I met Erdős for the first time in 1977, at a conference in number theory at Miami University, when I was an undergraduate. It was, if I remember right, my first scientific talk, and I spoke about my results on continued fractions with bounded partial quotients. Erdős was in the front row. I remember feeling crushed because in the middle of my talk, he fell asleep. But then, a few weeks later, I found a postcard in my university mailbox from him, asking for a reprint. What an honor it was for an undergraduate! I still have that card somewhere.
I must have seen Erdős speak in the years following that, but if so, I don't remember it very well. I think he spoke at Berkeley when I was a graduate student. My memory is that he was not a very good speaker. He would do things like say, "Let x be a real number" and then just write down "x" on the board. Then he'd say, "Let y be a power of x" and then just write down y on the board. Not the best way to express ideas! He also said something like "It's hard to be bold when you're old and cold and you fold."
But when I was a professor at Dartmouth College -- it must have been in 1989 or 1990 -- he came to spend a few days, and we talked about a problem on Pierce expansions that I was having trouble making progress on. In just a few minutes, he had an idea that he thought would reduce the upper bound in my problem to n1/4. I went back to my apartment and thought about it a bit, only to discover that Erdős had made a mistake! His idea only reduced the bound to n1/3. Nevertheless, it was a significant improvement. We put the result together with some other ideas and it was published in the Journal de Théorie des Nombres de Bordeaux in 1991.
While he was visiting Dartmouth, I was assigned the task of picking him up from his hotel room and taking him to dinner. I remember when I picked him up, I washed my hands in his hotel bathroom, and was amazed by the number of pill bottles he had laid out. Apparently he was a bit of a hypochondriac, and he was also known to take speed to stay awake. This was also the first time I heard him call a child "epsilon", as he famously did.
I didn't have the chance to work with him ever again after that. Too bad! I would have loved the chance.