### UGA Collaboration Graph

Just as actors have the "Bacon number" (the supposed "six degrees of separation" in which any actor is linked to Kevin Bacon in six films or fewer), mathematicians have the Erdös number (which was actually invented some 25 years earlier than the Bacon number, according to Wikipedia). Paul Erdös was a prolific Hungarian mathematician who wrote about 1,500 mathematical papers, mostly jointly written. A person who coauthored a paper with Erdös has an Erdös number of 1. A person who wrote a paper with someone of Erdös number 1 (but not with Erdös himself) has an Erdös number of 2. And so on. My Erdös number is 3, via the chain Brian Boe—Howard Hiller—Saharon Shelah—Paul Erdös. At MathSciNet, you can look up the collaboration distance between any two mathematicians (free tool).

A closely related concept is a collaboration graph, in which the vertices are mathematicians, and two mathematicians are connected by an edge if they have coauthored a paper together. The UGA Mathematics Department in 2008 had a very well-connected collaboration graph. I created this graph using the PSTricks graphics package for LaTeX.

There's a huge amount of information about Erdös numbers and collaboration graphs at the Erdös Number Project webpage.

### Math Genealogy

Mathematical ancestry is based on Ph.D. thesis advisors. We think of our advisor as our mathematical "father" (or "mother"), our advisor's advisor as our "grandfather," our advisor's other students as our "brothers" and "sisters," our Ph.D. students as our "children," and so on. We make family trees showing our mathematical lineage. You'd think that a mathematical ancestry graph would be pretty boring, just a simple chain, but it's complicated by the fact that some people have two advisors. In fact, there's a big online database which keeps track of the advisor-student relationships going back hundreds of years, and tools to help look up all the ancestors (or descendants) of a given mathematician and make a chart of the relationships. I made a graph of my own mathematical ancestors, going back to at least the early 1400s. There are some pretty famous people in the list, whom I've highlighted in red or blue depending on my own (subjective) opinion of how important they were. I've also included a handful of famous "uncles" (in green) whose names you might recognize.

### Family

My wife, Theresa Brunasso, is (essentially) a rocket scientist. She helped design the antennas that allowed the Mars rover Curiosity to land autonomously on Mars. She was one of three Georgia Women in Technology of the Year in 2008. She has her own engineering consulting business, D&S Microwave, Inc. You can also find her on .

My brother, David Melhorn-Boe, is a professional musician (performer, composer, director/conductor, teacher) in Ontario, Canada.