# The Irish Presence in the Mathematics Genealogy Project

The Mathematics Genealogy Project (or MGP) is a US-based website which aims to list all doctorates issued worldwide in mathematics and related fields. Theses are classified using the standard AMS mathematics subject classification system, and as such include history, biography, statistics, geophysics, astronomy, mathematical education, biology and other natural sciences, operations research, mathematical programming, and computer science, in addition expected areas like number theory, algebraic geometry, real functions, ODEs, PDEs, geometry, fluid mechanics, quantum theory, and so on.

The MGP started in 1996, and its history is surveyed in my article The Mathematics Genealogy Project Comes of Age at Twenty-one in the May 2017 issue of the *Notices of the AMS*. As May 2017 dawns, the project has accounted for over 212,000 people.

Its "Irish content" can be split into (1) those doctorates issued at third level institutions in Ireland, be they at TCD, QUB, UCC, UCG/NUIG, UCD, Maynooth, Limerick, DCU, or elsewhere, (2) those issued to Irish students overseas, and (3) those supervised by Irish advisors overeas. Only the first category is trackable at MGP, as theses can be searched by country or university; more about these anon.

The documented* diaspora *doctorate entries, however, provide merely the recipients' or advisors' names, and in most cases the years, institutions, thesis title and mathematical areas. There is no hint of the nationality of the degree holders or research supervisors. It's true that many of the hundreds of Irish postgraduates who have earned doctorates in Scotland, Wales, England, France, Germany, Italy, Australia, Canada, and the USA---some of whom were included in a recent blog here---are included in the MGP, as are those Irish researchers who have supervised doctorates all over the world, but their Irish origins are invisible to the casual viewer.

That didn't stop me searching on first names such as Colm (yielding 10 hits), Niall (8), Cormac (7), Sinead (5), Eoin (4), Siobhan (4), and Niamh (2). Many of those hits are indeed Irish, and some represent those hard-to-spot doctorates earned or supervised outside Ireland. None of the names Aodh, Eoghan, Gobnait or Tadhg appeared at all. The 1945 University of London statistics PhD of Cork's Tadhg Ó Ciardha, who rose to the rank of president of UCC, is not at MGP, not even under Timothy Carey.

Searching on last names is less likely to be fruitful, as Irish names are so common in Britain, the USA, Canada and Australia. Names *in Irish* are another matter, as UCC graduate Colm Art O'Cinneide (from Cork) shows: and he has the distinction of doing his PhD both with and at Purdue.

The free online Annals of Irish Mathematics and Mathematicians, started in December 2014, attempts to document all Irish postgraduates in maths and related fields, regardless of where they did their advanced degrees, as well as those people who did doctorates (anywhere in the world) under the supervision of Irish advisors; it now includes well over 2500 people.

Searching the Mathematics Genealogy Project under county Ireland yields about 430 people, representing doctorates earned in the Republic via the traditional advisor system as far back as 1931. There are also early Irish doctorates such as Hilda Hudson's honorary one, and doctorates awarded in recognition of prior research, such as John Synge's and James McMahon's. Searching by individual institutions reveals the following counts by institutions: TCD (91), UCG/NUIG (42), UCC (76), UCD (115), DCU (31), Maynooth (26), Limerick (20), DIT (6). Dundalk Institute of Technology (1), the Institute of Technology Tralee (1) and WIT (1) are present too, though the sole PhD from Waterford (in CS) is filed under Institiúid Teicneolaíochta Phort Láirge. I believe that the MGP count for maths doctorates earned in the Republic should be well over 500, but until the numerous missing ones are added, a more accurate public accounting remains an elusive goal.

Searching on Queen's University Belfast brings up 145 doctorates going back to 1951, but dozens more are certainly missing. A Ulster University/University of Ulster (i.e., Coleraine or Jordanstown) search turns up 13 more, but at least 50 people in this category are not listed at MGP at all, such as the 40 doctorates (many in stats) supervised by Sally McClean. For many years, the IMS Bulletin has encouraged submission of PhD abstracts which they then publish, but it seems that key information about many relevant doctorates never gets sent in.

UCC has done an excellent job of listed their PhD theses in maths on a website (click on "Former PhD Students"), though they miss two key early recipients: statistician Donal McCarthy, whose doctorate was conferred upon him on 17 January 1939, and analyst Siobhán Vernon, who got hers in 1964. Other third level Irish institutions would be well advised to follow this UCC webpage example. DCU has a useful search engine which helps with tracking down theses by looking under the name of the research supervisor. In this way, one can see that Brien Nolan has had 5 doctoral students, though not all of them have made it to his MGP listing at the time of writing.

The true count of maths (and related) PhDs earned on the island of Ireland is almost certainly over 800, and probably over 1000 if all of those in CS, operations research, theoretical physics, and so on, also also included. The total count of the doctorates earned (or supervised) overseas by Irish graduates has yet to be reckoned.

It seems that getting correct estimates in this context, just like accounting for money and voters, or residents in a census, presents difficulties often overlooked by pure mathematicians who assume that counting the elements in modestly-sized finite sets is an essentially trivial activity.