Category Archives: Mathematics


My Erdos Number is 4

Related to my previous post, I now have an Erdős number of 4. Another thing I’ve always wanted! Here are the details and an explanation of Erdős numbers for those who aren’t familiar with them.

I’ve posted previously about the mathematician Paul Erdős. Among other things, Erdős was insanely prolific and published 1,475 papers with 511 collaborators. Since one of his many areas of interest was graphs, it’s not surprising that a collaboration graph of his co-authors, and their co-authors, and so on…should be of interest. Courtesy of Wikipedia:

The Erdős number…describes the “collaborative distance” between a person and mathematician Paul Erdős, as measured by authorship of mathematical papers. It was created by friends as a humorous tribute to the enormous output of Erdős, one of the most prolific modern writers of mathematical papers, and has become well-known in scientific circles as a tongue-in-cheek measurement of mathematical prominence.

The Erdős collaboration graph is too huge to visualize, sadly, but the Erdős Number Project site has some interesting facts about the graph. Unfortunately, I think this information is skewed because it is based only on papers published in mathematical journals, while the high degree of interdisciplinary collaboration means that many people outside of mathematics have finite Erdős numbers. Anyway, according to this information, about 83,642 other people have Erdős number 4 (probably a gross underestimate.)

My relationship to Erdős comes from the fact that one of my co-authors, Michael Brudno, was a collaborator with at least two authors with Erdős number 2: Serafim Batzoglou and Lior Pachter. Each of those authors is a co-author with Daniel J. Kleitman, who not only has Erdős number 1, but has the lowest known Erdős-Bacon number: 3.

It’s conceivable that through one of Mike Brudno’s other collaborators, his number could in fact be 2, making mine 3, but confirming or disconfirming that would be too laborious. I’m more than satisfied with 4, which is slightly lower than the mean–especially considering that I never dreamed I’d have an Erdős number at all!

Visualizing Turbulence and Interpreting the Elements

I stumbled across two nice representations today. The first is a series of images visualizing turbulence. Some of these models took millions of processor hours to compute.

The second is a periodic table of the elements assembled out of 118 prints in various media. Sadly, no poster seems to be available just yet, but the project initiator hints that many things are in the works. Wouldn’t high school chemistry have been more fun this way?

Beautiful Minds, Strange Lives, and Large Hearts

I’ve admired the mathematician Paul Erdös for a long time: for his legendary eccentricity, heroic output, and his groundbreaking work on random graphs. Yet I only recently got around to reading his biography, The Man Who Loved Only Numbers.The most astounding aspect of the story to me was not his odd genious and single-minded—almost manic—pursuit of mathematical truth, but his unfailing generosity. A great man with an open brain and an open heart!

Other mathematical biographies I’ve enjoyed include A Beautiful Mind,the (un-Hollywood-ized) story of John Nash, and Andrew Hodges’ Alan Turing: The Enigma.Although probably a bit dated, E.T. Bell’s Men of Mathematicsis still on my to-read list (it’s a very long list!)

I owe my interest in the lives and personalities of mathematicians to one of my old math professors, a bit of a character himself, who interspersed nearly impenetrable lectures on complex analysis with stories of the quirks and foibles of mathematical greats like Riemann and Banach. By the standards of Waterloo math profs at the time, he, too, was remarkably generous.