Walter Ledermann: Encounters of a Mathematician

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(Sussex: 1962-97 )

Manchester: 1946-62

I had always been attracted by Manchester, a place of intellectual excellence and the home of the famous Hallé Orchestra. During the war, the Mathematics Department at Manchester University was small; but it included some renowned scholars. The Head of Department was I. J. Mordell, a distinguished mathematician, who, unfortunately, was of a rather selfish disposition. On a war-time visit to Manchester I asked Mordell whether there was any prospect of employment for me and he offered me the position of Lecture Assistant explaining that my duties would be to take over his lectures when he was away, also to keep lists and attendance records of his students (he hated administration) and, if the need should arise, go to his home for a stint of baby-sitting. I decided that it would be better for me to stay at St Andrews.

Soon after the war Mordell left Manchester to take up a senior post at Cambridge, and the Mathematics Department at Manchester was completely transformed. It was placed under the joint leadership of M. H. A. (Max) Newman and Sidney Goldstein. They were eminent mathematicians who had used their talents with outstanding success during the war. Goldstein, an expert in aerodynamics had made important contributions to the aircraft industry. Newman had been in charge of a section (called 'Newmanry' at the time) of the celebrated team of mathematicians at Bletchley Park who broke the German military code.

Now in peace-time Newman and Goldstein were determined to make Manchester one of the foremost centres of mathematics in the country. Their immediate task was to appoint new members of the teaching staff. The first advertisement was for the post of an applied mathematician. I was so keen to move to Manchester that I put my name forward; after all, my present position at St Andrews was that of an applied mathematician. I was pleased that I was called for an interview and I felt that is was going well. Professor Goldstein said: "If you get this job, you will have to do a fair amount of service teaching, especially for engineers, who have to study mathematics in some depth. Of course, also for physicists and you may even have to teach chemists. After a short pause he added in a low voice: "Mathematically speaking, chemists are the lowest form of humanity." I promised to do my best to teach all layers of humanity. I went back to St Andrews hoping that I should soon get a favourable reply. However, a few days later a hand-written letter from Professor Newman arrived, in which he told me that the Committee had decided not to appoint me to the post of an applied mathematician as it was felt ( quite correctly) that my main interest was still in the pure side. But he lessened my disappointment by adding that there would shortly be a vacancy for a lecturer in pure mathematics and that he would regard me as a very strong candidate. All I needed to do was to write to the Registrar saying that I was interested in this post. No further interview would be required. In due course I was happy to receive the confirmation that I had been appointed to a lectureship in mathematics for a probationary period of three years at an annual salary of £550.

Further appointments for the Department were soon authorized and before long, all those who had been candidates at the first interview, were added to the faculty. We became close colleagues. I formed friendships with some of them which extended to our families and that lasted long after we left Manchester to continue our careers elsewhere.

Max Newman was a highly efficient and resourceful Head of Department. His style of leadership was somewhat autocratic. At the end of the term one would find a piece of paper on one's desk saying for example: "Next term you will give a course of lectures on projective geometry," without having previously been asked whether one knew anything about the subject. At a personal level he appeared aloof and reserved; during the sixteen years that I was a member of his staff I was always "Ledermann" to him. Yet he could also show personal consideration towards me. When we moved to Manchester in the autumn of 1946 we initially stayed in furnished rooms as there was not enough time to look for a house and solve the financial problem of a purchase. Evidently, Newman noticed that Rushi and I were not very comfortable. But I was surprised when after the end of the summer term 1947 he invited us to stay at their beautiful house at Altringham near Manchester while he and Mrs Newman were on holiday in Wales. The only condition attached to this offer was that we should look after the hens kept in their garden. (In 1947 we were still living under rationing and people were encouraged to supplement their food supply.) I had no previous experience of keeping live stock. In particular, I did not know that hens indulge in racial discrimination: one of Newman's hens was brown, all the others being white. The brown hen was constantly being chased away from the bowl of food we put into the garden so that eventually we had to provide an extra little bowl for the persecuted creature.

I believe Newman respected my experience and interest in teaching. He appointed me to be a member of the committee, chaired by him, whose task was to review the teaching of mathematics at school. The committee sometimes met in Cambridge where the Newmans still had a house (Mrs Newman was a writer and Manchester did not suit her artistic temperament.) On such occasions I was his guest at their charming converted farm house and he even invited me once to dinner at St John's, his Cambridge College.

Soon after the war some of the leading British mathematicians who included Max Newman and his friend, the charismatic Oxford topologist J. H. C. ('Henry') Whitehead, decided that it would be desirable to have an annual meeting of mathematicians in order to stimulate research and to give younger mathematicians the opportunity to be seen and heard. The meeting, henceforth to be known as the British Mathematical Colloquium, would be held during the Easter Vacation at a university that was willing and able to be the host. The programme was to be strictly confined to high-grade mathematics. There was to be no provision for entertainment or for the introduction of guests. Newman and his friends had engaged the speakers but a great deal of administrative and domestic work had still to be done to launch the project. Remembering that I had taken part in organizing one of the Edinburgh Colloquia, Newman called me to his office one morning and said "Ledermann, I want you to make all the necessary preparations for the British Mathematical Colloquium that is to have its inaugural meeting in Manchester next autumn (September 1949). I want you to understand that the meeting will be devoted solely to mathematics - "no wives and no dogs."

This task placed a heavy responsibility on me. After sending out programmes and application forms, I estimated that about eighty persons would attend (the number is now several hundred). It was one of my duties to find suitable accommodation. I chose Dalton Hall, a residence for male students. The house was run by the Society of Friends. I had a personal connexion with Dalton Hall. Its principal at the time J. (Jock) Sutherland, whose wife was the former Mary Lakeman, the lovely leader of our chamber music at St Andrews. I had been appointed to give tutorials at the Hall in the evenings, which gave me the opportunity to get to know some of our mathematics students, who stayed at the hall, on a more personal level. Dalton Hall was a comfortable place and the food was good. As the Hall was at some distance from the University, I hired Manchester Corporation Buses to convey the members of the Colloquium in the morning from Dalton Hall to the University and bring them back in the evening. Also I had inspected and reserved suitable lecture rooms at the University and made arrangements for meals and refreshments to be served between the sessions. However, severe anxiety was caused when, only a few days before the start of the conference, I was admitted to hospital suffering from acute appendicitis. Fortunately, I was discharged just in time to receive the guests at Dalton Hall, although on doctor's order I was not allowed to carry their suitcases. Everything appeared to be going well until Henry Whitehead strode in. Even before I could show him his room, he demanded in a firm voice: "Ledermann, where is the bar?" The extent of my failure now became apparent. I am not a teetotaler, but the provision of alcoholic beverages did not occur to me as a prerequisite for a major mathematical conference. However, Henry Whitehead obviously had different views. I did not know that he was accustomed to drinking one or more pints of beer at various times of the day. It was therefore with deep regret that I had to inform him of the strict ban on alcohol at Dalton Hall in accordance with the rules laid down by the Society of Friends. I think Whitehead never forgave me my blunder. Despite all the work I had done to mount the Conference I was immediately dropped from the organizing committee. However, the British Mathematical Colloquium continues to flourish as an important annual event (needless to say, it is now always equipped with a bar).

By the early 1950's the mathematics staff had risen to about 30 members. There were not enough rooms to provide each of us with an individual office, so we had to share rooms. I believe the loss of privacy was amply compensated by the opportunity to have closer personal relations with some of your colleagues and, in particular, to exchange ideas about research topics. Moreover, for some obscure administrative reason, we had frequently to change our room mates, which presented us with welcome variety. During that period almost all my research papers were written either in conjunction with colleagues or had their origins in discussions with them.

The Mathematics faculty included several persons who, like myself, had escaped from Nazi persecution and found refuge in Britain. They were among those colleagues with whom I had the opportunity to engage in research.

G. E. H. (Harry) Reuter was the son of Ernst Reuter, a prominent member of the German Social Democratic party at the time of the Weimar Republic. When Hitler came to power, the Reuters left Germany to escape from political persecution. After the war Ernst Reuter returned to Berlin and was the city's successful mayor during the Soviet blockade. In gratitude for his leadership and service, one of the main squares in Berlin is now called the Ernst Reuter Platz. Harry was sent to England in 1935 at the age of 14. He lived with the family of the Cambridge mathematician Charles Burkill. Harry was educated at the Leys School from where he went to Trinity College, Cambridge. When I first met him on his appointment at Manchester he struck me as a typical young Englishman both in appearance and in speech; for he had changed his language before the critical age, said to be about 16, after which the stigma of a foreign accent cannot be eradicated. Harry was a very fine analyst with a profound knowledge of analytical methods and a sure judgment as to how and when to apply them. My collaboration with him gave me great pleasure. Also my wife and I enjoyed having him and his wife Eileen as friends while we lived together in Manchester. Harry and I wrote two papers about a topic in probability theory known as Markov processes. I was pleased that they were well received by experts in this field. The eminent scholar D. G. Kendall referred to them as "two path-breaking papers."

By any standards Kurt Mahler must be regarded as one of the most remarkable persons in 20th century mathematics. He was born in 1903 into a middle-class German-Jewish family of modest means. In early childhood he contracted tuberculosis of the knee which rendered him lame throughout his life. By virtue of his illness his schooling was irregular. But he was fond of reading. As a boy he came by chance across a book of geometry which fascinated him, although at the time he could hardly have understood its contents. He continued his self-study of mathematics and even started to write mathematical articles. One of these papers found its way to Carl Siegel, an eminent German mathematician. Siegel was so impressed that, together with a school teacher, he arranged for Mahler's formal education to be continued so that he could be admitted to a university. In 1927 Mahler obtained his Ph.D. degree at Frankfurt, and he also spent some time at Göttingen.

He realized early that he could not survive in Nazi Germany. He went first to Holland and then to Britain, where Mordell had offered him a modest position at Manchester. He remained in Manchester when Newman and Goldstein took over the Mathematics Department. His outstanding research contributions were soon recognized: he was appointed to a Personal Chair, an honour which had never before been bestowed, and he was elected to the Royal Society.

Although Mahler could make social contact at a superficial level he was fundamentally a lonely and self-reliant man. He remained unmarried and seemed to have had few close friends. Even the number of his research students was rather small. He lived in a comfortable residence, called Donner House, which was reserved for single faculty members. He arranged his life according to a strict time table: he would go to bed every day at 9.30 p.m. even when he had guests, whom he would then pass on to a colleague "for entertainment."

He seemed to have some anxiety about getting enough food. At the annual Vice-Chancellor's Reception the whole faculty were invited to a supper party in a large hall. Along the walls a set of tables bore delicious food beautifully displayed. When the doors of the hall were opened, the invited guests rushed forward to help themselves to as much as could decently be put on a plate. (Many of us had not yet overcome the greed caused by war-time deprivation.) To our surprise Mahler was already in the hall, seated behind one of the tables and lustily engorging. Evidently, the waitresses had let him in through a back door, perhaps out of pity for his disability.

Mahler had two hobbies: photography and the Chinese language. He made nice photographs, especially of children, and he liked to tell us that he had mastered about 2,000 Chinese characters and could read classical Chinese stories.

He must have been constantly preoccupied with mathematics. His output was enormous: at least one major research article each term. The obituary published in the Bulletin of the London Mathematical Society 24 (1992) 381-397 lists 221 papers by him.

It was my good fortune that, for a time, I shared an office with Mahler. He aroused my interest in the geometry of numbers, to which he had made major contributions. I was very pleased to be a co-author with Mahler of two rather long papers on this subject, the second of which had as a third co-author J. W. S. Cassels, whom I was very pleased to have as a colleague at Manchester.

Mahler frequently gave research lectures at the weekly seminar of the Department. His talks were well organized. Sentences that would have to be referred to subsequently were highlighted with a frame around them and the blackboard was quickly covered by a multitude of rectangles. Mahler spoke clearly, albeit with a strong German accent; what was more disconcerting was the fact that his writing had retained the features of Gothic-German script, which rendered some of the letters difficult to decipher. I remember that during one of Mahler's seminars, one of our colleagues was so irritated that he interrupted saying: "Mahler can't you write more legibly? You are boasting that you have mastered 2,000 Chinese characters, surely you can take the trouble to learn to write 26 English characters!" A crisis occurred in Mahler's life when Donner House closed down and he was obliged to find his own accommodation. Unfortunately, Mahler had a phobia about using the telephone and he was inexperienced in business matters. He asked me to find a house for him and to undertake all the necessary negotiations. We lived in Ashwood Avenue, a quiet street in a residential part of Manchester. A small house in our street was vacant. I thought this would suit Mahler since several mathematicians, apart from ourselves, lived in the same street. Of course, it would be necessary for Mahler to engage a housekeeper, since he completely lacked domestic skills. I suggested that he should put an advertisement into the local paper. But I warned him that he should not emphasize the fact that an unmarried professor was seeking female assistance. However, he seems to have disregarded my warning; for a few days later he appeared at our house carrying a suit case. He opened the suit case and said "These are all the replies I had," and dozens of letters from middle-aged ladies fell to the floor many accompanied by photographs. He appointed one of the applicants to be his housekeeper. But it was a dismal failure: the woman was domineering and ordered poor Mahler about. So after suffering for a few years he was pleased to accept the offer of a Chair at Canberra, where he would be looked after at University House in a dignified manner. I lost touch with Mahler after his move to Australia. He obviously remained active there, because he published about seventy papers after leaving Manchester.

Despite his foreign demeanour Mahler was strongly patriotic after he became a British subject in 1946. When the political changes after the war were being discussed, he declared emphatically that "we should keep India and not surrender any part of our empire."

All in all, Mahler could be good company. I am glad I knew him and I remember him with affection and admiration.

B. H. (Bernhard) Neumann joined the mathematics department at Manchester a few years after me. I remembered him well from my student days in Berlin. He was two years my senior and I always looked up to him because he was working for his doctorate while I was pursuing the more modest course for the State Examination (Teachers' Diploma). By the time he came to Manchester he had already a high reputation as an expert in group theory and he was elected a Fellow of the Royal Society in 1959.

I was very pleased when he invited me to collaborate in a piece of research which led to the publication of two joint papers.

P. J. (Peter) Hilton joined the mathematics faculty at Manchester around 1950. As a very young man he had been a member of the code-breaking team at Bletchley. Subsequently he was a student of Henry Whitehead at Oxford specializing in algebraic topology. I was interested in some purely algebraic aspects of this far-reaching and fertile subject. Peter and I published several joint papers on what we called topological ringoids. Peter and Margaret Hilton together with their two sons lived in a house opposite ours in Ashwood Avenue. We soon developed a warm house-to house friendship which, I am pleased to record, continues to this day even after the Hiltons had left Manchester.

With some of my colleague it was not mathematics but music that brought us together. Both Arthur and Dorothy Stone were members of the mathematics department. Arthur was an able violinist; he led the string quartet in which I played the viola. Our excellent cellist was Nancy Lighthill, the wife of James (later Sir James) Lighthill. James was a very good pianist. The Lighthills also lived in Ashwood Avenue, a few doors from us. Our string quartet met at their house. While we were playing, James came to our house and played piano duets with Rushi; although our drawing room was not large, we were able to place in it the beautiful Blüthner grand piano that had belonged to Rushi's parents and a Schwechten upright piano of good quality; it had been in my parents' flat in Berlin and they brought it with them when they emigrated to England. Rushi and James attempted some quite ambitious works, such as a Beethoven piano concerto, where one pianist played the original solo part and the other played the orchestral accompaniment. In the meantime we enjoyed ourselves with some of the classical string quartets. At coffee time, Rushi and James joined us at the Lighthills' house.

It was a great gain for the University of Manchester when Alan Turing joined the mathematics department in 1948. He was famous for the brilliant work he had done before and after joining the team at Bletchley and he had been awarded the O.B.E. in 1944 for his contribution to the war effort. Because of a minor speech defect he did not feel comfortable about lecturing to a large class of undergraduates, and Max Newman asked me to take over the course originally assigned to Turing, It was most stimulating to talk to him over lunch and to listen to his mathematical ideas. One of his greatest achievements was the construction of the computer, one of the first in Britain. It occupied a large part of the top floor of the engineering building, its vast size being due to the fact an enormous number (about one thousand, if I remember rightly) of electronic valves had to be used for its construction (transistor were not yet available). He invited Rushi and me to look at this astonishing machine. In order to demonstrate its various capabilities he used a programme for the valves to play "God save the Queen", which was very effective. Alan Turing had got into conflict with the law against homosexuality, which was then still in force. In the first instance he was put on probation provided that he underwent medical treatment. Rushi helped him to find a psychiatrist who took him on as a patient. But Alan suffered a relapse and he was afraid that he might be sent to prison. On 7th June 1954, a few days before his forty-second birthday, he died of cyanide poisoning. It was generally assumed that he killed himself in order to avoid the expected humiliation. But his mother believed that his death was due to an accident, since Alan was in the habit of carrying out chemical experiments even with dangerous substances. The law that condemned homosexuality as a criminal offence was repealed some years later, but too late to save the life of one of the most brilliant mathematicians whose work was of the greatest benefit to mankind.

As is the custom in British universities promotion is granted solely on the grounds of successful research. I was therefore pleased that in 1953 my position at the faculty was raised to that of a Senior Lecturer. In due course Max Newman asked me to take a share in the supervision of postgraduate students working for the Master's or Doctor's degree. He seemed to be of the opinion that I was a suitable person to take on the more exotic candidates. I remember a young man who came to us from Afghanistan. For the sake on anonymity I will here call him Abdul. He was a polite young man, tall of athletic build. It turned out later that his real talent was in the game of football. He had played for the national team of Afghanistan and was highly respected for his prowess in the game. Abdul had a degree in mathematics from a university in his own country and had applied to study under my supervision for the Master's degree in mathematics at Manchester. The initial interview with me was quite painful. "Do you know anything about the theory of groups?" Answer: "No." "Have you studied matrices?" Answer: "No." I went through several more topics in mathematics and always elicited the same negative reply. I got rather desperate and eventually picked out a well-known piece of school mathematics. "Tell me what is the Binomial Theorem." He said meekly: "I have heard of it, Sir; but I cannot recall it." I gave him a short paper on matrices by M. Fréchet, which, surprisingly in view of the eminence of the author, contained a minor mistake. I pointed this out to Abdul and asked him to make a correction and elaborate the point. He succeeded in doing this with a great deal of coaching. Finally, his M.Sc. thesis was accepted and he returned to Afghanistan as a proud owner of a Master's degree from a British university. According to the story which he told me subsequently, he was received by the King, who gave him a gold watch and said: "My son, any wish you express shall be granted." Abdul bowed before the King and replied: "Your Majesty, it is my wish that I shall be sent back to Manchester and register for the Ph.D. degree under the supervision of Dr Ledermann."

When shortly afterwards he turned up at Manchester. I was aghast. I said to Professor Newman: "This man is not fit to work for a Ph.D. degree. I feel that he should not be accepted as research student." But Newman replied: "Unfortunately, we cannot reject him. I had a letter from the Foreign Office supporting his application for admission. If we refuse to accept him, there will be a diplomatic incident. So, I am sorry, you have supervise him for a Ph.D." In contrast to us, Abdul was very happy to be back in Manchester, not least because he would now again be able to watch Manchester City, his favourite football club. He preferred it to Manchester United, whose followers, he said, were rather vulgar. Of course, it was difficult to think of a research topic that was not above Abdul's capacity. I suggested a problem in the theory of group characters which required a great deal of complicated calculations. I hoped that, given his diligence and perseverance, Abdul would make some useful contributions to this problem. But progress was very slow. He came to my office almost every day and asked for some help. Then it occurred to me that D. E. Littlewood in Bangor was interested in a similar problem. So I asked him whether he would accept Abdul as a research student in Bangor rather then in Manchester. But Littlewood replied saying that Abdul would be welcome to work in Bangor and receive appropriate advice; but he would have to remain registered in Manchester, so that we should have the ultimate responsibility. Although this was only of limited help, I was relieved when Abdul accepted Littlewood's offer and left for Bangor. However, my joy was of short duration. After less than a month Abdul appeared in my office at Manchester. He looked rather dejected. I asked him: "How do you like Bangor?" He said: "I cannot live in Bangor." I was surprised, I thought that Bangor was a nice little town and I knew that Littlewood was friendly and helpful. "Sir, I cannot live in Bangor, because there is only Second Division football." So I had to yield to his high standards of the game and take him back as my research student, however arduous the supervision would be. He came to my office almost every day and with my help pushed the thesis forward a line or two. One day he came when I was not in the University. At that time I shared the room with Sandy Green. Abdul opened his heart to him and complained how hard is was to write his thesis. But after a while his face brightened up and he exclaimed: "Allah and Dr Ledermann will not let me fail." Sandy, who was aware of Abdul's passion for football, gave the appropriate answer: "You may be sure that everything will be alright in the end, because Allah and Dr Ledermann are an unbeatable team." As always, Sandy was right. In due course, Abdul's thesis was accepted and he was awarded the Ph.D. degree. Of course, he was enormously pleased. He planned to get married and said: "I do not want to spend a lot of money on my wife. I shall buy a shopkeeper's daughter; a judge's daughter would be too expensive."

Abdul returned to Afghanistan and I never heard from him again. I was told that he was appointed to be vice-chancellor of a university. But belonging to the King's party he was assassinated during the revolution which abolished the monarchy.

Ay this point I want to express my gratitude to Professor Geoffrey Howson for helping me with my reminiscences about Manchester. He was an undergraduate there in the 1950's, a resident at Dalton Hall, where he had tutorials from me and finally became a successful postgraduate students and was awarded the Ph.D. degree. His interest in these memoirs and his staunch support are invaluable to me.

The high reputation of the Manchester Mathematics Department attracted numerous visitors from this country and from abroad. I remember in particular the visit from the famous Russian mathematician P. S. Alexandrov. I do not remember the subject of his seminar lecture. But it was well received although Alexandrov had difficulty in speaking English, whilst he had an excellent command of German. His travel schedule made it necessary for him to spend the night at Manchester. Newman thought that, rather than being put up in a hotel, Alexandrov would feel more comfortable if he could stay with someone who speaks German. So he asked me if Rushi and I would be willing to give hospitality to this eminent visitor. Of course, we were very pleased to do this, and Alexandrov came with us to our house in Ashwood Avenue. While Rushi prepared the supper, Alexandrov and I went for short walk in the neighbourhood. When passing a newsagent we saw the large headlines in the evening papers announcing the successful launch of the Russian spaceship sputnik. I asked Alexandrov how it was possible for Russia to get ahead of America in space technology. His answer was that in the Soviet Union a young person is told to study what is useful to the country and not what he would like to study. Thus if he shows abilities in mathematics or engineering he has to study these subjects even he prefers to do medicine. In this way Russia acquired a large number of well-trained scientists who succeeded in building the space craft. It was evident that America agreed with this policy. For almost immediately the American government decided to expand the teaching of mathematics by providing substantial financial support, from which, incidentally, I was going to benefit a few years later.

The programme of undergraduate teaching was well organized by Newman and Goldstein. Generally I enjoyed the teaching that was assigned to me. As I was warned at the initial interview, this involved a certain amount of service teaching. But this was not an unpleasant duty. In particular, I found that the engineering students were a responsive and serious group of men (I do not think there were any girls in the class). The only problem was that they were reluctant to buy any of the text books that were recommended on the reading list. They pointed out that each term the lecturer covered only a small part of the book and different books were recommended for different terms. As the books were rather expensive, it was a waste of money to invest in them because most of their contents was irrelevant to the degree course. I took their point and proposed to design a series of inexpensive paperback, short text books, each of which would cover only the work of one term of one course of lectures. These books would be more elementary than the Oliver & Boyd series of University Texts. In fact, they would be principally designed for students for whom mathematics was a subsidiary subject. The volumes would be of uniform price (initially five shillings) and a student would have to buy only one volume for each term of a lecture course and he would gradually build up his library. I was going to call the series a Library of Mathematics. Modifying a phrase from financial policy, which was current at that tine, I said: "Pay as you learn." The manager of the University Bookshop was my friend Ernest Hochland. I told him about my project and he communicated it to a representative of the publishing firm Routledge & Kegan Paul. They liked my idea and gave me a contract for publishing the series. One of the first volumes to appear in print was my short volume Complex Numbers. At the same time the notorious novel Lady Chatterley's Lover by D. H. Lawrence, which had been banned for obscenity, was allowed to be published and aroused a certain amount of curiosity. A few weeks after my book had appeared in the shop, I asked Ernest how the sale as going and he replied: "You are running neck to neck with Lady Chatterley's Lover." It did not remain like this: but on the whole my series was well received by the public. It grew to more than twenty volumes. Unfortunately, when Routledge was taken over by a large American firm, it was decided that even a substantial sale of small books does not generate enough profit, and the whole series was deleted. This was a great disappointment to me; I had acted as editor for each of the volumes and had been in close contact with the authors. I had myself contributed three volumes. It is a shame that the greed for profit should deprive students of useful tools for their work.

In many respects Manchester was an ideal place for my private and professional life. Of course, the most important event during this period was the birth of Jonathan in 1954. Rushi's training as a Jungian psychotherapist made good progress. She had a consulting room in the house of a colleague not far from where we lived. But, as the training proceeded, it became necessary to make frequent visits to London. The train journey from Manchester to London was tedious. In those days some of the trains were still pulled by steam locomotives. Jonathan, who had just started primary school, saw his mother off at the station and said: "Mummy has gone to London in a stinker." For Rushi's sake it would have been better if we moved to London or at least somewhere near London. Moreover, there were changes in the Mathematics Department that made my work there less attractive. Most of my friends and colleagues who had joined the Department in the early years had left by 1960, mostly in order to take up senior positions elsewhere: Peter Hilton had been appointed to the Chair at Birmingham, Harry Reuter at Durham. The Neumanns and Kurt Mahler had settled in Australia and the Stones had gone to America. In addition Max Newman expressed the bizarre view that there was not much more to do in Algebra and that henceforth he would concentrate on Topology.

I was now planning to leave Manchester. A few applications for Chairs at London Colleges were unsuccessful; but a promising opportunity presented itself in 1962. We were on a farm holiday at Offham, a small village near Brighton, when I noticed that major building project was being carried out in the neighbourhood. The workmen explained that they were building a university in this beautiful part of Sussex. I made some enquiries and was told that the appointment to the Chair of Mathematics was to be made soon. I applied and was called for interview. But the appointment was given to Bernard Scott as the first and, so far, only Professor of Mathematics at the University of Sussex. He had been trained at Cambridge. His application had strong support from the mathematical establishment. He had seen me in the waiting room, together with the other applicants before the interview and therefore knew that I was interested in the University of Sussex. Shortly afterwards Bernhard invited me to join him at Sussex as a non-professorial member of the faculty. But he added that The Council of the University had decided that the usual hierarchy among members of the faculty should be simplified and that there should be only Professors and Lecturers but no Readers. In my reply I stated that I was already a Senior Lecturer at Manchester and that I was unwilling to move to another university without improving my status. Accordingly I declined his offer. I was surprised when, a few days later, John Fulton, the Vice-Chancellor of Sussex University invited Rushi and me to visit him at his home in Brighton. As guests of the university we stayed at a nice hotel on the sea front and spent a pleasant evening with John Fulton and his wife. We discovered that I had a long-standing connection with his family: my first university appointment was a temporary lectureship at University College Dundee in 1938. On my arrival I was introduced to the Principal of the College, whose name was Fulton. It now transpired that he was John Fulton's father. I indicated that I should be pleased to join the new university; but I expected to be offered a position that was more senior than the one I had in Manchester. John Fulton agreed and he said that he would ask the Council to reverse their decision not to have Readers. He would offer me a Readership in Mathematics. I accepted his proposal and decided to move from Manchester to Sussex.

On my return to Manchester there was just enough time to observe the statutory time for handing in my resignation. Max Newman was very angry. He had lost quite a large number of experienced staff and he had expected me to stay. I had been in Manchester for sixteen years. But there would be no ceremony; no glass of sherry, let alone a farewell dinner for my departure. On my last day, which was during the summer holidays, I went to my office at the University, packed all my books and papers into some boxes which were sent to my home. There was none of my colleagues to say good-bye. Elsie Connery, our nice Secretary noticed how depressed I was; but she only offered this advice: "Don't indulge in self-pity; it will do you no good."

Twelve years later I saw Newman again. The twenty-fifth meeting on the British Mathematical Colloquium was held in Manchester where the first meeting took place in 1949. The organizers invited Newman and me as guests of the Colloquium because Newman had been the Chairman and I the Secretary of the first Colloquium, Newman was quite friendly towards me. He seemed to bear no grudge. But he was deeply worried because his wife was suffering from a terminal illness at that time. I never saw him again.

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