Standing on the Shoulders of Giants (19101959)
In Ireland, prior to the 1900s, advanced training opportunities in mathematics and related fields were limited. While William Hamilton (18051865) and George Salmon (18191904) had distinguished careers in academia in the land of their birth and education, other notable Irish people with maths talent, such as Robert Adrain (17751843) and George Stokes (18191903), spent their working life overseas. Of course, many younger mathematicians apprenticed under the likes of Hamilton and Salmon, at Trinity College Dublin, and to a lesser extent (under others) at the Queen's Colleges in Belfast, Galway and Dublin, as well as at the Catholic University of Ireland in Dublin.
Hamilton, Salmon, Adrain, Stokes
The whole concept of postgraduate study was slowly changing, arguably driven by French and German models. Studying with a master for several years, leading to a significant new result written up as a thesis, slowly became the new expectation for research mathematicians. For instance, Father John Donaghey from Kilmoveer, Mayo, earned his PhD in 1907 in Munich with Wilhelm Röntgen, before undertaking a career teaching at St Eunan's College (Raphoe), Maynooth, the University of Munich, and (in the USA) at Marquette University and Incarnate Word College.
Starting just over a century ago, in part spurred by the National University of Ireland's Travelling Studentship scheme, Irish graduates of mathematics and mathematical physics started to travel to Britain or further afield in greater numbers to pursue postgraduate study. Some of them did research directed by very well known and influential people, and on occasion these mentors had Irish connections.
These stays in Cambridge, London, Paris, Edinburgh, Princeton, and elsewhere generally lead to advanced degrees, in most cases a doctorate. While not all of the newly minted mathematicians returned to Ireland, many of them stayed in academia, and of those, several played major roles in starting up or advancing research programmes wherever they ended up, and often supervising PhD students of their own.
In the period up to 1960, Irish postgraduates trained overseas with talents as diverse as Picard, Bateman, LeviCivita, Baker, Whittaker (who had worked at TCD), Hardy & Littlewood, Born, Smithies, Artin, Wright, Hayman, Higman, Besicovitch, and Feller, as well as an impressive array of top notch (and sometimes Nobel prize winning) physicists. Needless to say, in this period there are also some examples of doctorates earned in Ireland for research done under the guidance of distinguished advisors (some of whom, e.g., JL Synge, were themselves Irish).
Below we survey numerous notable cases which correspond to postgraduate work completed between 1910 and 1959 (actually, as it happens, between 1913 and 1957). The focus is on pure maths and theoretical physics; obviously other people in this era pursued postgraduate work in applied and engineering maths.
Starting in 1960, the numbers of people in this category skyrockets: later decades will be surveyed in future blogs here.
1. Paddy Browne (aka Pádraig de Brún, 18891960) was born in Grangemockler, Tipperary, and was educated at UCD and at the Sorbonne (19101913), culminating in a PhD ("Applications des complexes lineaires a l'etude des surfaces et des courbes gauches") under Émile Picard. He spent three decades at St Patrick's College, Maynooth, before becoming president of UCG. A priest and a classics and Irish scholar, as well as a mathematician, he wrote the famous poem "Thánaig Long ó Valparaiso". 


2. Frank Murnaghan (18731976) was born in Omagh, Tyrone. He was educated at UCD and then (19141916) at Johns Hopkins, culminating in a PhD (on "The Lines of Electric Force Due to a Moving Electron") under Harry Bateman. He later spent 30 years on the staff at Johns Hopkins and wrote 16 books on various topics in mathematics and mathematical physics. 


3. Statistician R. C. (Roy) Geary (18961983) was born in Dublin. After study at UCD and the Sorbonne (19191921), he had a long career in the Department of Industry and Commerce, before leading both the Central Statistics Office and the Economic and Social Research Institute. His name lives on in the Stone–Geary utility function, the Geary–Khamis dollar, and elsewhere. 


4. Albert J. McConnell (19031993) was born in Ballymena, Antrim, and was educated at TCD and at La Sapienza University in Rome, culminating in a PhD (on "Stability inside a gravitational field") under Tullio LeviCivita in 1928. He spent his entire career at TCD, serving as provost and writing two books, one on Riemannian geometry and tensor calculus. 


5. Jack Semple (19041985) was born in Belfast, and was educated at QUB and at Cambridge, culminating in a PhD ("Surfaces Of Intersection Of Cubic Primals. 2.Cubic Cremona Transformations Of 4D Space") with Henry Baker in 1930. He lectured at QUB and at King's College, London, and coauthored 3 books on algebraic geometry. 

6. Physicist Ernest Walton (19031995) was born in Dungarvan, Waterford, and his family moved around Ireland a great deal when he was young. He studied maths and physics at TCD (earning an MSc under JL Synge) and Cambridge, culminating with a PhD under Ernest Rutherford in 1931. His "splitting the atom" with John Cockroft lead to the two men later sharing a Nobel prize. He lectured at TCD for four decades. 


7. James R. (Dick) Timoney (19091985) born in Belleek, Fermanagh. He was educated at UCD, and studied with E. T. Whittaker (who had once been on the staff at TCD) at the University of Edinburgh (19301932), before serving 47 years on the staff at UCD. 


8. Philip Gormley (19101973) was born in Claudy, Londonderry, and was educated at UCD and at the University of Edinburgh, culminating in a PhD (on "A correspondence between null and ordinary geodesics, its properties, and Straneo’s unified theory") with Edmund Whittaker in 1933. He taught at UCD for 40 years, and was a keen translator of Russian mathematics. 


9. Jack Todd (19112007) was born in Carnacally, Down, and studied at QUB and at Cambridge, where he studied (19311933) with Hardy & Littlewood. He worked at QUB and King's College, London, and later at the National Bureau of Standards and Caltech in the USA. He was an early proponent of using computers to do numerical mathematics. His efforts in the late 1940s helped to ensure the preservation of the Oberwolfach Mathematical Research Institute in Germany. 

10. Statistician M. Donal McCarthy (19081980) was born in Midleton, Cork. He was educated at UCC, and studied at University College London. The latter stay led to a 1939 PhD, awarded by UCC, where he then taught for a decade. He served as director of the Central Statistics Office, before returning to UCC as president of the college.  
11. Theoretical physicist Barry Spain was born in Londonderry. He was educated at TCD and at the University of Edinburgh, where in 1939 he got his PhD (on "A nuclear statistical model with applications to stability") under Klaus Fuchs, a man who later passed nuclear secrets to Moscow. His career included stints at Imperial College and TCD, followed by four decades at Sir John Cass College. He wrote five books. His son Philip is also a mathematician.  
12. Mathematical physicist David Bates (19161994) was born in Omagh, Tyrone. He was educated at QUB and University College London, and later taught at both institutions. His doctoral studies with Harrie Massey at UCL were interrupted by WWII, and never formally completed, but the two worked together extensively. Bates worked in atmospheric and molecular physics, and was a founding member of the Alliance Party of Northern Ireland.  
13. Theoretical physicist Jim McConnell (19151999) was born in Dublin, and was educated at UCD and in Rome, where he was ordained as a priest and also earned his doctorate ("The Lorenz formula  The Lorenz for the refraction index") from La Sapienza University (in 1941). His career started at the newly founded Dublin Institute of Advanced Studies, but was mostly spent at St Patrick's College, Maynooth, where he also served as registrar. 


14. Mathematical physicist Sheila Tinney (née Power, 19182010) was born in Galway, where her father was professor of maths. She was educated at UCD, and then at the University of Edinburgh. Her 1941 PhD there, on "The stability of crystal lattices", done with Max Born, made her the first Irishraised woman to get a doctorate in mathematical science. She worked at DIAS and UCD, introducing generations of students to quantum physics. 


15. Theoretical physicist Jim Hamilton (19182000) was born in Sligo town, and brought up in Belfast. He was educated at QUB and Manchester, earning his 1948 PhD ("Quantum Theory of Radiation Damping") with Patrick Blackett. His career included notable stints at DIAS, Cambridge, University College London, and Nordita in Copenhagen. At DIAS, he helped develop the theory of of cosmicray mesons, and his later work included Smatrix theory research. 

16. Richard Ingram (19161967) was born in Belfast, and was educated at UCD at and Johns Hopkins, earning his 1948 PhD (on "Characters of the Symmetric Group") with fellow Irishman Frank Murnaghan. A priest, his interests included geophysics and algebra. In addition to teaching maths at UCD for two decades, he spent many years running the seismological observatory at Rathfarnam Castle. A founding member of the IMTA, he also coedited Volume 3 of the complete papers of Hamilton. 

17. Derek Burgess (1924 ) was born in Tyrone and educated at QUB, and at Cambridge, leading to a 1950 PhD ("Abstract LebesgueStieltjes Integrals, LaplaceStieltjes Transforms and Moment Problems, with Applications") with Frank Smithies. After a few years in Paris and at Magee in Londonderry, he returned to QUB where he served for four decades. He supervised several PhD theses in topology, and authored the 1966 textbook Analytical Topology. 


18. A. Murray MacBeath (19232014) was born in Scotland and brought up in Belfast. He was educated at QUB and worked at Bletchley before continuing his studies, first at Cambridge, and then at Princeton, where he got his PhD (on "The Geometry of NonHomogeneous Lattices") in 1950 under Emil Artin. His career was mostly spent at Dundee, Birmingham and the University of Pittsburgh. 

19. Barbara Yates (19191998) was born to a Dublin family who soon moved to Belfast. Like her father and two brothers before her, she got a maths degree from TCD. Her 1952+ PhD from Aberdeen ("A differencedifferential equation") done with Edward Wright, made her the first Irish woman and Irish graduate to receive a doctorate in pure maths. Her long academic career was mostly spent at Royal Holloway. 


20. Informatics and computing pioneer Gordon Foster (19212010) was born in Belfast, and was educated at QUB, and at Oxford, where he got his PhD (on "Some Problems in the Mathematical Theory of Probability") in 1953 under David Kendall. His career included stints at Bletchley Park, the University of Manchester (alongside Alan Turing), the London School of Economics, and many years at TCD. He devised a 9digit code upon which the International Standard Book Number (ISBN) is based, and later worked to connect remote areas of the world to the internet. 


21. Mathematician, geophysicist and social activist Gerry Gardner (19262009) was born in Tullamore, Offaly. Educated at TCD, Carnegie Mellon and Princeton University, he got his 1953 Phd ("The concept of a rigid body in special relativity") at the last named institution. He worked in the USA in the oil and natural gas industries. A statistical analysis of his was used in a US Supreme Court decision. 

22. Paddy Kennedy (19291966) was born in Claremorris, Clare, and was educated at UCC and the University of Exeter. At the latter he earned his 1954 PhD ("The Minimum Modulus of Integral Functions of Small Order") with Walter Hayman, but it was awarded by NUI. After a decade teaching at UCC during which he published extensively in analysis, he became the first professor of mathematics at the new University of York. Sadly, he died a few years later. 

23. Sean Tobin (1930 ) was born in Moneygall, Tipperary, and was educated at UCG, and then at Manchester, culminating in a 1954 PhD ("On Groups of Exponent Four") with Graham Higman. He spent 40 years at UCG, spearheading an algebra and group theory focus there. He is perhaps best known for his early work on the Burnside Problem. 


24. Maurice Kennedy (19241994) was born in Dublin, and was educated at UCD and at Caltech, where he got his PhD ("Ergodic Theory for a Certain Class of Markov Processes") in 1954 with Samuel Karlin. His career was spent at UCD, where he also served as registrar. His research interests included analysis, functional analysis, and point set topology. 


25. A. Cormac Smith (19262009) got his BSc and MSc from UCD. His 1954 PhD on "Generalized Quaternion Algebra of Hamilton" was awarded by UCD, for research (originally suggested by Phil Gormley) done while he was teaching at Sandyhurst College, with input from Jean Dieudonné at Nancy. The bulk of his career was spent in Canada, at the University of Windsor.  
26. S. James Taylor (1931 ) was born in Carrickfergus, Antrim, and was educated at QUB and at Cambridge, culminating in a 1954 PhD ("On the Theory of Hausdorff Measures") with A. S. Besicovitch. His career was spent at Birmingham, Westfield College, Liverpool, and the University of Virginia. His expertise includes Brownian motion, "small sets" and fractals. He has three books to his name, as well as seven joint publications with Erdős. His son Charles is also a mathematician.



27. Brian Murdoch (1930 ) was born in Dublin and educated at TCD, and at Princeton, where in 1955 he earned a PhD on "Preharmonic functions" under probabalist William Feller. His career was largely spent at TCD, where his principal interests were in random walks, stochastic processes and probability. 


28. Mathematical physicist John Stewart Bell (19281990) was born in Belfast. He was educated at QUB and the University of Birmingham, where in 1956 he got a PhD under Rudolf Peierls He spent much of his career at CERN, and is known for a 'nogo theorem' named after him.



29. Theoretical physicist Ron McCarroll was born in Ballymena, Antrim, and was educated at QUB, where in 1957 he got his PhD under Alex Dalgarno. His career has been spent at QUB, CNRS, Bordeaux University, and Pierre & Marie Curie University. 


30. Vincent Hart (1930) was born in Hull, and brought up in Cork. He was educated at UCC and at DIAS, earning a PhD on "The Method of the Hypercircle in the Solution of the Biharmonic Equation" in 1957 with John L. Synge. His career started at UCC and DIAS, followed by three decades at the University of Queensland.  