While I was writing some words to say about Professor Kurt Gödel's major works for his 2006 centenary celebration at the University of Vienna, it suddenly came to me that for everyone who gathered in his honor, Gödel's extraordinary contributions to and tremendous influence on mathematics would be something of which we were already deeply aware. Thinking that perhaps a repeat of Gödel's results would be unnecessary with this group, I decided to share some of my own personal memories that are recalled when I remember Professor Gödel.
I met Gödel for the first time at the Institute for Advanced Study in Princeton in January 1959, when he was fifty-two years old. At the time, I was a very young thirty-two-year-old whose only interest was my own problem within logic; I knew little of logic as a whole. Throughout my first stay in Princeton, Gödel taught me many new ideas, specifically about nonstandard models and large cardinals. On certain occasions, he would lead me to the library and show me the precise page of a book on which a pertinent theorem was presented, and he advised me on which books I should be reading. He even counseled me that I needed to improve my English to communicate with other mathematicians.
Gödel showed a keen interest in the problem on which I was working then: my fundamental conjecture, that is, the cut elimination theorem on the generalized logic calculus, which is the higher type extension of Gentzen's logistischer klassischer Kalkül sequent calculus, as introduced in 1934.