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 note 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 photos section of this page, and more besides over time.

The bones (longer details below)

  1. Born in Bailieboro(ugh), County Cavan, Ireland, on Saturday 5th January 1946. Attended local school, where my best teacher, for my final three years, was my father.

  2. 1958-65. Attended two boarding schools in Ireland (I ran away from the first of them three times) and one in England. In the second one (in Dundalk) I made an initial discovery of Mathematics (via elementary Euclidean Geometry), and in the latter (in Cowley, Oxford) my love for Mathematics blossomed, while at the same time I discovered music. These two continued as the great themes of my life. As this page develops I will briefly outline my musical discoveries as the years went by.

    Recently I used the re-discovery on nineteen letters that I wrote from Nigeria (1974-75) to friends Bob and Judy Sandling in Manchester, I used those letters to greatly expand the Nigeria section below. I also recently re-read three diaries from the years 1963, 64 and 65, and they have brought back some long-forgotten memories - or exactly pin-pointed memories - from those years. I will - when I have time - use those to expand on entries below. An example, the first classical music concert that I attended: Yehudi Menuhin in the Sheldonian Theatre, Oxford, on Thursday 26th November 1964.

    Here is my diary entry and ticket.

  3. January 1965: awarded Open Scholarship in Mathematics to Royal Holloway College (R.H.C.) of London University. Undergraduate at R.H.C. 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 R.H.C. 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.

    Mary and I married on Saturday 24th July 1971; there are some photos at this page.

    1971-72. Temporary lectureship in Pure Mathematics in the Mathematics Department of R.H.C.. Marie, our first daughter, was born on Monday June 5th, 1972.

  4. 1972-74. Temporary lectureship in Pure Mathematics in the Mathematics Department of Manchester University.

  5. 16th October 1974 - 26th November 1975. Temporary lectureship in Mathematics in the Jos Campus (now the University of Jos) of Ibadan University, Nigeria. Catherine, our second daughter, was born in Nigeria on Wednesday April 30th, 1975.

    Note of August 2023. Although we only spent just over one year of our lives in Nigeria (I like to say one year, one month, one week, and one day), it is the best documented period of our lives. From Nigeria I wrote nineteen letters to our Manchester friends Bob and Judy Sandling - Bob used to circulate copies in the Manchester department - and, shortly after we left Nigeria, Bob presented me with copies of those letters, letters which I have just re-read in recent times. I have decided to scan them and enter in the appropriate place below, together with partial commentary. Re-reading those letters has reminded both of us of some events which we had long forgotten.

  6. January 1976 - June 1988. Lectureship in Mathematics in Carysfort College, 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. When the opposition (Haughey and his gang) became the Government before the College closed, they closed it anyway...

    (Once, while this 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 had told her she could have gained a masters degree had she applied herself. Wow!, so impressive. What a brain.)

    Highlights of my Carysfort years: the quality of my Mathematics students, some enduring friendships, the visit - to give a talk to my students - by a mathematical hero of mine (Heini Halberstam), and - most of all - the concert that I arranged in the college by the legendary Nikhil Banerjee (I am still adding to that page).

  7. 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.

    Met Karl Dilcher 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, during which time we completed out first research paper (it's available at this page.) When I first wrote this (summer of 2007), Karl was about to give a talk on that very work at the 18th Czech and Slovak International Conference on Number Theory (see 'Participants' at conference page).

    February 2007. Resigned from St Patrick's College, four years ahead of normal retirement age. My resignation took effect from the end of August 2007. About to depart St. Patrick's College at the end of August 2007 I wrote here that I was about to embark on a new mathematical life, and a new life altogether. And that proved to be the case.

  8. Life after leaving St. Patrick's College. Oh, I may never get around to this... , but it was (is!) good.

Outdated: I have a Photographs section 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 some of my life up to the present. 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 paragraph I did not think that I would ever again be able to edit my site. Dublin City University took down my site (they evidently had no interest in the notion of an Archive), and it was only through the efforts of a son-in-law (Fiachra Lennon) that I was able to get it up and running again, and be able to add to it periodically. The following photos section has been greatly added to since August 2007:

Longer biographical details (expansion of the above bones)

Expanding #1 above. 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 Lisball school a few miles out the Kingscourt Road; I owe this photo to Kieran Campbell). 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 and senior infants 1952.

The grandfather of William and Henry James left Bailieboro for the 'States', sometime in the last century. The renowned Francis Sheehy Skeffington was born in Bailieboro. 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 Tom Barron, a remarkable man, who donated the renowned Corleck Head 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 years before he made his gift to the museum. I spent many happy hours in Tom's company, being driven by car here and there to see something of interest.

(My most memorable trip with Tom was in August 1974. I had returned on my own to visit my father weeks before we headed off to Nigeria, and Tom offered to drive me back to the airport. He asked if I would like to visit the famous Knowth Megalithic Passage Tomb... of course I would, but isn't Knowth currently closed to the general public? Indeed it was - as it was then being excavated by George Eogan and his team - but Tom told me that he was a friend of George Eogan, and he knew that he would make an exception for us... , and he did! Friends in high places!

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A Bailieboro film (featuring Tom McIntyre and Tom Barron). TEXT to be added here when I have time. Youtube video

Expanding #2 above. 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 he 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 hospitalisations 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.

Everyone has fork-in-the-road moments that determine their lives (I do not subscribe to the notion that we have a 'Fate', or that our lives are pre-determined; there is no 'god' who has a 'plan' for each of us, we simply live out a life in this extraordinary place called Earth, a tiny insignificant place in a vast, unfathomable Universe), and running away from Gormanstown was certainly such a moment in mine.

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Second boarding school. 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.

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?

In all of my time in that school we never heard even the name of a single scientist; we never heard of Galileo, Newton, Faraday, ... , not even - by was of possibly inspiring us - Ernest Walton, our very own Irish Physics Laureate.

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 teaching of 'History' was execrable: in the first 'History' lesson at the start of our two-year cycle leading to the Intermediate Examination. the teacher told us that he had studied examination questions in recent years and he had identified six probable topics in both Irish and European history. I cannot even recall what the Irish topics were, but in European they were Feudalism, Peter the Great, ... , the Causes of the First World War. We had no text books, we simply absorbed all the rubbish given to us...

As for 'Religion' (mercifully not examined as a State Examination... nowadays youngsters digest Christianity, Islam, Hinduism, ... ) well we were subjected to 'proof' after 'proof' that 'god' existed... watches found in the desert and all that sort of stuff... ; if you don't know the reference then count yourself fortunate). We were breathed upon by a priest who seemed to be permanently drunk on 'altar wine' (I recall serving mass with him and having to offer him the two glass containers, one with water, the other with altar wine... more, more, more... to the altar wine.)

Once a year we were marched out to St. Brigid's Shrine, some miles from the school. This marching always took place on some day in early February (her 'feast day'?) - it was usually wet and miserable - and my abiding memory is the piteous looks that we used to elicit from the going-about-their-business members of the general public.

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 completely 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 (I simply don't want to sully my webpage) - ... ; his nickname was 'Groucher'). One Saturday, early 1962, my parents visited, and waited for Groucher to call on them... What then happened 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... (Another of those fork-in-the-road moments: had my mother not had that encounter with the reprehensible Groucher then my mother could have had her way, and I've had stayed there...)

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 (page 1 and page 2) - 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.

Aside. The Intermediate Certificate Mathematics examination papers for 1962. Here are the Algebra, Geometry and Arithmetic papers that we sat for the Inter in 1962. Only the Geometry paper contained anything of interest.

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). That September - before heading off to school in England - I returned to Dundalk for the school's opening evening, probably with a friend Eddie Caffrey, and hoping to meet up with some of the others... Groucher spotted me and told me to leave...

Here is a photo from a rare happy day at school in Dundalk: John, Eddie, James. Once, in my final year there, we - the boarders - were brought to Dublin for a day out (imagine!) 'John' is me, 'Eddie' was my friend Eddie Caffrey (he was from County Cavan, like myself, he was from Mullagh, about 8 miles from my hometown Bailieboro), and 'James' - James Nugent - was from Malahide, just north of Dublin. On our day out in Dublin - accompanied of course (unlike what I was to experience in my third boarding school)! - we took this photo in one of those booths, a novelty at the time.

One of the places we visited was the famous Christ Church Cathedral, and while there we saw some old tombs, for one of which we bought a postcard on which we wrote "Wish you were here" and sent it to Fr. Morris (i.e., Groucher). We thought it was the height of humour. (He never made any attempt to discover who sent it.)

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Third boarding school. In September 1962 I went to the Salesian boarding school in Cowley just outside Oxford. Here is a photograph taken on the day I left Ireland to go there. It's one that my mother sent to my sister Marie in San Francisco, and on the back of it my mother wrote: that's your kid brother, now sixteen. Left to right are my brother Tony, Dad, Mum, John Clarke and myself (cigarette in hand). (Mum and Dad never owned a car, and whenever we went anywhere - not by bus - we went with John, a hackney man, who lived just across Henry St. from us.)

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...

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.)

I went up to Cowley early in September and, after an initial few days when I was homesick, I simply fell in love with the school. Not so much with the school itself, but with the new-to-me freedoms that I enjoyed there (my fellow English class mates didn't feel the same; they felt they lived in a prison). The first freedom that I enjoyed was being able to go out of the school - unaccompanied! - and visit the local public library (my first library!), where I discovered books the likes of which I'd never seen before.

In particular I fell upon a wonderful book called From Zero To Infinity by Constance Reid, a book that - and I couldn't have known this at the time - determined my eventual mathematical life.

The great new freedom was to be able to leave the school outside classroom hours. You want to go to the public library? Just go. You want to get the bus down to Oxford? Just go. You want to see a play down in the theatre (say, the Oxford Playhouse)? Just go. You want to attend a music concert down in Oxford (say, the Sheldonian Theatre)? Just go. You want to visit the Motor Show down in London? Just go. Unaccompanied. You want to attend the London funeral of Winston Churchill? Just go.

At Cowley I discovered classical music...


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Expanding #3 above. How did I become a Mathematics undergraduate at Royal Holloway College of London University?


In my Cowley-Oxford school's library there was a small section displaying university prospectuses, and R.H.C.'s caught my eye: the beauty of its building, that it had been a women's only college (London was the first British university to allow women study for a degree, R.H.C. admitted its first cohort in 1879) about to admit male undergraduates for the first time in October 1965, and that amongst the research interests of its Mathematics staff was none other than my beloved Number Theory.

It was a no-brainer, I had to get there! (Here is the R.H.C. current prospectus.) Applying to go to university involved choosing up to six possible places through U.C.C.A., ranked in order of preference. I submitted my application, with R.H.C. ranked first, Westfield College London ranked second (it too, like R.H.C., had until that year been a women's only college, and was also admitting male undergraduates for the first time in October 1965... I had had enough of boys' boarding schools for six years!)

In the prospectus I read that one could apply to sit an entrance scholarship examination, I applied, sat a two-paper examination at my own school, and waited...

Before the end of the year 1964 I received an invitation to attend an interview at R.H.C. in early January, and my interview panel consisted of no fewer than five members of the Mathematics Department staff: the Head of Department Professor William McCrea, Professor F.R. Keogh, Dr. Mary Bradburn, Dr. Barbara Yates and Dr. Gearoid De Barra.

They had evidently been told about a minor discovery of mine and they asked all about it: how had I discovered it, how had I proved it (since I had by then constructed one myself), and they asked me about my interest in Number Theory. All of this at a board, with chalk (only on one other occasion - in Manchester - did I have such an interview), and lasting for about one hour. I also had a one-on-one with the wonderful Marjorie Williamson, the College's Principal. (Her Guardian obituary.)

Within a few days I was informed that I was being offered an Open Scholarship in Mathematics, and a place in the College for the next academic year. Since I was the first scholar alphabetically, I like to claim (not seriously, of course) that I was the first official male undergraduate student at R.H.C. (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 tongue-in-cheek claim, he remarked: "sad".)

My first days at Royal Holloway. From my 1965 diary I read that the day on which I went up to R.H.C. was Thursday 7th October 1965. "Went out to Kingswood [Hall of Residence]. Met Vivian [Rynne] and Dan [O'Leary, Dan was a day boy at the Salesian College I attended in Cowley, Oxford] in the Coach House [adjoining Kingswood]. After supper we went by coach to the College for the Principal's address (she was wonderful). Afterwards we had departmental coffee parties. While unpacking that night the lights went out, evidently some students from the nearby [male] teacher training college.

The following day all the Mathematics students went to a talk by Professor McCrea, the then Head of Department, and later we were subjected to our first lecture by a Professor Ken Smith (this particular Ken(neth) Smith has no internet presence; there are others, but none are the one with whom we suffered). This Smith fellow prattled on for a full hour about "cotravariant and covariant vectors and tensors in 'n-space'..." (a non-mathematician could not possibly understand the level of idiocy involved here), and at the end he asked if any of us had any questions... A deathly silence, broken by one Robin Shakeshaft, who ventured: You have been telling us about ... ; but, what is this "n-space"?

Smith spluttered: "n-space? n-space? You mean to tell me that you don't know what n-space is!! My god, what the hell are they teaching you in schools these days?! I'll write up the names of some books and you can find out in them what n-space is." He did indeed write up the names of four books, and I - like a complete idiot - bought all four... All Smith had to say was that by "n-space" he meant n-dimensional Euclidean space... . Smith certainly wasn't a good teacher, nor was he even a mildly inspiring lecturer. (Each of us had a personal tutor, and Robin's happened to be this Smith character... After some weeks Robin called on Smith in his office to get some guidance concerning study; Smith's response: "work like hell for six days, then go out on the seventh night and have a good ... (since this is a family-values web page I refrain from completing Smith's advice.)

(Here I confess that I too should on one occasion have been awarded the Ken Smith medal for the worst ever introductory lecture to novice students... but that will have to wait until I relate about January 1976 when I gave my first to students in Carysfort College...)

I simply loved my time at R.H.C., 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 me, sometime in the summer of 1970; I think it's the earliest photo of the two of us together (no, here is an earlier one, from June 1969. Anyone who knows Royal Holloway will recognise that we were standing on the bridge crossing the road, directly in front of the college. Mary had just completed her final French BA examinations, and I was at the end of my first year as a PhD student.)

One of Mary's fellow students was 'Flott', the renowned soprano Dame Felicity Lott (who - at the time of originally writing this - 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 degree!)

Graduating in 1968 I remained at R.H.C. for the years 1968-71 to do a Ph.D. in Number Theory. My official supervisor was John H.E. Cohn (best known for his 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). (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.)

1971-1972. Temporary lecturer in Pure Mathematics at R.H.C.

How did I get a one-year temporary lectureship at my own college? Sometime in 1971 R.H.C. advertised two new permanent posts in its Mathematics Department. It was a difficult time for any young mathematician looking for such a post, there were (I believe) some 150 applicants, I was shortlisted, but the posts were filled by two brilliant applicants: Roger Baker and Tony (later Antonia) Jones (the great Harold Davenport's final PhD student).

Tony (as he was then) asked to be allowed to remain for the year 1971-72 at the prestigious Institute for Advanced Studies - a request readily granted - and I was invited to fill the position for the year (I heard just the week before my marriage to Mary).

Mary and I married in her home town of Plymouth, Devon, on 24th. July '71 (by chance it was my father's 65th. birthday). Our friend Flott sang at our wedding (there are some photographs from that happy day here).

Normally a junior person would not get to teach a desireable course, but Professor H.G. Eggleston (the lovable Head of Dept.) invited me to teach the second year course on Functions of a complex variable, a course that he himself had taught until then. I also taught a third year honours hotch-potch year-long course called Pure Mathematics, the hotch-potch consisting of four unrelated topics: Fourier Analysis, Divergent Series, Games Theory, and Inequalities.

Mary and I lived in an apartment in Slough that year (upstairs at 36 Cornwall Avenue, just found it using Google street view! It hasn't changed a bit. The weekly rent was £10, almost one half of my after-tax income.) We lived also on £10 a week, which included five daily return bus journeys to R.H.C. Mary taught French in a school on (I'm not making this up) 'Shaggy Calf Lane' (it's still there). A memorable question: Miss, my dad wants to know: why do we have to learn French?

Our daughter Marie was born in the Canadian Red Cross Memorial Hospital on Monday June 5th, 1972. I used to cycle out there from Slough, and leaving the hospital on the evening of the previous day I was assured that nothing was about to happen... But back in Slough (no phones to use) I just had an inkling, and cycled back out in the dark, just in time to see our beautiful daughter come into the world...

The following week I had an interview in University College Cork (I should add that I had only applied there reluctantly, as I had no great desire to return to Catholic Ireland, but, 'beggars cannot be choosers'). U.C.C. had advertised a lectureship, stating that the preferred candidate should have a research interest in Algebra, but that all applications would be considered. I (a number theorist, not an algebraist) had a friendly interview there, but days later I was informed that the post had been offered to an algebraist (Timothy Porter, if I remember correctly).

Now, on to Manchester:

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Expanding #4 above. 1972-74. Temporary lectureship in Pure Mathematics in the Mathematics department of Manchester University.

How did I get a job at Manchester University? Sometime in August 1972 - when I was coming to the end of my one-year temporary lectureship at R.H.C., and with no prospects on the horizon - there appeared an advertisement in the Times Higher Education Supplement (T.H.E.S., 1971-2008, now T.E.S.) for a one-year temporary lectureship in the Mathematics Department of Manchester University, I applied, and was called for an interview on the 5th/6th of September.

(Aside. Only subsequently did I hear why this post was being advertised so late in the day, with the academic year 1972-73 about to begin. A permanent member of staff had tendered a late resignation, and the university administration agreed to a one-year only replacement. Also subsequently I learned that there had been some ninety applicants (all with a Ph.D.), and that twelve were short-listed... I was one of the lucky twelve...)

There I had the best interview of my entire working life, and by that I do not mean that I gave the best account of myself, but rather that the interview board conducted themselves in the best possible way (as I'll explain). And what an interview board!: just the two most senior mathematicians in the department (interviewing for a mere one year appointment), Ian MacDonald, FRS and Professor Fritz Ursell, F.R.S.. (Now, that is professionalism, as the task could so easily have been undertaken by two less senior members of the department.)

After some initial general chit-chat (perhaps to set one at ease), they pointed out a board and chalk, and asked some mathematical questions (that had never happened before, nor subsequently): could I explain my work to them in simple terms, and then asked me to imagine I was half-way through a standard course on introductory Analysis: how would I explain the difference between a convergent series and a conditionally convergent series?

As I rose to leave, and was about to exit the room, I turned to them and said something like: well, I hope to see you again, but if not then I'm off to Sierra Leone. I intended that just as a throwaway remark, but it piqued their interest, and they asked me to explain what I meant... I told them that in recent weeks I had met a visiting Indian mathematician who was working there, and, knowing of my precarious job situation, told me that there were jobs a plenty there, and that if the worst came to the worst then I would easily get a job there... (Compare that Manchester interview with one I had in St. Mary's College, Twickenham, London; I've written about that one further down, in relation to my December 1975 Carysfort interview.)

They must have taken pity on me since the following day a letter arrived in Slough offering me the one year position, an offer that I accepted immediately. (Aside. Two days later a letter arrived from U.C.C.'s Mathematics department offering me a one-year appointment, and further informed me that they had been promised that in one year's time they would be allowed to appoint two new permanent posts, and assured me that one of those would be mine... . Decision to be made: would I accept their offer of what amounted there-and-then to a permanent job (and inform Manchester) or would I stick with the already-accepted Manchester temporary appointment? Mary agreed to my decision to take our chances with Manchester, and just hope that job opportunities would improve in England, where I wanted to stay. I wrote to U.C.C. to say...)

We journeyed up to Stockport later that month - I had found an ancient two-bedroom house there (11 Carmichael Street; it's still standing, and may be viewed using Google's little yellow man) - bought a bicycle (the one I had in Slought fell apart one day), and I used to cycle from there into the (18-19 storey) Mathematics building on Manchester's Oxford Road.

What kind of teaching was I required to do? Pretty basic, undemanding stuff it should be said: service courses for chemists, engineers, ... , some tutorials (Andy Baker was one of my students. Andy and Carole - his wife-to-be - had dinner out with us in Stockport on one occasion, and years later - while he was Reader in Glasgow - he acted for a three year period as external examiner when I was in charge of Mathematics at St. Patrick's College, Drumcondra.)

Although I wasn't required to do so, I nevertheless offered two advanced post-graduate courses: one on transcendental numbers, the other on Pisot-Vijayaraghavan (P.V.) numbers.

I began my transcendental numbers course with basic routine material (Liouville, Hermite, Lindemann), and the climax was presenting Gelfond's solution of Hilbert's renowned seventh problem (dear Ian MacDonald sat in on that, which pleased me greatly). People who are familiar with such things will know that in the full Hilbert problem the entities are complex numbers, and I don't know how well-known this might be, but Gelfond, together with Linnik, wrote a book called Elementary methods in analytic number theory, Moscow, 1964 (there's a 1964 review by Mordell in the Bulletin of the American Mathematical Society, and - as one may see - Chapter 12 deals with The transcendence of some classes of numbers, a chapter in which, and this was a revelation to me, they present a real variable solution to Hilbert's seventh problem in which the entiries are entirely real numbers... (Wow!!) When I read their presentation I came upon some thirty (?) typos/errors, and, tidying those up I presented their solution in my course (recently, tidying up our loft here ar home I came upon my hand-written notes that I gave out to those who attended... Now, some forty years later, who would be interested? ... Into the skip!

Before going to Manchester I had only had a vague idea as to what a P.V. number was, I wanted to know more, and so I studied Raphaël Salem's classic book - Algebraic numbers and Fourier analysis - and presented a course. Sadly that beautiful book has gone out of print, and I no longer have the Gelfond-Linnik, nor the Salem book (I gave them away to the T.C.D. student Mathematics Society).

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 (Will is on the left in the photograph on that page; books by Will). 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').

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Expanding #5 above. Oct. 1974 - Nov. 1975. Lecturer in Pure Mathematics at the Jos Campus of Ibadan University, Nigeria.

How did I get a lecturing post in Nigeria? It happened like this: in early June 1974 - with my temporary Lectureship in Manchester coming to an end that August - I received an unsolicited letter - page 1, page 2 - from the Deputy Registrar of Nigeria's Ibadan University offering me an appointment as lecturer in Mathematics at the Jos Campus of Ibadan University, and around the same time I received a letter from a Professor E.A. Ayandele (Principal of the Jos Campus of the University of Ibadan) telling me he was delighted that I wanted to go to Jos (I cannot find his letter as I write now, August 2023). The only job application I had still outstanding at that time was for a post in the Jomo Kenyatta University in Kenya, and - as I hadn't heard from them - then following a discussion with my wife Mary, we decided to accept Ibadan's offer (about three weeks later I was offered the job in Kenya - without even an interview - but I had already accepted the Nigerian offer... How differently life would have turned out if... )

(Here, just for the record, is the rather tacky Memorandum of my terms of appointment: page1a, page1b, page2a, page2b.)

In the following weeks our time was taken up with visiting Mary's parents in Plymouth, visiting my father in Ireland organising travel visas, getting the appropriate vaccinations for yellow fever etc, including - as it still existed - smallpox... By the time vaccinations were organised Mary was pregnant with our second child, which prevented her from having the smallpox vaccination, and it was so stamped into her passport (the understanding being that Mary would be vaccinated in Nigeria in the weeks after our child was born... this, as I'll later relate, had very serious consequences).

At that time we were almost entirely ignorant concerning Nigeria... of course we knew (everyone did) that there had been a recent brutal civil war in Nigeria, but apart from that we knew precious little else. We investigated Nigerian literature, especially through the historic Heinemann African Writers Series, and I bought many of those (which, subsequently, about to leave Jos at the end of November the following year, I donated to the Jos Campus Library, a library which, incidentally, didn't have a single one of them: Achebe, Soyinka, Ekwensi, Okigbo, ... )

Then everything happened in a rush. Having waited for weeks for visas to travel to Nigeria, we suddenly obtained them, along with air tickets for departure on Tuesday 15th October. We had to make arrangements to store what we weren't bringing with us, and pack up the rest for the delivery men. We flew from Stockport to London, and thence to (historic) Kano in Northern Nigeria.

Our arrival on the 16th of October, and our early days in Jos are perhaps best (though only partially) described in a letter I wrote to our friends Bob and Judy Sandling in Manchester - Bob circulated copies to people in the Mathematics Department - and some weeks after we left Nigeria (late November 1975) Bob presented me with copies of the nineteen letters I wrote.

That first letter was some six pages long, on paper larger than A4 size, and to upload here I had to scan each page twice, and then suitably crop into pages numbered 01a, 01b, 02a, 02b, ... , 06a, 06b.

Some - but not all - of the content letter's content needed extra commentary, so this is what I have done: uploaded part-page by part-page, and only commented if I felt the need:

Letter #1, 15th October 1974, page 1a.

Comment. We got off quite lightly, possibly because although we were European, we were clearly not well-off Europeans (one of our suitcases was held together with a bit of rope) and were clearly not cash-rich (what self-respecting customs officer would waste his time on squeezing a few pounds out of us?) The ones who got done were the returning Nigerians, with their expensive suits and solid baggage, their bags flung open and contents thrown all over the place...

One should read Africa correspondent Karl Maier's this house has fallen (NIGERIA IN CRISIS, Penguin, 2000) in which he recounts that, on his first visit to Nigeria in 1991, a customs officer seperated him from ₦1000 as the eventually agreed price for allowing Maier to bring into the country his work computer (the officer had initially requested ₦5000; the stark choice presented to Maier was: pay me the money or I will confiscate your computer.)

The following year we had a friend who was returning to England with her friend, and they had reserved seating on a Nigerian Airways (N.A.) flight. At Kano airport to collect their boarding passes, the N.A. checker indicated he would like to have a chat with them behind a screen, and there he put a simple, brutal choice to them: if you give me ₦150 - then worth about £75 perhaps, the ₦ still hadn't crashed, as it subsequently did - then I will give you the boarding cards, otherwise I won't. They didn't pay up and so missed their flight.

(Naive folk might well ask: why didn't they seek out someone who might have done something about this? It's very simple: they would have asked for more. Overnight, meeting others who has suffered the same fate, they went en masse to the N.A. desk and made it clear they would cause an uproar if... ; they were put on that day's flight to London.

Recently, in conversation with a Nigerian (I'll call hin 'A') who had become an Irish citizen, he related to me that on a visit to the Dublin Nigerian Embassy to make a routine enquiry, the official (I'll call him 'B') with whom he was dealing wrote down the account number of a U.S.A. bank and told A that when a sum of 150 U.S.A. dollars was paid into that account, he (B) would deal with A's (routine) enquiry. Stupidly I said: why didn't you go to the ambassador to report this fellow?, which brought this response: you must be joking! The ambassador would have looked for 300 U.S.A. dollars!)

Letter #1, page 1b.

Letter #1, page 2a.

Comment 1. That hotel - the Jos Plateau Hotel is still there (defying gravity!) - but now (August 2023) the cheapest room costs ₦2,875 per night (the Central Bank of Nigeria has an informative website about the history of the Nigerian currency, which is based on the Naira (₦), and it had this equivalence in January 1973: £1 = ₦2).

After breakfast on our first morning we were visited by David Rodney, a member of the Mathematics Dept., who had only arrived before us, and David filled me in on the Dept. It had a 'co-ordinator' (not a Head of Dept.) - one Habibullah (see below) - David himself, now me, and two others who would shortly arrive. David had a PhD from Keele University, and the two about-to-arrive were Walt Potter (PhD from Madison, Wisconsin) - David and Walt were both algebraists (group theorists) - and Amin Patani (Amin had a PhD from Imperial College, London, where Amin's supervisor was no less a person than the renowned Physics Nobel Laurate Abdus Salam).

Not long after Walt and Amin joined David and me, it was clear that we were the only ones committed to doing real work in the Department - Habibullah was completely detached from what was going on; he had absolutely no interest in making anything of the Department. We had to develop everything from scratch as the so-called Mathematics department down in Ibadan had given no thought whatever as to what ought to be taught to their students in Jos (in short: there were no course outlines, no syllabi; and good luck to anyone trying to find out nowadays (Oct. 2023) what Ibadan Mathematics staff teach their students...)

The four of us were naive enough to set as a target: make the Jos Mathematics department be the best in Nigeria.

I should add that although Ibadan University itself had established this Jos Campus of itself, and although the Mathematics Department in Ibadan had allowed this entirely unsuitable Habibullah character to be the 'Co-ordinator' of the Jos Campus Mathematics Department with the Ibadan Mathematics Department, they had given absolutely no thought whatever as to what should be taught to students in Jos. Thus when I met up with this Habibullah and asked what I was supposed to teach (Ye Gods! This so-called university writes to offer me a job without giving any thought whatever as to what I was supposed to do there... , what any of us were supposed to do...) he had nothing to say... Just teach the students something...

In fairness to Ibadan I should also say that when I left Jos, and was recruited at Carysfort College in Dublin... well, that's all further down.

Comment 2. My declaration that "₦14 is £10" was wide of the mark, and was based on the local bank (the Standard Bank of Nigeria) only giving me ₦28 when I tried changing a £20 note at its foreign exchange desk. In my ignorange the guy at the exchange desk blatantly robbed me. Since then the value of the Naira against Sterling has totally collapsed; the current (August 2023) quoted exchange rate is £1 = ₦1000 (yes, one thousand; in fact the actual quotation is ₦1 = £0.001000).

Letter #1, page 2b.

Letter #1, page 3a.

Comment. Re 'The Principal', the utterly reprehensible E.A. Ayandele; I could write a whole book about him... I'll have quite a bit to write about him below, but for the moment I'll stay with simply commenting on my initial letter.

Letter #1, page 3b.

Comment #1. Re '... we are now living... '. Of course we could not continue staying in that, or any other hotel (even though the university was paying); we would have been driven demented. Breakfast on the first morning took two-and-a-half hours, we had an active two-and-a-half year-old daughter (imagine trying to have her sit for that length of time at mealtimes), there was no public transport, and neither of us drove a car.

Concerning driving, all academic staff (Nigerian and expatriate), besides salary, were also given a car loan commensurate with salary. The loan was for a period of four/five years, which was paid for by deduction from salary, but that was counter-balanced with a monthly car allowance, one which - in practice - not only covered the deduction, but left ample over to pay for petrol/gas (IF one could buy petrol/gas...)

We only stayed in that hotel for perhaps another two/three nights, and then we moved into a university house by taking the law into our own hands, aided by Mustafar Habibullah (the Mathematics Department 'co-ordinator' with the main department down in Ibadan). How did this come about? It happened that on a site (then) just outside Jos - between the town's central (run-down) Campus and the building site that would eventually become the location of the new University of Jos, and just beyond an army baracks - on that site were twelve bungalows, six of which were occupied by government civil servants, and six owned by Jos Campus, only five of which were occupied at that time.

Habibullah and his wife and young daughter (a year older than ours) lived in one of those five, and just beside him was a single un-occupied one (on the other side of Habibullah's house lived Sonny Oti and his wife Gladys). Habibullah was mad keen for us to be living beside him, because, as he said, his daughter would be able to play with ours (he wasn't to know that our Marie would spend all her time playing with the Nigerian children in the other houses, and would after no time at all speak English with a definite Nigerian accent (I have recordings...))

Here are two photos of Marie (from May of the following year) with some of those friends, and Mary and Marie in the other two. To Marie's right in the photo in the upper left-hand corner was Marie's special friend Chi-Chi (an Ibo), while to Chi-Chi's right is another friend, Yewande (a Yoruba); both lived immediately across from us. From morning until night we hardly ever saw Marie, for as soon as she's had breakfast she was out the door to be with her Nigerian friends... all of their parents spoke English, but in the Ibo household they spoke Ibo, and in the Yoruba household Yoruba. Those parents told me that Marie showed understanding of what they said in their own language to their own children, and I often reflect that had our life path been that we remained there, then our Marie would have been fluent in Nigerian English (she already spoke English with a definite Nigerian accent, and used Nigerianisms like open de light - for 'switch on the light' - or close de light for 'switch off the light'), Ibo, Yoruba, (Hausa? ...)

After we left Nigeria (late November '75) and settled in Dublin (via Mary's parents in Plymouth), Marie said to me one day: us is not having beouffen? - her word for 'television' - and I said no, no, we are not going to have a television. Marie absorbed this and then said (by was of trying to make sense of why we didn't have, and weren't going to have one): us is not black people? How wonderful, a child's view of the world.

Comment #2. Re 'My neighbour is Mustafar Hab[b]ibullah...'. This character said he had a PhD from East Anglia University (E.A.U.), and his supervisor was a Nigerian mathematician in its department; Habibullah's route to Jos seems to have been from E.A.U. to Ibadan itself, and thence to the Jos Campus of I.U.

(Aside. When Ibadan set up an off-campus of itself in Jos this seems to be what happened: the vast majority of Ibadan staff were southern Nigerians, mainly Yorubas or Igbos (Ibos) - these, since colonial times, would have been mainly 'Christian' - who would not have felt at home in the 'middle belt' (where Jos is) or in the (mainly Muslim) North. How could Ibadan persuade some of those to move to Jos? Simple: offer promotions. A Junior Lecturer would be offered a Lectureship, a Lecturer would be offered a Senior Lectureship, etc. Habibullah moved from Ibadan to Jos, and Ayandele (who had held a 'Professorship' (how?!) in History in Ibadan) was tempted to move by being 'Principal' of the Jos Campus.)

Letter #1, page 4a.

Letter #1, page 4b.

Letter #1, page 5a.

Comment. Re 'I haven't driven a car...'. I had never owned a car (I may have inherited that from my parents), but an older sister did. When I was about sixteen she gave me some rudimentary lessons, and I obtained an Irish driver's licence without having to sit a test (those days have long gone). But, I imagine, I only ever drove for perhaps two hours (not the best preparation for driving in Nigeria!)

Letter #1, page 5b.

Comment. 'King's College' should have been 'Imperial College'.

Letter #1, page 6a.

Comment. Re 'I'll have to do something to get rid of him...' In fact he continued to park himself outside our house every night until we left at the end of the following year. He didn't have a word of English; he had a ritual: he would turn up just before sunset, use an outside tap to do his Islamic cleansing, then kneel on his mat pointing towards Mecca. Frequently Marie would join him (with a teddy bear wrapped around her back, in imitation of the way that local women carried their babies) and he regarded her with affection.

There used to be a local Fulani man who would come around selling bread - he too didn't have a word of English (all Nigerians who had some schooling did speak English). One day, in May '75, just after our daughter Catherine was born, we happened to be out on the road in front of our bungalow (47 Bauchi Road, I can't find it on the map) and when he saw Catherine his face lit up. By gesture Mary indicated that he could hold her - you would think we had offered him a fortune - and he held her declaring (my memory tells me it was something like adelaan, adelaan, ... , which someone told us meant wonderful, wonderful, ... ) over and over. A happy memory from Nigeria. (If only he could have been the Principal of the Jos Campus instead of the wretched Ayandele.)

Letter #1, page 6b.

I have eighteen other letters which I have scanned... I may just upload them all here (without commentary) when I have time, and only later add comments in dribs and drabs.

Letter #2, 5th Nov. 1974. single page.

Comment. The Pink was a local Manchester weekend newspaper that detailed the fortunes of the two big local soccer rivals - United and City - and I used to pour over it in my time there. It ceased publication in August 2000: The Pink slips into the sunset.

Letter #3, 14th Nov. 1974, page 1.

Comment. This letter mostly deals with my first visit to Kano airport to find our undelivered baggage... ; see letter #5 for a description of my second visit to same.

Letter #3, page 2.

Letter #3, page 3.

Letter #3, page 4.

Letter #3, page 5.

Letter #3, page 6.

Letter #3, page 7.

Letter #3, page 8.

Letter #3, page 9.

Letter #3, page 10.

An interlude between letters #3 and #4. There was much more going on in our lives - and in Nigeria generally - than I reported in letters.

Going to the bank. (John, who will believe this?) Incidentally, our bank in Nigeria was the Standard Bank of Nigeria (see Standard bank; Anthony Barber, was a Director). Before going to Nigeria I had the habit of going to the bank once a week to sign a cheque for £10, our housekeeping money for a whole week. Easie-peasie: I'd go into our bank, sign a cheque, hand it to the teller, he'd look at it and hand me £10. How long would that take? Less than a minute. Here, though, is what happened in Nigeria when I first attempted to cash a cheque for ₦20, our housekeeping money for a week: I approached a teller, handed him the cheque, and waited... Although I was the only customer he seemed in no particular hurry, perhaps he was engaged in some other matter... But after a half-an-hour of waiting, and no sign of him doing anything about it, I coughed into my hand to attract his attention... He looked up, and I asked if he would kindly give me my requested ₦20.

(Before going out to Nigeria I read what I could about it, and there was one memorable, but puzzling, item I came upon about illnesses in West Africa amongst Europeans: I read that mental illness was the most common... . Mental illness?! Surely one couldn't contact mental illness?! After some time in Nigeria I began to see how that could happen.)

My teller looked down again at what was engaging him (the sports page in the newspaper?), and I waited and waited... . Again, after perhaps another half-an-hour, I ... , and this time he took my cheque and went to some room behind him (where, I supposed, the money might be stored), and after some consideralbe time he emerged... , but, without any sign of my ₦20. ... . I assumed that what was going on was this: his job was just to take my cheque into some room, and there hand it to someone else, whose job might have been to bring out the money... . Wrong, John, wrong.

This went on/off for a full two-and-a-half hours, when I finally got my money. Relating this to some people in a local hotel the response was: John, you don't understand... this chap would expect you to have offered him something for you to get your money immediately. How much? Ten-per-cent of what you wanted. What!? Ten-per-cent!! You must be joking. No, John, if you want to get in and out of the bank quickly that's what you'll have to do. I'm damned if I'm going to give some bloke one tenth of our weekly shopping budget just to cash a cheque...

So, what did I do from that point onwards? I decided I'd only try to cash a cheque once a month, bring some books with me, and that's how I came to read so much Tolstoy and Dostoevsky in that year.

Letter #4, 20th Jan. 1975, page 1.

Comment. Mary and Marie both unwell.

Letter #4, page 2.

Comment. Reference to 'army on alert'.

Note. When I looked at letter #5 (which details a second visit to Kano airport; see letter #3 for the first visit) I could see that quite a bit of the writing had faded and the scan quality was very poor. I tried to got over it with a pen to make it clearer... hence the rather patchy appearance. I also had to do this with some subsequent letters.

Letter #5, 28th Jan. 1975, page 1a.

Comment. This letter mostly deals with my second visit to Kano airport to successfully find the remainder of our undelivered baggage.

Letter #5, page 1b.

Letter #5, page 2a.

Letter #5, page 2b.

Letter #5, page 3a.

Letter #5, page 3b.

Letter #6, 7th Feb. 1975. single page.

Comment. I am surprised that I didn't give details of the 'boring meeting', since it was the one in which the ignoramus Principal Ayandele subjected us to a research homily, one that demonstrates this Ayandele's arrogance, ignorance/stupidity.

On that Saturday 1st. February '75 Ayandele summoned all the campus academic staff (Mathematics, Classics, History, Geography, Biology, Religious Studies, ... ) to subjected to his ignorant analysis of what was involved in doing research work (he must have just read something in the latest issue of the Reader's Digest). I can clearly recall his advice to historians (he considered himself to be one) and mathematicians.

His homily to historians: To do historical research all you need do is find a good story that no one has ever written about, and, well, write it up. I'll give you an example: take the well-known George Bernard Shaw (that made me sit up and pay attention, for up until then I had been listening to the BBC football broadcast through an earphone up the sleeve of my shirt, and communicating scores to my mathematician friend David Rodney who was sitting a few rows in front of me)... everyone thinks he was a socialist and a non-religious person, but not many people know that when he was dying he had some rosary beads in a desk by his bedside. Now, there you are, all you have to do is write that up and you've done some history research.

(Ye Gods! It's impossible to imagine anyone saying anything so palpably stupid... Well, perhaps not impossible, as there's something even more foolish coming up:)

His homily to us mathematicians: Everyone has heard about Einstein and his famous equation "E equals m c squared" - (that's E = mc2) - well, all you have to do, to do mathematical research, is just make up another equation and write it all up.

Did this Ayandele chap really think that he was helping us? Our weakest student in Jos would have had more brain power than Ayandele. I recall David turning back to look at me, and the expression on his face read what the !?!?. (This is a family values website.)

Letter #7, 2nd April 1975, page 1.

Comment. Re "... we have 13 vacancies [in Mathematics] for next year..." and - continuing into page 2 - "The Ibadan registrar was given an advert. on Jan. 5th and has done nothing about it which has made us pretty mad - hence we've taken our own action (with blessing of Jos Campus Principal)."

By the end of '74 we (David, Walt, Amin and myself) had had enough of the useless Habibullah and sought a meeting with Ayandele (although we knew he was stupid in the extreme, we gave him the credit of thinking that he was ambitious - indeed he has, but not in the way we naively believed! - and would want to make something of the Jos Campus), a meeting in which we expressed our dissatisfaction with Habibullah, and outlined our ambitions for the Department. Oh, Ayandele was so thrilled with our enthusiasm, and asked us to bear with the situation as he too had great plans for Jos... in Mathematics, by October '75, we would have thirteen (so precise!) new staff: Professors, Senior Lecturers, ... you name it, we would have it!! (how could we have been so foolish/stupid to take him at his word?!) An advertisement would be placed anywhere and everywhere by the Ibadan registrar...

Letter #7, page 2.

Comment. In the second page of this letter I wrote: Some time ago I bumped into [a] wonderful girl who used to be at univ. [Royal Holloway College] with Mary & I [oops! me]. This is [the] best thing to have happened since coming here.

That wonderful girl was Clare Williams, and she did her degree in English in the year below us at Royal Holloway. I had known her but slightly as she was friendly with some of my fellow mathematicians; a happy memory is of her playing darts in the room opposite mine in the Kingswood hall of residence (her sight was so poor she was more likely to hit the door than the darts board).

One day in February/March '75, driving from where we lived on the Bauchi Road into what was then the main location of the Jos campus, I just happened to stop at a garage where I never been before...

Standing in the garage forecourt was an unmissable young woman (the only non-Nigerian) wearing dark glasses... and then I heard: John!, John Cosgrave!, ah, Clare! Clare Williams! What are you going here!? And what are you doing here!? It was a beautiful moment, one of the most memorable in my life. We exchanged our stories, and Clare's was that she was teaching in a remote bush school somewhere further north, and - on a school break - just happened to be passing through Jos, stopping to fill up on petrol... We headed back to our home on the Bauchi Road to meet Mary, invited Clare to stay, but she was committed to being elsewhere, though she stayed with us when returning to her school. And a friendship developed.

Jumping ahead with our life in Nigeria, we left (or rather escaped) Nigeria at the end of that year, and I started working in a new place in early January '76, and I must have written to Clare in December '75 or early January '76 to tell her about how this happened, for she wrote to us on January 17th '76 - here is the last page of that letter.

It is especially poignant to re-read (now, Sept. 2023) Clare's And what of Marie? [Our Marie was only two years and nine months old when Clare first set eyes on her.] It's a whole new world for her, eh, --- all those lovely Yorubaisms will all be lost and forgotten. Give her our greetings.

A note on Marie's Nigerian English. In early 1976, finding myself working in Carysfort College, and having a colleague who had taught Latin in a girl's school in Jos before our time there, I brought in a cassette recording for this colleague to hear that I had made in Nigeria of Marie declaming some nursery rhymes (twinkle, twinkle little star...). I said only that it was a recording I had made while in Nigeria. My colleague's comment: ah, those Nigerian children were so lovely...

Whatever happened to Clare? I have three letters and two cards that Clare wrote to us: her first letter of Jan. '76, a second from May '76, and the third from July '79; her first card from Dec. '76, the second from Dec. '77. She was very fond of our Marie, and in that card of Dec. '76 - home in England from Nigeria, but returning there - she wrote Ah well, na so did worl' be (as Marie would say), and in her second card she wrote that she was permanently back in England, and about to start a new teaching job in London in Jan. '78.

I met up with Clare in London in Dec. '79 (I had been at a Mathematics meeting in Cambridge), she was about to move north, address as yet unknown, but would let us know as soon as she found somewhere... We never heard from Clare again and at first we made nothing of it, but as the months and then the years passed, we feared the worst.

No one from College who knew her had any news whatever about her. We did hear that she was related to Michael Williams, husband of Judi Dench. Clare was a ray of sunshine.

Letter #8, 16th April 1975. single page.

Letter #9, 13th May. 1975. single page.

Comment. Reporting birth of daughter Catherine on 30th April. When we did - eventually - get four copies (all different, only one correct) of Catherine's birth certificate, the tribe of her father was given as being Irish, while the tribe of her mother was given as being English.

In later years I worried Catherine by telling her that I had contemplated calling her Carla Frederika, after the great German mathematician Carl Frederik Gauss, whose birthday also fell on 30th. April.

Aside. Years later - between 2007/8 and 2015 - my German colleague/friend Karl Dilcher and I published ten papers (see here), seven of which were on the topic Gauss factorials (so named by us), and we also named in his honour a new class of prime numbers as being Gauss primes (paper #8 at the above publications page).

Letter #10A, 9th June 1975, page 1.

Letter #10A, page 2.

Letter #10B, 9th June 1975, page 1.

Letter #10B, page 2.

Letter #11, Started 4th Aug. 1975, continued on 5th, page 1a.

Comment. Re "when along came this coup". There is an account of the background to that coup here and (continued) here. The frontman for the coup (named in this letter), was a Col. (later General) Joseph Garba . I had a cassette recorder at the time and I recorded his radio address (I still have it somewhere) on Nigerian radio. To me it was interesting that Nigerians I knew simply didn't trust their own broadcasting station for news, instead tuning into the BBC World Service.

Letter #11, page 1b.

Letter #11, page 2a.

Letter #11, page 2b.

Letter #11, page 3a.

Letter #11, page 3b.

Letter #11, page 4a.

Letter #11, page 4b.

Letter #12, 14th Sept. 1975, page 1.

Comment. Re "I've decided to leave here next year for two reasons..." At the time I wrote that I really did think that it would be the following year when we would (indeed could) leave. It wasn't realistic to leave at the time I wrote letter #12, as I had no job prospects back in England (and Ireland didn't seem a possibility...).

Letter #12, page 2.

Comment 1. Re "Mary has had to go into hospital (since Frid. 5th Sept.) as she has acute hepatitis (jaundice)..." Mary was pregnant when we were leaving Manchester for Nigeria, was disallowed having the mandatory smallpox vaccination before travel, but the understanding was that some three months minimum after our child (Catherine) was born, she would then be vaccinated against it. (Only in May 1980 did the WHA declared that smallpox had been eradicated.) Mary's great misfortune was that the reliable hospital (two Irish nuns, two German doctors) in which Catherine was born did not have a license to administer smallpox vaccinations, rather she had to go to a Nigerian government institution to obtain it...

Within days of being there vaccinated Mary went down with acute hepatitis... It was a Nigerian neighbour (Gladys, the wife of Sonny Oti, whom I knew, a colleague in the Jos Campus) who filled us in what would have happened: the person doing the vaccination would have pocketed the phial - to sell on the black market - and just injected some rubbish with a dirty needle...

Gentle reader (if I have any): can you get it into your brain, that some Nigerian imbecile would knowingly put my wife's health/life at risk simply because he wanted to sell a vaccination on the black market to make a few nairas?

Comment 2. Re "I have started to write around again to make job enquiries - I've written to two places in Ireland..." I wrote (what must have been a grovelling letter) to U.C.C. perhaps saying I regretted that I didn't take up their offer of a permanent job there in Sept. '72, and if anything came up again to please let me know... , and I also wrote to Ted Hurley in University College Dublin (U.C.D.) - Ted and I did our Ph.D.s in London at the same time, and he was the only mathematician I knew in Ireland - to ask if he would let me know of any job opportunities should they crop up there.

U.C.C. wrote back to say there was nothing there at that time, but they would keep me informed of any job vacancies (and, true to their word, they let me know of the post in Carysfort College weeks later; it may have been Finbarr Holland who wrote to me), and then - something that seemed like a miracle at the time - see page one of the next letter #13.

Letter #13, 1st Oct. 1975, page 1.

Comment 1. Re "You've probably seen the letters I wrote to Jeff [Paris] and Nige [Ray] since I last wrote to you [14th Sept., Letter #12]. The Dublin job has fallen through. I got a letter from U.C.D. on Sept. 18th. saying..."

On Sept. 18th. I received a letter from a Professor J. R. Timoney - the (then) Head of Mathematics in U.C.D. - informing me that as a result of my recent letter to Ted Hurley, they had had a meeting in the Department, and had decided to offer me a one year Lecturship in Mathematics, to start from the 1st of October (!!), and that once I was there they would take steps to ensure that my post would eventually be a permanent one. (There was a background: U.C.D. had just appointed a new Professor of Mathematics (who would become the HoD when Timoney retired) - Don McQuillan, a number theorist, like myself - and he wanted to have a number theorist working there.)

It is impossible to recall the utter joy I/we felt on receipt of Timoney's letter on 18th Sept... I rushed into see Mary in the hospital (we've been saved...). Of course I gave no thought as to how we could get out of Nigeria, no thought to how we could afford to pay for air fares etc, but the very fact that Dublin seemed within our grasp made all of these relatively minor worries seem utterly insignificant. I also thought that in the circumstances - especially with Mary still being in hospital - Timoney would extend the 1st of October deadline (surely U.C.D. could manage without me for just a little longer?)

Comment 2. Re "Yesterday [30th Sept.] I got the reply from U.C.D. saying "sorry, has to be October 1st". " I don't care to recall the pain this caused us at the time. It must have been terrible for my father to have heard from me something like "Dad, we're getting out of here! I've got a job in U.C.D. ...", and then later to hear from me that...

Comment 3. Re "I've already handed in my letter [26th Sept.] of resignation... ."

Here (page 1a), continued (page 1b), and here (page 2) was my letter.

Comment 4. Re "There are only four of us here and three years of students to teach! " Amin Patani had left, having been offered a research post at the (Abdus Salam) International Centre for Theoretical Physics in Trieste.

Letter #13, page 2.

Letter #14, 17th Oct. 1975, page 1.

Comment 1. Re "Yesterday [16th October], I got a reply to my letter of resignation from Ayandele..., and here it is."

Comment 2. Re "What a bastard! This Ayandele fellow is leaving here next month ... [all the way down to] were grinning from ear to ear!" The departure of this toad and the imminent arrival of his replacement proved to be the best thing that could have happened for us - THANKS to the military folk who promoted this Ayandele! You did us a great service! Though Jos's gain was Calabar's loss!

The "Ibo man from Nsukka" turned out to be a decent individual, the admirable Professor Gilbert Onuaguluchi, of whom more shortly.

Letter #14, page 2.

Comment 1. Re "Just when Mary will come home is not certain yet... . " In fact Mary was discharged from hospital later that very day, after I had posted this letter #14. When Mary was discharged she appeared to be on the mend, though shortly afterwards she rapidly deteriorated and it became imperative that we leave. (It did, however, provide Ayandele with one last opportunity to prove beyond reasonable doubt that he was an A1 reprehensible scumbag. Details later.)

Comment 2. Re "Pete Lambert is up here for this term..." Peter Lambert was an English mathematician (a Group theorist, like David and Walter) who had been in the Mathematics Dept. of Ibadan ('72-'76). In fact it was because of him that I ended up in Jos: when I was coming to the end of my two years in Manchester ('72-'74) my friend Bob Sandling (also a Group theorist) told me that he had heard from a Peter Lambert in Ibadan who wanted to exchange for a year with someone in Manchester... I had to remind Bob that I didn't have a post to exchange, and thought that was the end of it... But now it is clear to me what must have happened: Lambert must surely have mentioned me in Ibadan and...

Letter #15, 23rd Oct. 1975, page 1.

Comment 1. Re "The Principal in co-operation with... and I'm refusing." On 20th Oct. (see Letter #16) I received a puzzling letter from Habibullah telling me that the Principal wanted me to teach an extra course, and Habibullah asked me to teach - in that first term - a course on 'conformal maps etc'. I write 'puzzling', because I failed to see what interest this Ayandele character would have in what I (or indeed anyone else) would teach, and I was just too taken up with life to see the wood for the trees. I wrote to Habibullah to tell him what to do with his request, but he told me that Ayandele was insisting, his status was offended by my letter of resignation, for I appeared to insinuate that he - Ayandele - was a liar, and he (A.) wanted me to apologise. I told Habibullah to get stuffed, he could teach this course... (Actually this course couldn't possibly be taught in the first term to first year students, as any serious mathematician would know, and Habibullah certainly wasn't one of those.)

Letter #15, page 2.

Comment. This letter of 23rd Oct. was already posted before events of that same day happened, as set out in Letter #16 of the following day.

Now, things began to move quite quickly!:

Letter #16, 24th Oct. 1975, page 1.

Comment. Re "(5) 23rd Oct. In Habibullah's office... " On that day, sitting in my office, I was visited my two students whom I had never seen before, and they told me that Dr. Habibullah had sent them to arrange with me the details of the (new, extra) course that I was to teach them. I told them there was some mistake, and I went along to H.'s office to give him a bit of my mind... A fracas ensued, and Pete(r) Lambert had to rush in to defuse the situation...

I went home where I found Mary conversing with our friend Helen Potter... Why was I back home so early? They were soon to discover why:

A whole fleet of Campus cars pulled up outside our house... (and there really was a person with the title Acting Acting Assistant Registrar!) They had had a report of an incident involving Habibullah and myself, and they wanted to hear my side of the story, and they all agreed that Ayandele shouldn't have done what he did, Habibullah shouldn't have done what he did, they listened with real sympathy (I was impressed, and indeed still am).

Letter #16, page 2.

Comment 1. Re "Since starting this letter I've had a visit from Pete Lambert, who rang the [Ibadan university] Vice-Chancellor [at that time a man called Orishejolomi Thomas, who only continued as V.C. until December '75] last night and also the Registrar [a man called Sam Okuku] (here in Nigeria this is a man of importance) this afternoon. They say that Ayandele was wrong to refuse me my request to leave and they are over-ruling him, I am not being sacked as I was severely provoked; the Registrar is coming up here on next weekend [he didn't] and will give me air tickets, baggage allowance, F.S.S.U. policy, pay to end of December - we can leave at any time, and this we will do as soon as Mary can travel...."

Well, this was all good news, music to our ears.

But in the meantime I was still under Ayandele's whim... A deputation went to talk with him: my colleagues (without Habibullah, of course) and a wonderful classicist called Professor White (I believe he came out of retirement from the UK University of Reading to set up Classics in Jos; he was an old-school proper gentleman). With them he shed all pretence at being civilised and told them that if Cosgrave didn't apologise for calling him a liar then he would call up his friend the Chief of Police and have Cosgrave cast out of the country. But, but, but, his wife is seriously ill... Well then, he would have her wrapped up in a blanket and thrown out with Cosgrave.

Comment 2. Re "They say the new man coming here is quite different from Ayandele." That was an understatement, for Ayandele's successor - Professor Gilbert Onuaguluchi - was a decent human being, as I'll detail soon.

Letter #17, 25th Oct. 1975, single page.

Letter #18, [Wed.] 29th Oct. 1975, page 1a.

Comment. It comes as something of a surprise all these years later (Sept. 2023) to read that as late as 29th Oct. '75 I still held out hopes for U.C.D. ... I must have been completely naive.

Re I still haven't had a reply: I never received a reply, and when I met up with Timoney the following year - after I started working in Carysfort College - he never made any reference to what had passed between us at the end of '75...

Letter #18, page 1b.

Comment. Re "Ayandele hasn't left here yet; he's in the bush at the moment and gets back here on Friday [31st. Nov.] (same day as the Ibadan Registrar [Okuku] comes up here to sort things out) but leaves early November) - Okuku didn't honour his word, and one might wonder why... was it because he saw Ayandele's star in the ascendent with the (wretched) Military? - ... and if all goes well we could leave here this day four weeks from now - which would be Wednesday 26th November (which turned out to be the very day we left!) - (it all depends on the results of Mary's blood tests on Nov. 22nd-23rd.)"

So, Ayandele was still with us, and there there continued to be no appearance by Okuku, the Ibadan Registrar...

Letter #19, [Wed.] 12th Nov. 1975, page 1a.

Comment 1. The 'College of Education' was Carysfort College.

Comment 2. Re "The situation is now very complicated. As nothing has been happening here since Ayandele returned (apart from his making threats of deportation against me - what a story, tell you when we see you) we (Pete lambert and I) rang thro' to Ibadan last night to the Registrar (who had given Pete his word on Oct. 25th that we could leave here when we wished etc. - as I told you in the last letter) to ask what the hell was supposed to be happening " CONTINUES INTO PAGE 1b:

Letter #19, page 1b.

"...what the hell was supposed to be happening. He [Okuku] said it was now in Ayandele's hands completely and they (in Ibadan) were now awaiting a report from Ayan.[dele] before making a decision."

The Ibadan Registrar obviously didn't appreciate that I was an employee of his own university, and so honouring his word should not have depended on awaiting a report from Ayandele... , but that's all water under the bridge.

Comment. Re "So late last night [Tues. 11th Nov.] Pete, Dave and Wally called on Him in his house to ask what was he doing to facilitate our leaving here and his answer was "nothing"."

At that point, Wed.12th Nov., our hopes to "be in Manchester from Nov. 26th to ..." didn't look possible...

And then, all of a sudden, Ayandele vanished. Oh joy of joys! Did he leave that day, or the following day, or...? I do not know, but, once the word went round that the new Principal had arrived, I arranged to speak with him, and it's to his eternal credit that he agreed to grant me a meeting so soon after his arrival (when he must have had so many other matters to see to).

I can recall the details of our brief encounter as if it was yesterday: I'm John Cosgrave, a member of the Mathematics Department, and you may or may not have heard something of me from the previous Principal. Indeed he had, a lengthy report on me had been left by him, but he - this wonderful human being, one Professor Gilbert Onuaguluchi - had absolutely no interest whatever in reading it, all that he cared about was the fact that my wife was seriously ill, and he wanted her to be able to leave at the earliest opportunity. Heavens, I was actually talking to a decent human being!!

He told me to go to the Bursar and tell him to make arrangements re flights etc, and that I promptly did.

Down in the Bursar's office I explained all of this to him, but he immediately started saying there were procedures to be followed, there was this, there was that, there was the other, blah, blah, blah. Then - oh what a happy moment! - the Bursar's phone rang, he answered, and his face just changed... Yes Sir, he's with me at the moment, I'm going to see to all of that immediately, yes, yes, I'll see to that ... This marvellous human being - this Gilbert Onuaguluchi - knew what I would have to face with the Bursar, and ensured that the Bursar did what he was told to do.

The following days were a blur - so much to do before leaving - and on Wednesday 26th November we headed out to Jos airport, accompanied by our friend David Rodney, for the internal flight to Kano. I had never bribed anyone in Nigeria, but I did think that if asked for a bribe at the check-in desk I would reluctantly pay anything just to get out of that place...

I wasn't asked for a penny, the staff were courteous in the extreme, we got our boarding passes, smiles all round, and when I related this to David he enlightened me: we were flying out with British Caledonian, not Nigeria Airways, the latter renowned for corruption. Our flight was called, we took our leave of David, headed out to the tarmac and up the steps to the plane... Announcement: the flight has been delayed because of...

Traipsing back towards the airport I noticed David standing there... Why are you still here? David said he had promised himself he would not leave until he saw our plane up in the sky... Thank you David! Eventually we did take off; bliss.

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Interlude between leaving Nigeria and ... Dublin. Leaving Nigeria (wearing Summer clothing as we were ill-prepared to leave) on Wed. 26th Nov. '75 (oh happy days!) we arrived at Gatwick in a very cold London, but the relief of finding things that worked: waived through customs/immigration without looking for a bribe, a phone I could pick up and immediately get through to a nearby hotel, book a room for the night, have someone pick us up to bring us to our hotel, register without difficulty, ... a phone in our room that worked. A quick call to Mary's parents in Plymouth to let them know we were safely back - imagine their relief! - and that we would be on a train to them the following day; I also phoned Bob Sandling in Manchester to let him know, and he had some good news for me: I was being called for interview for the lectureship in Carysfort the following week (phew! so we just made it out of Nigeria in time!). My father, not having a phone, so I phoned my sister Kitty/Kay (Ballyjamesduff 11; those were the days).

Mary's parents had the joy of seeing their new grand-daughter Catherine - not to mention Mary and Marie - and those first days were pure bliss. I made arrangements to fly to Dublin the following Tues. 2nd. Dec. - meeting up with my father and staying in a hotel on Kildare Street, before making my way out to Carysfort College the following morning for my interview.

My interview. Despite my application giving all my personal details (schools I'd attended - all Catholic - etc), before entering the interview room I was given a form to complete: name, ... , religion, ... This religion business set off alarm bells in my head, and I'll divert to explain why:

Diversion. While still holding my temporary position in Manchester I applied for a permanent post in a place called St. Mary's College (Strawberry Hill, Twickenham), a (Catholic) College of Education, and one in which my brother Aidan had trained - in the 1950s - to be a secondary teacher. I applied there on foot of the college introducing a university level programme in Mathematics (one evidently sanctioned by London University), and the college needed new staff to deliver such courses.

My St. Mary's interview was initially no more than a fireside chat, the five-member interview panel was headed by father someone-or-other (the college principal/head), two men to his left (evidently from the mathematics contingent; they didn't ask me a single mathematical question), together with some woman (X, for reference), and some other man. The chat was all about where I was from, where I'd gone to school, that my brother Aidan had been a student there in the 50s - all of which would have alluded to my Catholic background, so that was well established.

X wondered if I had any other interests besides Mathematics... of course I did: music, reading, ... . She said she was a historian, and wondered if I had any interest in History (now, that's a big subject!), and if I'd read any history books of late. Indeed I had, I'd just been reading E.H. Carr's What is History?, and it was clear she'd never heard of him (a historian of some considerable reputation), so - as they say - we moved quickly along... I don't recall anything that the fifth panel member asked.

And then came the crunch question: one of the two mathematics men shifted uncomfortably in his seat and said (you couldn't possibly make this up!) now, Doctor Cosgrave, we all know that there is no such thing as Catholic and non-Catholic Mathematics - that must surely be one of the most stupid things ever said by anyone (where is he now?) - and while we don't insist that everyone employed here be a Catholic - there's a Muslim working here - we would like to feel that everyone employed here is sympathetic to the broad outlines of Catholic education [pause], can we assume that you are such a person?

I replied that no, he couldn't assume that at all. This was followed by a deathly silence, broken only by a light-hearted comment from father so-and-so: well, Doctor Cosgrave, when we get you here we'll work on that. I, in my turn (and stupidly thinking that I had the job in the bag) replied in a similar light-hearted vein: well, we'll see about that. Ha, ha, ha, laughs all round.

The following day, back in Stockport, I received a letter thanking me for attending interview, but informing me that the post had been offered to a mister so-and-so, and even went so far as to say that he had a master's degree from Huddersfield Polytechnic. [end of Diversion]

A return to my Carysfort interview. I had this pre-interview form to complete, and the 'religion' request presented me with a dilemma: I imagined that if I wrote something like this is my own private business... then I was doomed, and I certainly wasn't going to lie and write Catholic (for although brought up as one - no choice, youngsters don't have choices - I most certainly wasn't one (by choice), but now my years at school in England came to my rescue: before going there I only knew the term Catholic (and, of course non-Catholic), but at school in England I learned that they were Roman Catholics (RC's), and on my Carysfort form I wrote 'RC', telling myself that if they asked me about this I would say Rational Convictions... Fortunately the topic didn't come up... (What would I have told her - Sister R. - if she had asked? Well, I would have told her; I wasn't to know at the time that she and I would have some run-ins... But that all lies ahead.) (Actually I don't have anything at all like 'rational convictions'; indeed I feel uncomfortable about words like rational (except if applied to 'rational numbers'), logical, ... I absolutely hate it when people say things like being a mathematician you must be very logical...)

The interview panel consisted of five people: Sister Regina (the college's president), Sister Casimir (a gentle, kindly soul, the then Head of the Education Department; she had previously been the college's President, but was removed from that post - appointees were chosen by the Catholic Archbishop of Dublin - by the (wretched) Dermot Ryan), Professor Don McQuillan (U.C.D.), Dr. Tom Laffey (U.C.D.), and a Mr. Brian McEvoy (the sole member of the College's Mathematics Department, but with absolutely no university teaching background; how he came to be recruited to launch a university level Mathematics programme is a mystery).

The interview itself was a complete blur - I was still in recovery mode from having just made it out of Nigeria - they must have asked me about my recent past life, my only firm memory is of Sister Casimir's kindly smile. (Later, when I took up my post in the college I learned something of its recent past: there had been a student strike, Sr. Casimir was President at the time (the strike wasn't against her, but against the system), and when the strike was resolved this Dermot Ryan character fired her as she was considered to kind to students... a colleague told me she was in tears, wondering what would her parents think of her, the shame of being fired... .

A few days later - back with my family in Plymouth - I got the good news: I was offered the post (and of course my father - in Ireland - was delighted.

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Expanding #6 above. 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 [an 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").

Background to my employment as a Mathematics lecturer in Carysfort College. Up until the summer of 1974, students who studied in the teacher training colleges - of which Carysfort was one - followed a two-year course of studies which prepared them to teach all subjects in primary/elementary schools (i.e., children aged roughly 4 to 12). There had been a difference in salaries between primary and secondary/highschool teachers, traditionally justified by the latter having a three-year university degree (as opposed to a teacher training two-year diploma).

I understand that for some time the Irish National Teachers Organisation (I.N.T.O.) had been pressing for a three-year degree programme for primary teachers to justify equality of salaries, and the government and universities agreed on this, the universities stipulating that there would have to be a considerable increase in the so-called academic content of the agreed Bachelor of Education (B.Ed.) programme. The B.Ed. degree was launched in the year 1974-75, with academic subjects Mathematics, Music, Irish, English, French, History and Geography, and typically a B.Ed. student would (besides all the regular education subjects - History, Philosophy, Sociology of Education - and the methodologies of teaching all the primary school subjects) would choose two of those subjects to study in their first year, and then drop one of them for their final two years. While the other two major teaching training colleges offered Mathematics from 1974, Carysfort - uniquely - didn't offer it as a subject choice (on the grounds that girls wouldn't want to study Mathematics, wouldn't be good enough to study it) until the following year, starting in September 1975.

Students didn't know until they went up to College which two academic subjects they would choose, and this is what would happen: each department would make a presentation to possibly interested students, and try to sell - as it were - their subject. Students then made their choices...

Brian McEvoy had been recruited (in the summer of '75?) and you would indeed buy a second-hand car from him, he must have made Mathematics out to be such a wonderful subject that some 96 (out of 300, I think) students opted for Mathematics. He couldn't possibly cope with those numbers on his own, and so it was decided to recruit a second person in Mathematics... [end of Background]

Arriving in Dublin and starting work in Carysfort. I arrived on my own in Dublin on New Year's Eve ('75->'76) and stayed with Dermot Fleming (Dermot had taught in my father's school in Bailieboro for a couple of years from '64, and I first met him when I went home from boarding school an Crristmas '64) and his family for a few nights while I looked for somewhere for us to live. I knew absolutely nothing about the geography of Dublin, and I wanted somewhere to be not far away from where I was going to work (Carysfort College on Carysfort Avenue, Blackrock). As it was, I just had to take whatever I could find, and ended up renting a small house for six months in Ballinteer.

Mary and our girls arrived on Monday the 5th of January 1976, my 30th birthday, the best present I could have had. Mary was still poorly, but recovering. (Mary, Blackrock seafront, Dublin, Summer 1976, our first summer back in Ireland.)

I had got used to driving in Nigeria (there was no other safe choice there), and would have bought a car here but simply didn't have the money to do so (those were the days when it wouldn't have occurred to go to a bank and ask for a loan). Ibadan University did me a favour by cheating me out of monies owed to me, and I ended up buying a bicycle on which I cycled from Ballinteer to Blackrock every day: from Superquinn in Ballinteer to Marlay Park, then left up to Lamb Doyles pub in Sandyford, and from there downhill to Newtownpark Avenue, and left into Carysfort Avenue. In those days it was essentially traffic-free country roads all the way, not like now... (Sept. 2023)

My work in Carysfort college commenced on the Monday following Mary's arrival (the college was closed until that very day, the 12th, and I had no meetings with McEvoy until then). That was when I discovered that the College shared much with Ibadan University and its Jos Campus: a university level programme in Mathematics had been insisted upon by U.C.D. as a quid pro quo for the B.Ed. (N.U.I.) degree, but nobody - absolutely nobody - had invested any thought as to what would be taught in the Mathematics programme. No syllabus, nothing. So, what will I teach the students? Whatever you like. How about I teach them some Analysis? Yes, do that...

So, off I went to teach ninety-six students some Analysis, but where to start? (And they were divided into eight groups of twelve for tutorials - a classic thing to do, assign homework, grade it, meet to discuss solutions, ... ). And, fearful that I wouldn't be sufficiently occupied, I was asked to take the entire student body of all second and third year students - not just those who were studying Mathematics as one of their academic subjects - and break them up into groups of thirty (each of those thrity once per fortnight), and teach them something... . But what? Whatever I liked... (I used to give them puzzle problems to think about, e.g., suppose you have twelve identical coins - eleven of which weigh exactly the same, but the twelfth is just slightly off (above or below) - how many weighing do you need using a simple balance to determine the nature of the twelfth coin? It soon became clear that thinking was not something they had encountered in school. Little has changed over the years.)

I made a terrible mistake in starting my teaching of Analysis... I began with Dedekind cuts... (for mathematicians: yes, I know, that was a poor starting point...) and after a week McEvoy asked me to come and see him. The students had (rightly) been complaining to him about me: they hadn't a clue what I was talking about, and he wanted


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 here.

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.)

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 bizarre 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 Carysfort 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 here).

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Expanding #7 above. 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.

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 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 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, and then he 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. Our papers are here.

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