Paul Cohen

"To the average mathematician who merely wants to know that his work is securely based, the most appealing choice is to avoid difficulties by means of Hilbert's program. Here one regards mathematics as…"

"The object of mathematics is to discover "true" theorems. We shall use the term "valid" to describe statements formed according to certain rules and then shall discuss how this notion compares with th…"

"However, in all honesty, I must say that one must essentially forget that all proofs are transcribed in this formal language. In order to think productively, one must use all the intuitive and informa…"

"The theorem of Löwenheim–Skolem was the first truly important discovery about formal systems in general, and it remains probably the most basic. It is not a negative result at all, but plays an import…"

"It is now known that the truth or falsity of the continuum hypothesis and other related conjectures cannot be determined by set theory as we know it today. This state of affairs regarding a classical …"