Elizabeth first pointed me at today's xkcd. My friend Giuseppe also sent it to me from Italy, saying, "I'm sure you will appreciate it, especially the awareness of being one in a thousand that can do so :-)" The comic (linked below) is about Paul Erdös and Erdös Numbers. Erdös was a completely remarkable mathematician, brilliant (that is a serious understatement), and eccentric in many, many ways. I highly recommend the Wikipedia article about him, it captures his character well. He was essentially homeless, and not equipped for modern life, but rather traveled from one mathematical institution to another, often towing his mother along, being put up by those he visited. He was an amphetamine addict, and a lot of his life was necessarily organized by another, the important mathematician Ron Graham.
In his travels, he collaborated with very many mathematicians, often several at a given place. A massive body of significant mathematics appeared with him as a co-author. It was joked that he had once written a paper with a train conductor on his way between institutions. Because he coauthored so many papers, the concept of Erdös numbers arose. It's a little like (but way predates) the Six Degrees of Kevin Bacon. If you wrote a paper with Erdös, you have Erdös number 1. If you wrote a paper with someone with Erdös number 1, you have Erdös number 2, and so on. In general, your Erdös number is one more than the lowest number of any of your collaborators.
Low Erdös numbers are a source of humorous but serious pride among mathematicians, so I am really proud to have an Erdös number of 2. Here is an alphabetical list of all 8,674 people with Erdös number less than or equal to 2, including his more than 500 direct collaborators (who thus have number 1). I got my 2 by writing a paper with Ron Graham and Frank Harary, who each have number 1. The one-page paper is below. It, and the short paper (by just me) that preceded it, are pretty much the sum of my mathematics research career. I had solved a problem in Graph Theory (by constructing a counterexample to a conjecture), and this was an easier (but less powerful) alternative solution. (This was during the nanosecond that I thought I would call myself Joshua Fisher when I published, so that is the name that's there, but it's me.)
But I also had a more direct interaction with him: I taught Paul Erdös how to throw a frisbee. I was a graduate student in math at McGill University during 1968-69, and Erdös visited our department, gave a talk, and worked with some people. (In 1973, my advisor at McGill, Will Brown, wrote a paper with him.) He came to our department picnic (bringing his mother along, in a wheel chair). He saw me throwing a Frisbee with a friend and asked me about it, saying he had never seen one before (the modern Frisbee first appeared in 1964, and was just getting popular). I showed him how to do it, and we threw it back a forth a few times. He seemed thrilled.
The xkcd strip and most of my paper are below.
I wondered whether you'd seen that...
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