[John Nash] was in my class at [Carnegie Tech]. In fact, in this class there was Nash and also Hans Weinberger, a very good applied mathematician now at Minnesota, and maybe two or three others. [Richard] Duffin was teaching us a very amusing course on Hilbert spaces. One of Duffin's principles was never to prepare a lecture! So we were allowed to see him get confused, and part of the fun was to see whether we could fix things up. We were reading von Neumann's book on quantum mechanics, which developed Hilbert spaces at the same time. And it soon became clear that Nash was ahead of all of us in understanding the subtleties of infinite-dimensional phenomena.
He was an undergraduate, yes, and the rest of us were graduate students. I was friends with Nash; he didn't have any close friends, really, but we often talked about this and that. When he later got sick and had a really bad bout, he would sometimes send me a postcard with some very strange associations, usually with religious overtones. My closest contact with John was at Carnegie Tech. When I came to the Institute in Princeton, he came to Princeton as a graduate student, and then I only saw him casually. Later when he came to MIT and started his work in geometry, I unfortunately wasn't at Harvard yet. I would have been glad to have been part of the development of geometry by Ambrose and Singer at MIT at that time. However, this whole development turned Nash off. Eventually he went to Ambrose and asked for a "real problem". And then of course Nash proved his remarkable embedding theorems. But I was at Michigan at that time. Unfortunately, Nash's great gifts were marred by his terrible disease.