Paul Cohen > Quotes

“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

“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

“Historically, mathematics does not seem to enjoy tolerating undecidable propositions. It may elevate such a proposition to the status of an axiom, and through repeated exposure it may become quite widely accepted. This is more or less the case with the Axiom of Choice. I would characterize this tendency quite simply as opportunism. It is of course an impersonal and quite constructive opportunism. Nevertheless, the feeling that mathematics is a worthwhile and relevant activity should not completely erase in our minds an honest appreciation of the problems which beset us.”
― Paul Cohen