Born in Bailieboro, County Cavan, Ireland, on 5^th January 1946.
Attended local school. (See BAILIEBOROUGH (A PICTORIAL PAST), by Leslie McKeague, is a wonderful tribute to my hometown of Bailieborough, County Cavan.)

Now I embark on a new mathematical life, and a new life altogether.

In those days Bailieboro - a small town with a population of about 1,000 - didn't have a secondary school; now it does, the Bailieboro Community School. In September 1958 I was sent off to boarding school at Gormanstown College, County Meath, out in the countryside between Drogheda and Balbriggan.
     I didn't like Gormanstown and I ran away from it three times, roughly after my third, fifth and sixth weeks there. After my third escape my Dad remarked - quite perceptibly I thought - that it seemed I didn't like the school, and my parents removed me. I spent the rest of that year back at Dad's then newly opened school, spending most of my time reading texts on Latin and French grammar, and chopping sticks for the fire.

In September 1959 I went to the Marist boarding school in Dundalk, Co. Louth, and I remained there for three years. One of my friends there - Brian Donnelly - later became a colleague (first as lecturer in, and later the head of the English Department - succeeding Seamus Heaney) in Carysfort College, Dublin.

In September 1962 I went to the Salesian boarding school in Cowley, just outside Oxford. I spent three very agreeable years there.

In September 1965 I became an undergraduate student of Mathematics at Royal Holloway College (RHC) of London University. That year was an historic one for RHC: it was the first year that male undergraduates were accepted. As I won an open scholarship there, and as I was the first scholar alphabetically, I like to claim that I was the first official male undergraduate student at RHC. (My scholarship money enabled me to start a record collection.)
     I simply loved my time at RHC, and it was there that I met my-wife-to be, Mary (she was studying major French, with Italian as her minor subject). We began 'going out together' on Friday 16th June 1967, just at the end of our second year at college; we had been friends since early in our first year. Here is a photo of Mary and I, sometime in the summer of 1970; I think it's the earliest photo of the two of us together.
     One of Mary's fellow students was 'Flott,' the renowned soprano Dame Felicity Lott (who will be singing here in Dublin this November 1st, 2007 in the National Concery Hall Celebrity Series). Mary (fourth from left) and Flott (sixth from left), and another friend Lesley, are in this photo from Sept 1967, taken at the start of a year spent in France as part of their degree studies. I still have letters that Mary, Flott and Lesley wrote to me form Potiers (France), when they were there for the final term at the end of their first year of studies. (How we in Mathematics envied their travel as part of their degree!)

Here is an excerpt from a review of a Royal Festival Hall concert of Friday, 4^th March, 1989, marking the 60^th birthday of the conductor Bernard Haitink:

"The tumultous applause which followed Bernard Haitink's spellbinding interpretation of Mahler's Fourth Symphony with the London Philarmonic at the Royal Festival hall on Friday evening ...
   It had been a remarkably happy evening from the first, for the evening had started with an impressive, full-hearted performance of Elgar's Introduction and Allegro ...
   Strauss's Four last Songs followed, and here too there was in the performance the affecting ability to range effortlessly between an intimately lyrical expression and something more grandly mysterious and universal. Felicity Lott was a radiant soloist and moved with grace and charm in Strauss's timeless retrospective world
    Her lines flowed with a natural musicality and poetry and, together with the subtly coloured strands of the orchestral texture, were woven into a gorgeous tapestry by Mr Haitink.
    And then there was the Mahler ...
    Finally, there was an exquisite rendering of the child's view of heaven, the orchestra tenderly rocking, Miss Lott perfectly attuned to the vision. It formed a blissful end to a memorable evening's music-making."

Graduating in 1968 I remained at RHC for the years 1968-71 to do a Ph.D. in Number Theory. My supervisor was John H.E. Cohn (best known for his beautiful proof of the difficult result that 144 is the largest square Fibonacci number). In those years I held one of the College's 'tutorial research studentships,' which meant that I was paid for giving tutorials and correcting scripts on behalf of the head of department, the great convexity theorist, Professor H.G. Eggleston. For the year 1969-70 I shared a house in nearby Staines with a friend Paul Goodey (who was then doing his Ph.D. with H.G. Eggleston), and Malcolm Woolings (doing his Ph.D. with Coulter McDowall).

1971-72. Temporary lecturer in Pure Mathematics at RHC. In that year the number theorist Roger Baker came to RHC as a lecturer, and we became friends. Roger subsequently became a full Professor at RHC, before departing for the USA. Mary and I married in her home town of Plymouth, Devon, on 24th. July (by chance it was my father's 65th. birthday). Flott sang at our wedding.

1972-74. Our daughter Marie was born on June 5th, 1972.
Temporary lecturer in Pure Mathematics, Manchester University.
Ian MacDonald, FRS, was head there in my time. I played five-a-side soccer in a team chosen mainly from Jeff Paris (in goal), Nige Ray (midfield), Mick McCrudden (general position) and Will McLewin. Once we defeated the Maths. dept. team from Salford university (just up the road) by 40-1, and I scored 27 of our goals (a fact which Nige remarked upon at his 60th birthday celebrations, which Mary and I attended in November 2005). In the year 1973-74 we were on occasion joined by visiting Research Fellow Charles Van Loan ('Charlie').

October 1974 - November 1975.
Lecturer in Pure Mathematics at the Jos Campus of Ibadan University, Nigeria. Our daughter Catherine Siobhan was born in Jos, Nigeria, on 30th. April, 1975 (in later years I worried her by telling her that I had contemplated calling her Carla Frederika, after the great Carl Frederik Gauss, whose birthday also fell on 30th. April).

January 1976 to June 1988. Lecturer in Mathematics, Carysfort College, Dublin (where my mother was a student for one year, away back in 1921-22). Michael Barry was a great mathematics colleague; he left Carysfort in 1987, and since then has been in the Mathematics department of Allegheny College, Meadville, PA, USA. We still meet from time to time, usually here in Dublin, and once - on my 49^th birthday (January 5^th 1995), while attending the American Mathematical Society winter meeting - dined out in Chinatown in San Francisco.

Following the bizzare closure of Carysfort College by the Irish government in June 1988 I transferred to St Patrick's College (Drumcondra) in September 1988. In June 1988, a senior civil servant put it to me that I had three choices: to emigrate, to retire (at 42!!), or to transfer to St. Partick's College. The Mathematics departments of University College Dublin and St Patrick's College (Maynooth) both wanted me transferred to them, and hearing from the latter before the former I opted to go there. The then Government minister for Education - one Mary O'Rourke - was approached by a number of TDs (members of parliament) - Brady and O'Connell - to arrange for my transfer to Maynooth. While initially the minister was all in favour of my going to Maynooth, she later informed them that the Department of Finance (no less) were insisting that I go to Drumcondra.

For the final graduation ceremony at Carysfort College in October 1988, Seamus Heaney composed some Valedictory Verses. (Years later, in 2002, after I had been introduced before a talk I gave at the Southern Methodist University of Dallas, I said something like: you know, one of the things that annoys me about Stanford folk is that they are always going on about how many Nobel laureates they have on their faculty; they have twelve or thirteen. Who cares? ... I once worked in a place where about two percent of faculty (eventually) won a Nobel Prize... (I could see them sit up!) Thing is, there were only about fifty people working in the place anyway, and one of them was Seamus Heaney. It got a laugh.)

In June 94 I came to know of Mathematica (until then I was entirely ignorant of Computer Algebra Systems), and immediately realised that I had made a gross error all those years in avoiding - like the plague - computers. I didn't get to do anything about it until a year later when - following the advice of Tony O'Farrell - I investigated Maple, and that determined my future professional work.

In November 1994 - while attending a course on Chaos in St. Patrick's College, Maynooth - I met Dr. Mark Daly. Was I impressed!! Mark Daly worked part-time hours with me for the months Jan. 95 through to May 95, helping me get the use of Maple off the ground in my first and second year courses. Mark worked with me for the years 1995-98 while I was acting head of department. I would not be able to do today, what I can do today, had it not been for him. I continued to work in St Patrick's College until I resigned my post as head of the mathematics department in February 2007 (four years ahead of the normal retirement age), and I began a new life centered on my collaboration with Karl Dilcher.

Note of February 2011. Details of recent papers that Karl and I have written available here.