# Who’s your Doktorvater?

* Happy father’s day and more to all *

Harry Coonce is a retired mathematician, formerly of Minnesota State University–Mankato. On Father’s Day we think of descendants and family trees, and tracing one’s “Roots” has been a popular objective since the 1970′s. Harry Coonce started tracing a different kind of family tree, in which the question is not “Who’s Your Daddy?” but rather “Who’s your Doktorvater?” That’s German for “doctoral father.”

Today Ken and I would like to talk about the Mathematics Genealogy Project, which was founded by Coonce.

While visiting Princeton University in 1996, Coonce looked up the dissertation of his PhD advisor, Malcolm Robertson. The Princeton Library’s copy did not indicate who was Robertson’s advisor. This made Coonce curious to find out who that was. He realized that this was an important datum that might not be well preserved in the world’s academic libraries. Thus he began a grand project to collect all PhD advisor information for mathematicians and those in related sciences.

Of course there have been many “doctoral mothers,” and they should have their own story. But that is for another day.

** Roots and Routes **

The Mathematics Genealogy Project is now managed by the Mathematics Department of North Dakota State University in Fargo, ND, with support from the American Mathematical Society. It is now directed by Mitchel Keller. Although we don’t know him, Keller himself shares some attributes with both of us: he obtained his PhD in mathematics at Georgia Tech under William (“Tom”) Trotter, and now has a Marshall-Sherfield Fellowship sponsored by the same Marshall Aid Commemoration Commission as Ken’s Marshall Scholarship thirty years ago. The project recently crossed the **150,000** mark in number of people listed.

Here’s how I (Dick) was able to trace my roots. The project correctly dates my PhD to 1973 under David Parnas at CMU. Click on Parnas, and some of the complication appears: two advisors for his 1965 thesis (also at CMU) are listed. Since I know Alan Perlis better than Everhard Williams, I clicked on Perlis and this took me back to 1950 at MIT under Philip Franklin. Continuing gives:

- Franklin, 1921, under Oswald Veblen, for a dissertation titled simply,
*The Four Color Problem*. - Veblen, 1903, University at Chicago under Eliakim Moore.
- Moore, 1885, Yale, under Hubert Newton. Here Moore is listed as having over 15,000 descendants—more than 1/10 of the entire tree—and Veblen has roughly half of them.
- Newton only earned a BA. This is somewhat like being adopted. However, an advisor Michel Chasles is listed for the B.A., and the other descendants include the renowned mathematical physicist Josiah Gibbs.
- Chasles, 1814, ‘Ecole Polytechnique under Siméon Poisson. Now we are in even more august company—Poisson’s other doctoral students were Lejeune Dirichlet and Jospeh Liouville.
- Poisson, 1800, also ‘Ecole Polytechnique, and another co-advisee: Joseph Lagrange and Pierre-Simon Laplace.
- Going through Lagrange hits Leonhard Euler, while Laplace’s advisor was Jean d’Alembert.

Now Ken’s route goes this way: His Oxford University D.Phil. was in 1986 under Dominic Welsh, and Welsh’s advisor was John Hammersley but no year is listed. Hammersley obtained his doctorate in 1959, but his advisor is unknown according to the database, so the road ends here—for now. The project is continually being updated, and the idea of doing this post made Ken realize his own information needs to be provided. Hammersley is famous for many things, including his work on the traveling salesman problem (TSP), before it was routinely called that. His paper joint with Jillian Beardwood and John Halton on *The shortest path through many points* is a seminal paper: it proved that the length of the TSP for random points in the unit square is almost always order .

** The Family Not-a-Tree **

The presence of co-advisor situations shows that the graph is not a tree. Well this is true of human geneaology too when someone’s father and mother are found to have a common ancestor, though we still say “family tree.” In fact, the graph is not even planar. To follow up our recent discussion of graph minors, the graph embeds the forbidden minor for planarity as follows:

This figure is from the project’s “Extrema” page, and it was thoughtful that they made it easy to save the figure separately. Of course Carl Friedrich Gauss is involved. Note that the links can be both advisors and students, thus the paths from Gauss wind up and down. The above is also a contradiction to the graph’s being bipartite, as there are odd cycles through Gauss.

** Open Problems **

Both Ken and I are dads, and we both miss our fathers very much. We wish all a happy Father’s Day.

Thanks for the nice discussion of the MGP, Dick, and I hope that Ken does come along and submit his data update. Further tracing of Ken’s lineage beyond Hammersley runs into the common difficulty with British mathematicians—the late adoption of the PhD. Perhaps some investigation might turn up who Hammersley’s most significant mathematical influence early in his career was, as that’s usually who gets recognized as the informal Doktorvater in our database in those cases.

I’ll encourage readers to be sure to search and check their own information (including their list of students, where applicable). We’ve always taken a broad interpretation of “mathematics” to include computer science, statistics, and operations research.

P.S. It’s been a few years, but perhaps Dick will recall serving on a search committee (provost) with me in 2006.

Happy Fathers Day to You.

I think one of the most interesting entries for complexity theory is Manuel Blum. Take any famous complexity theorist, with w.h.p. the complexity theorist is one of his decedents.

re: “Hammersley obtained his doctorate in 1959, but his advisor is unknown according to the database, so the road ends here—for now.”

I used to have coffee with John Hammersley most mornings when I was a graduate student, as he was an emeritus professor with an office down the hall from mine. I recall he once said that he didn’t have a D. Phil., only “a real doctorate” (meaning his D.Sc.). So I doubt that he had an advisor.

You might want to mention a TCS precursor to Coonce (if indeed he did not get started until 1995):

“The genealogy of theoretical computer science: A prelminary report,” D.S. Johnson, SIGACT News 16:2 (1984), 36-49. There is also a 2004 followup by Johnson and Parberry available on the web.

David,

Thanks for pointing this out

David,

As Dick has said, very good to add to the discussion here. Harry did have student workers work through the TCS genealogy and incorporate its contents into the MGP early on, as can be seen on the acknowledgments page.