Note of April 2017. When I began this page away back in 1999 (on June 24th, to be exact) my intention was to include (for my intended readers: other mathematicians) only the barest details of my life, and certainly not to relate ... Now, some eighteen years later - and after I thought that my original site had vanished altogether (having been taken down by DCU and the college where I once worked) - I find myself (see the
at the top of my home page) able to do something I thought I'd never be able to do: correct errors/broken links and add new material. I also intend including many more photographs in the
section of this page, and more besides over time.
The bones (longer details below)
on Saturday 5th January 1946. Attended local school (where my best teacher, for my final three years, was my father).
1958-65. Attended various boarding schools in Ireland (I ran away from the first of them three times) and England.
January 1965: awarded Open Scholarship in Mathematics to
Royal Holloway College
(RHC) of London University. Undergraduate at RHC for 1965-68. Mary, my wife-to-be, was a student (B.A., French major, Italian minor) there at the same time.
Summer 1968: awarded Tutorial Research Studentship at RHC for the years 1968-71, while I did my Ph.D. there.
I completed my thesis - Transcendental numbers in the p-adic domain - in 1970-71, and was awarded a London university Ph.D. in 1972.
1971-72. Temporary lectureship in Pure Mathematics in the
Mathematics department of RHC. Marie, our first daughter, was born on June 5th, 1972.
1972-74. Temporary lectureship in Pure Mathematics in the
Mathematics department of Manchester University.
October 1974 - November 1975. Temporary lectureship in Mathematics in the Jos Campus (now the
University of Jos)
of Ibadan University,
Catherine, our younger daughter, was born in Jos on April 30th, 1975.
January 1976 - June 1988. Lectureship in Mathematics in
Blackrock, County Dublin, Ireland. The College was closed - in an act of gross vandalism - by the then Irish Government, headed by
Garret Fitzgerald (aka Garret the Good).
The full story of the closure of the college would provide good material for an undergraduate essay. When Fitzgerald's government were in office (its Minister for Education was a certain Gemma Hussey) the then opposition - headed by the notorious 'Charlie' Haughey - made much political capital of the poor judgement of Fitzgerald and Hussey, protested the closure of a historic establishment... ; the usual behaviour of opposition politicians everywhere.
(Once, while Mrs. Hussey was still plying her trade as a politician, she gave an interview to the Sunday Tribune - a leading Irish Sunday newspaper - and she wanted us to know she was so brilliant that, on one occasion John Kelly, a university Constitutional Law lecturer and a previous government minister (from her political party), had told her that she could have gained a masters degree had she applied herself. Wow!, so impressive.)
Within a short time the Fitzgerald government fell, were replaced by Haughey's party (Fianna Fáil (the "Republican Party")) ... More to add here,
or to move elsewhere...
September 1988. Moved (" the permanent gift of the [Government] Department of Education," according to an uncivil senior civil servant) to the Mathematics department of
St. Patrick's College
(the college hasn't had an independent web site since September 2016, when it became fully absorbed by
Dublin City University),
Drumcondra, Dublin 9, Ireland.
at the July 2006 Vancouver Meeting of the Canadian Number Theory Association, a most happy event for me, as we agreed to collaborate, and I spent a very fruitful two weeks with Karl at Dalhousie in May 2007 (see
my colloquium talk there).
As I write this (summer of 2007), Karl is about to give a talk on our work at the
18th Czech and Slovak International Conference on Number Theory.
Resigned from St Patrick's College, four years ahead of normal retirement age. My resignation took effect from the end of August 2007.
Now (2007, at the time of writing) I embark on a new mathematical life, and a new life altogether.
I have a
elsewhere on my site, and I also have many individual photos distributed in several places - some further down this page. Here, however, in a final
effort (August 2007) to finish work on my site before leaving St Patrick's College, I have created a single collection of photographs which covers the period of most of my life. Because of time I can only comment briefly of those I include; it had been a longterm ambition to put hundreds of photographs up on my site, but that will not now happen.
Comment. At the time I wrote that last section I did not think that I would ever again be able to edit my site. In fact my site vanished for a while (the college/university shut it down), and it was only through the efforts of a son-in-law that I was able to get it up and running again, and be able to add to it periodically.
Longer biographical details
Born in the middle of a poker game at my home on Henry Street (the second house on the left as you go down the street from the top, just after what
used to be known as
Peetie Rodgers' field)
in Bailieboro, County Cavan, on 5th January 1946. Peetie Rogers and his family lived in the left hand-side of the house you see in the
photograph, and a Miss Connolly lived in the right-hand part of it. Miss Connolly was - like my parents - a primary school teacher (she taught in
a few miles out the Kingscourt Road; I owe this photo to
Miss Connolly ran a school-supplies shop (behind the four glass panes in the photo), and I spent many an hour there as my mother and Miss Connolly were great friends. The shop had a very distinctive aroma, of paper, pencils, ink, rubbers, dust, ... . To the left of the house is 'wee' Tom Carroll's egg processing plant, and at the back is the foundry that Peetie Rogers operated. It gave out great plumes of smoke and sparks, and occasionally he - Peetie - would come out wearing a frightening gown to scare us - who were playing in the field behind - and we ran like hell. My home, where I grew up, was just beyond that field (the road on the right - Henry Street - leads down to it). Also in the photo, just behind the house, is a shed. Once, hiding out in the loft of that shed, I stood up, and a nail protruding from the rafters went into my skull. Hair never grew back there, and I still have the mark, the size of the end of a fingernail. My great pal Brian McFadden was one of the others fooling about in that loft. I don't suppose he remembers (do you Brian?)
My parents - Seán and Annie (née Sands) Cosgrave - were both primary school teachers, in three-teacher schools. My father taught me in my final three years at primary school, in 4th, 5th and 6th classes. Dad was a wonderful teacher (in fact, the only great teacher I ever had), and I will only mention that he took us through a Shakespeare play - in class - each year; in my time with him we acted through The Merchant of Venice, Macbeth and Julius Caesar. He also taught us simultaneous equations, the Euclidean Algorithm (though Dad wouldn't have known that it was called that; he called it the 'ladder method') for computing the gcd of two integers, and some Latin and French.
The three-teacher primary school I attended was called "Saint Anne's Boys National School" (S.A.B.N.S), and my father was the 'principal' for all my years there (1950-1958). As the principal one of my father's daily duties was to 'take the roll' (i.e. keep attendance records for all the pupils). Visiting my friend Brian McFadden in 2010 (to attend the launch of Leslie McKeague's wonderful collection of Bailieboro(ugh) photographs), I got around to doing something I had put off for many years: to visit the (new since 1958) S.A.B.N.S and enquire if they had possession of the old roll books. I had never met the man - a Mr Seán Hanley - who had succeeded (in 1972) my father (after 48 years as a teacher), and as Brian and I approached the school I asked Brian who was the man up ahead (he was this Mr Hanley). When Seán saw me he immediately said: "you must be Seán Cosgrave's son..."
And the purpose of my visit? The roll books ... (it had always been my worst fear that they might have been thrown out... or ended up in the government Department of Education (where they would almost certainly have lost the key to the store room...). But - joy of joys! - they were still in the school, and Seán kindly gave me a photocopy of the roll-page from 1952 (I'm there as Seán B. MacOscair, the Irish form of my name; my father was Seán MacOscair; incidentally the 'B.' is not some sort of 'Junior' or 'II', but is simply the initial of my second (given) name: Berchmans. Long story...). On a single large page were the names of everyone in my class (we would have been then at the very end of the final year of "first class"), together with those of the year below my cohort (who would have been then at the end of the final year of "senior infants"). And here are two scans of that single photo copy:
first class 1952
senior infants 1952.
The grandfather of William and Henry James left Bailieboro for the 'States', sometime in the last century. Outside the town - in the townland of
Kilinkere - was born the well-known US Army General Phil Sheridan. He was reputed to have made the (shocking) remark that the only good Indian was a dead one, and in recent years I heard a report on the radio that some native Americans had visited Kilinkere in a spirit of reconciliation.
Francis Sheehy Skeffington
was born in Bailieboro.
See also this
County Cavan Library reference.
In more recent times Bailieboro lays claim to the well-known architect Patrick Shaffrey, the author Tom MacIntyre (whose mother taught me in the
'infants division'), and Captain James Kelly. The last three were all taught by my father. In my time in Bailieboro the principal of the local
Protestant primary school was
a remarkable man, who donated the renowned
to the National Museum of Ireland (has it been transferred to the County Cavan Museum, according to the terms of Tom's will? That was my understanding.).
That head was in Tom's school for many, many years, before he made his gift to the museum. Many's the happy hour I spent in Tom's company, being driven by car here and there to see something of interest.
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. (At that time Drogheda and Balbriggan were sleepy country towns - though veritable cities compared to my native Bailieboro - while nowadays they are infested with murderous drugs gangs.)
Why? - someone familiar with Irish geography might ask - why did my parents decide to send me to the relatively remote Gormanstown (no bus there, and my parents didn't drive a car), instead of to Saint Patrick's College in Cavan town (some twenty miles away by direct bus), and the usual place for boys from Bailieboro to attend? I had two older brothers - Aidan (b. 1933) and Tony (b. 1934) who went to 'Pats' (Tony missed out on a lot of of early schoolong as he spent years in and out of hospitals) - and Aidan hated 'Pats' with a hate that knew no bounds. I must have been in my late teens when I heard why it was that I didn't also get sent to 'Pats': evidently my brother Aidan told my father that he would break his neck if I got sent there...
Not only did my parents not own a car (which every other teacher had), but neither did they own their own house (which every other teacher had) - they rented all their lives - and it was only in later life that I heard (from my sister 'Kitty') why that was: evidently Tony's hospitalisation had carved holes into my parents' joint incomes...
I didn't like Gormanstown (in fact, I disliked it intensely) 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.
At the time I was in Gormanstown the notion of intellectual level would not have been one with which I would have been familiar, but even when I was not much older I could look back on my time there and realise my good fortune to have left it. I have but one memory of a 'Mathematics' lesson there: a teacher (the college folklore was that he was a genius) asked if we knew how many metres there were in a mile (this at a time long before the metric system was common)... There followed a deathly silence. The question was asked again, and again a silence... Eventually I stuck up my hand. Well then, how many? 1609. Praise was heaped on me as if I had just solved some difficult problem; my father would have expected everyone to know that, not as 'Mathematics', but just as a common fact, and not a question fit to be asked during a 'Mathematics' lesson.
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
in Carysfort College, Dublin.
Even I who went to that school find it hard to believe just how truly awful a place it was - oh, compared to Gormanstown I was happy there - the whole system was geared to state examinations (what's changed you might ask? I'll come to that); the teaching of 'Science' (for example) was beyond laughable. In my first year we had some Marist priest (as I recall he had studied 'History' at college) for 'Science', and a typical lesson went like this: he'd draw a tree on the blackboard, under which he wrote the word 'coal'. Then, on the branches he would write the names of the by-products of coal (Oh! Just found on the internet: by-products of coal. This is just what we saw, except that the only one I now recall was 'nylon'... ). A typical school examination question was: what are the by-products of coal?
I should say that we had a very likeable Mathematics teacher - a Mr. Hannaway - who introduced us to Geometry (Euclidean, of course). Of course he taught is in a way that was probably universal: definitions, theorems, proofs, 'cuts' (as they were called, i.e. problems based on theorems). I daresay that most found it dull in the extreme, but I just fell head-over-heels with it: the very idea that one could prove that (e.g.) the angles at the base of an isosceles triangle are equal filled me with joy... . And, we had an actual book full of it: Hall and Knight's Geometry (I cannot find a copy on the internet). The proof of the Theorem of Pythagoras (was it numbered as being Theorem 29?) was (and still is) simply marvelous; what an educational travesty that later youngsters have been deprived of seeing it.
In our second year, at the start of the two-year cycle that led to sitting the state examination known then as the Intermediate Certificate (commonly known as the Inter. Cert., with subjects Irish, English, History, Geography, ... ), we had to make a choice between French or Commerce, and Science or Art. Since from our first year we hadn't the least clue as to what 'Science' was, we had a meeting with the 'Science' teacher (a Marist priest), and - although I didn't have the with then to realise what was going on - his sole aim was to scare off as many as possible from making the choice for 'Science'.
And, how did he go about doing this (the year was 1960)? Simple. He began by telling us that 'Science' was really difficult, and to illustrate he said he'd take a random question from that year's Inter. Cert. Science paper, just to let us see... The question went something like this: if into a copper jar - which contains water at such-and-such a temperature - if into that jar is placed some object whose specific heat capacity (what?!) is something-or-other, what will the eventual temperature be after ... ?
At the end of all of that - and more besides - he asked for a show of hands: who wants to do 'Science' and who wants to do whatever (was it Art or Commerce?)? The room emptied pretty sharply, and I think I only stayed because my legs couldn't move. 'Science' was simply awful (though one didn't know enough to realise this at the time): we never heard the name of a single scientist, never heard about atoms, molecules, elements, didn't know that there was such a thing as a science book, and there was no decent library in the school where one could have learned about such things by accident, by stumbling upon a decent book.
The path that my life could have followed at that time was this: spend five years at the Marist school, sit the Leaving Certificate, then ... (go to University College Dublin?)... But, it didn't go like that... Why?
My eldest brother Aidan and my father had decided between them that I ought to go to boarding school in England (the thinking behind this - as I later came to understand - was that I could sit A-levels, specialising in Science subjects (this daft idea being based on my performance in 'Science' at the Marist school), and then ...), but evidently my mother was firmly set against all this...
Then something happened which made my mother change her mind...: in the Marist (boarding) school you were only allowed out if (say) your parents called at the weekend, and this is how it worked. They called and were admitted to a room in the school while they waited for a certain priest (I could name him, but I refrain - not for any legal fears - ... ; his nickname was 'Groucher'). One Saturday, early 1962, my parents visited, and waited for Groucher to call on them... What happened then I only heard about in later years: Groucher threw a fit... he wanted my parents to know that their son John B. was a wretched creature... he had been cast off that month's 'Board of Honour' (a school disciplinary procedure; I could explain, but...). Years later I heard that my poor mother was so shocked by this attack that she said to my father: Seán, he can go to school in England...
On my last night at that school - with one final Intermediate Certificate examination paper to sit the following morning - in the dormitory (wash basins down a central aisle, and three rows of beds on either side), I was out of my bed, chatting with a friend in another part of the dormitory, when the lights went on... It was Groucher, leather strap in hand, delighted to find that I was one of six boys who were not in their beds. We were directed to his room, and he said: Master Donnelly, you've been here often enough, show them what's to be done... - that was Brian, my dear friend - of whom the poet Enda Wyley later wrote a beautiful two page essay (below) - and Brian proceeded to lie across the arm of an arm chair to receive six clatters of Groucher's leather strap. Six for everyone else, except me, the last one; I received a bonus seventh.
The following day, having a final lunch after sitting an exam, I got up to leave, and Groucher - who was sitting at another table with some others - said aloud (for my benefit): faraway hills are green (it was known that I was leaving)
In September 1962 I went to the Salesian boarding school in Cowley, just outside Oxford. I spent three very agreeable years there. (Oh! The wonders of the internet: I have just discovered this short Oxford mail article about the
school; the Raymond Mallon and Michael Willis mentioned therein were exact contemporaries of mine.)
Why did my parents take me out of school in Dundalk and send me to boarding school in England? My older brother Aidan left Pats in Cavan sometime in the 1940s, and went to the Salesian School in Battersea (London). Why did my parents send Aidan there, rather than to some other boarding school in Ireland? I do not know, and it is now too late to find out.
What I do know is that Aidan's going to school in England explains why I also followed in his footsteps...
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 (not seriously, of course) that I was the first
official male undergraduate student at RHC. (When I told my friend Mick Ganley - a fellow student and scholarship winner (and much later the
first of Fred Piper's 50+ PhD students) - of my claim, he remarked: "sad".)
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 from Poitiers
(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
Here is an excerpt from a review of a Royal Festival Hall concert of Friday, 4th March, 1989, marking the 60th birthday of the
renowned 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
(who was then doing his Ph.D. with H.G. Eggleston), and Malcolm Woolings (doing his Ph.D. with Coulter McDowall). (Paul eventually moved to the USA - "a loss to British Mathematics" - spending a week here in Dublin with us before departure, and I last saw him when he and wife Pat came down to spend a few days with Mary and myself in Dallas, in 2002.)
Temporary lecturer in Pure Mathematics at RHC. In that year the (eventually eminent) number theorist
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.
The wonderful and loveable Ian MacDonald, FRS,
was head there in my time. I played five-a-side soccer in a team chosen mainly from
(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
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; I quote from the College records: "From page 97 of Register No. III: Annie Marie Sands came here on 19th September 1922, and left this college on 28th June 1923. She had already completed her first year of training in Marlboro' St Training School... Miss Sands was 21 years of age [that's in error, as she was 22 in August 1922] when she came here and, prior to her going to Marlboro' St, she had been a monitress since 1st September 1918").
The non-mathematical highlight of my life while I was in Carysfort was arranging for the remarkable Indian musician Nikhil Benerjee to give a public performance there in June 1985. I have written about that
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.
Note of 6th Dec. 2018. On occasions in the past I contemplated writing a detailed account of my personal experience of the closure of Carysfort College, and mentioned first as early as "05 October 2000 14:08:25 +0100", see
this Internet Archive page, where I wrote:
" Following the bizzare closure [about which much could - and may, in time - be written] of Carysfort College by the Irish government in June 1988 I transferred to my present College in September 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.) "
Until now I had never given an account of my experience - partly because I didn't think it would be of any interest to anyone (and so why bother?), but at the same time I always felt I ought to record it, if only to set down that this is what happened (worse happened to others, but it is for them to set the record straight) - and I almost certainly would not have done so had it not been for a passing footnote by a Professor Jim Walsh - a former colleague in Catysfort College - in a publication CARYSFORT COLLEGE REMEMBERED. This footnote was like a knife being stuck into me - Professor Walsh named this 'senior civil servant', but for a quite different reason.
That footnote, and my response to it, is here. That response documents my experience. [End of note of 6th Dec. 2018.]
Postscript. Every cloud has a silver lining...(which will only make sense to someone who has read my response to Jim Walsh's footnote). At the time that I was prevented (by this S.O'N. (of the response to footnote) and Minister O'Rourke) from moving to the Mathematics Department at Maynooth - and forced against my will to move to St. Patrick's College (Drumcondra) - it seemed to me to be a small personal end-of-the world... But, it wasn't, and for two reasons. First, had I moved to Maynooth I would have almost certainly had to teach some truly awful, ugly Mathematics (yes, such exists: maths for commerce students, differential equations for chemists, ... ), and would have had no control over what I taught (whereas in Carysfort I had complete control), and secondly I continued to have complete control over the content of my courses, and it was there where I would, in time, begin the best original mathematical work of my life (which started with a very happy, thrilling discovery on the evening of Tuesday 23rd November 2004, and which I have written about
For the final graduation ceremony at Carysfort College in October 1988, Seamus Heaney composed some
(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 computers. I didn't get to do anything about it until a year later when
- following the advice of
Tony O'Farrell -
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
Our papers are here.