Slow on the uptake & the history of mathematics

Despite being active in the blogosphere for over two years, for some reason I never thought to add links to the various research groups I was associated with while completing my PhD at St. Andrews. My advisers were Edmund Robertson and John O’Connor whose perhaps most well-known work is the MacTutor History of Mathematics Archive. It was under these auspices that I performed my research since it was a technical study of Eddington’s Fundamental Theory. Edmund and John are also part of CIRCA, best known as one of the centers for the GAP project. Hence I am a product of group theorists (it was, in fact, a major component of Eddington’s work, though not as evident in the portion I covered for my thesis).

That got me thinking (actually, this post by The Pontiff did) about my mathematical genealogy. It turns out that penchant for group theoretic thinking can be traced back to Arthur Cayley, arguably the first person to recognize a group in its modern form. There is one jump in this link to Cayley that still needs filling in (I have submitted a form to add this to the project). Via John O’Connor, I can trace my mathematical genealogy back to W.V.D. Hodge (who was a geometer). It appears that Hodge never received a PhD (not a prerequisite for university positions back then). However, the project recognizes “mentors” as well as “advisers” since their goal is to trace the dissemination of ideas. As such I have submitted Edmund Whittaker as Hodge’s mentor since it is clear Whittaker had an enormous and profound influence on Hodge’s early career (it was Whittaker who urged Hodge to continue his studies at Cambridge – Whittaker was also an influential friend and collaborator of Eddington, as it happens). The Wikipedia biography of Hodge suggests that the geometer Henry Baker had an influence on Hodge, but there is no citation. Oddly, it wouldn’t matter since Baker and Whittaker both descend from Cayley.

In any case, I find this dissemination of ideas and the strength of a particular line of study fascinating. Even with bumps in the road in which students diverged from the path in one way or another, there is still a line from Cayley, the first to suggest the modern group, to Edmund and John, my former advisers, who are group theorists! Interestingly enough, Whittaker was also an historian of science, having written several historical books including A History of the Theories of Aether and Electricity. Volume I: The Classical Theories, A History Of The Theories of Aether & Electricity VOL II: The Modern Theories, and From Euclid to Eddington: A study of conceptions of the external world. The latter was actually a published version of the 1947 Tarner Lectures. So they’ve got a bit of “historical” blood too!

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