Some Ulam quotes from his autobiography Adventures of a Mathematician.
One of the luckiest accidents of my life happened the day G. D. Birkhoff came to tea at von Neumann's house while I was visiting there. We talked and, after some discussion of mathematical problems, he turned to me and said, “There is an organization at Harvard called the Society of Fellows. It has a vacancy. There is about one chance in four that if you were interested and applied you might receive this appointment."
I came to the Society of Fellows during its ﬁrst few years of existence ... I was given a two-room suite in Adams House, next door to another new fellow in mathematics by the name of John Oxtoby ... He was interested in some of the same mathematics I was: in set theoretical topology, analysis, and real function theory.
... While l was at Harvard, Johnny came to see me a few times and I invited him to dinner at the Society of Fellows. We would also take automobile drives and trips together during which we discussed everything from mathematics to literature and talked without interruption while still paying attention to our surroundings. Johnny liked this kind of travel very much.
... Edward [Teller] took up my suggestions, hesitantly at first, but enthusiastically after a few hours. ... Teller lost no time in presenting these ideas ... at a ... meeting in Princeton which was to become quite famous because it marked the turning point in the development of the H-bomb.
... It seems to me this was the tragedy of Oppenheimer. He was more intelligent, receptive, and brilliantly critical than deeply original. ... Perhaps he exaggerated his role when he saw himself as the "Prince of Darkness, the destroyer of Universes." Johnny used to say, "Some people profess guilt to claim credit for the sin."
... Banach once told me, "Good mathematicians see analogies between theorems or theories, the very best ones see analogies between analogies." Gamow possessed this ability to see analogies between models for physical theories to an almost uncanny degree ... It was along the great lines of the foundations of physics in cosmology and in the recent discoveries in molecular biology that his ideas played an important role. His pioneering work in explaining the radioactive decay of atoms was followed by his theory of the explosive beginning of the universe, the “big bang" theory (he disliked the term by the way) and the subsequent formation of galaxies.