Yesterday I watched the documentary N is a Number. It is the story of Hungarian mathematician Paul Erdos, the most prolific author of mathematical papers in the modern age, and my favorite of all time. He has written so many papers with so many collaborators that mathematicians celebrate him with a half-joke the call the Erdos Number. It is a Six Degrees of Separation game, where Paul has a number of zero, his collaborators have number one, the collaborators of his collaborators two, and so on. A child prodigy, he disproved the popular notion that math is a young person's game by continuing ground-breaking work well into his eighties.
There are many reasons to love Erdos. He had a wonderful sense of humor. He is credited with the notion that "a mathematician is a device for turning coffee into theorems." Coddled so much by his mother, who lost his two sisters to fever just before he was born, he remained delightfully helpless throughout his adult life. He is reported to have been incapable of buttering his own toast. Perhaps most famously, he was a man without home or country. He would show up on the doorstep of a friend with the announcement "My mind is open," which meant that he had a question that when answered would probably create an entirely new branch of mathematics. As I said, there are many reasons to love Paul, but to me his true legacy is not as a mathematician, but as a math teacher.
Erdos embodies all of the qualities a good teacher should. He was wonderful will children, entertaining them with original nursery rhymes and tricks of dexterity with his pill bottle. He was skilled at matching the right problem with the right person. If Paul posed a question, you could be sure that it was one which you were uniquely suited for and he was known to work on some 200 open questions simultaneously with friends around the globe. He communicated with the elites in the field and with high school students curious about the world. This indiscriminate mentoring led to his being described as a "bee spreading intellectual pollen." He would travel the globe with two half-full suitcases containing all his worldly possessions, and arrive just in time to ask the right question at the right time, thereby propelling his friends and students further in their understanding of the world. He had his politics, to be sure, but they did not stand in the way of the acquisition of knowledge. During the Cold War, when scientific discoveries were dashed against the impermeable Iron Curtain, Paul Erdos ushered them through, acting as the link between Uncle Sam and Uncle Joe.
I could go on and on about Erdos. He was kind, compassionate, never arrogant, and always generous with his time and with his mathematics. A math teacher couldn't find a better roll model.