbert for help and Hilbert said the only time he had ever had anything to do with matrices was when they came up as a sort of by-product of the eigenvalues of the boundary-value problem of a differential equation. So if you look for the differential equation which has these matrices you can probably do more with that. They had thought it was a goofy idea and that Hilbert didn't know what he was talking about. So he was having a lot of fun pointing out to them that they could have discovered ³§³¦³ó°ùö»å¾±²Ô²µ±ð°ù’s wave mechanics six month earlier if they had paid a little more attention to him.”
― Edward Uhler Condon

“But in the present century, thanks in good part to the influence of Hilbert, we have come to see that the unproved postulates with which we start are purely arbitrary. They must be consistent, they had better lead to something interesting.”
― Julian Lowell Coolidge, A istory Of Geometrical Metods

“To the average mathematician who merely wants to know his work is securely based, the most appealing choice is to avoid difficulties by means of Hilbert's program. Here one regards mathematics as a formal game and one is only concerned with the question of consistency ... . The Realist position is probably the one which most mathematicians would prefer to take. It is not until he becomes aware of some of the difficulties in set theory that he would even begin to question it. If these difficulties particularly upset him, he will rush to the shelter of Formalism, while his normal position will be somewhere between the two, trying to enjoy the best of two worlds.”
― Paul Joseph Cohen

“To the average mathematician who merely wants to know his work is securely based, the most appealing choice is to avoid difficulties by means of Hilbert's program. Here one regards mathematics as a formal game and one is only concerned with the question of consistency ... . The Realist position is probably the one which most mathematicians would prefer to take. It is not until he becomes aware of some of the difficulties in set theory that he would even begin to question it. If these difficulties particularly upset him, he will rush to the shelter of Formalism, while his normal position will be somewhere between the two, trying to enjoy the best of two worlds.”
― Paul Cohen

“The sign for Wittgenstein partakes of a logical dimension that cannot simply be taken in through an act of Hilbertian immediate perceptual apprehension that is prior to all thought or language. To put this dimension of Wittgenstein's teaching in our earlier Kantian idiom: an employment of language in which no symbol is to be recognized in the sign - so that we're confronted with the occurrence of a mere sign - involved a kind of exercise of our linguistic capacity whose very possibility presupposes the prior capacity successfully to employ signs as the sensibly perceptible aspects of symbols. In this area of philosophy - as in some of the others explored earlier in these replies - contemporary philosophers are prone to assume that the order of logical priority must be the other way around. They are inclined, with Hilbert, to regard the (to borrow Kant's term) problematic mode of occurrence of the sign as the logically simpler phenomenon and the comparatively less problematic case as the product of an enhancement of the 'mere sign' - an enhancement that breathes life into a sort of something that is, regarded in and of itself, logically mute and inert.”
― James Conant, The Logical Alien: Conant and His Critics