Throughout his life, Paul Erdös never seemed to age. I met him in the early sixties, and I last saw him a few months ago. He always looked the same. He spoke the same way, he dressed the same way. Only his theorems changed. In the second half of his life, all his lectures invariably had the same title: "Problems in combinatorics and number theory". The content of each lecture varied as the problems he had proposed were solved and new problems were added. He was shrewd enough to propose problems that could be solved by good mathematicians with the techniques of the day; only on occasion he would state a problem that he knew would require a genuinely new idea, and then he would offer an unusually large sum for its solution.
If we were to include among his publications those inspired by his valuable hints, we should increase the number of his published papers from fifteen hundred to tens of thousand.
Like Norbert Wiener, Erdös liked to pretend to be absent-minded, to avoid dealing with the humble chores of everyday life. His associates and collaborators were glad to plan his entire day for him, and to help him out with all that he needed, all the way to buttering his toast. But he was quick to notice when something went wrong. He always memorized his travel schedules, and did not fail to remind his hosts when the time came to drive to the airport.
He was good at sizing up people. His incisive remarks on personalities, casually stated in the middle of a mathematical argument, were invariably surprising and always true, though they never hurt.
His elementary proof of the prime number theorem (with Selberg) is often cited as some of his best work. Actually, several of his ideas are more likely to survive than many theorems: his idea of proving the existence of combinatorial objects by probabilistic methods and his infinite Ramsey theory are now two of many thriving chapters of mathematics that he initiated, and that are a long way from being concluded.
One evening in the seventies, I mentioned to Paul a problem in numerical computation I was working on. Instantly, he gave me a hint that eventually led to the complete solution. We thanked him for his help in the introduction to our paper, but I will always regret not having included his name as a coauthor. My Erdös number will now permanently remain equal to two.