Walter Ledermann: Encounters of a Mathematician


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(Edinburgh: 1936-8 and thereafter)

Emigration: St Andrews 1936 - 1938

From the outset it was clear to me that I should have no chance of surviving in Nazi Germany. I made strenuous efforts to emigrate. Eventually, owing to a chance remark my brother had overheard in Edinburgh, I obtained a scholarship through the good offices of the International Student Service at Geneva: the students at St Andrews University had decided to support two refugees from Nazi Germany, one who was persecuted on account of his political affiliations and the other because he was Jewish. It was my exceedingly good fortune that I was selected for the second award. As I understood later that the money for our maintenance had been collected from the citizens and students of St Andrews. Indeed, it is no exaggeration to affirm that I owe my life to the people of St Andrews.

I vividly remember the circumstances of my emigration. I was due to leave on 3rd January 1934. It was my wish to spend my last evening at the opera. My father obtained two tickets for a performance of Tristan und Isolde at the State Opera House unter den Linden. This being a long opera the performance was scheduled to start at 7 p.m. Normally the timing was strictly adhered to; but on that evening the lights did not go out at 7 p.m. and it was clear that something unusual was happening. Then when all members of the audience were in their seats, we saw that there was some movement at the grand "imperial" box in the centre of the Dress Circle. Hitler came in; he was wearing a dinner jacket. He was accompanied by a young lady. They sat down in the first row and were followed by Goebbels and a woman who took seats behind Hitler. But the lights still did not go out. We observed that Goering had come in wearing his uniform with numerous medals. He did not sit with Hitler but occupied a box in the second circle quite near where my father and I were sitting. Then, finally, the performance began. It was beautifully done, Furtwängler conducted. As always, the orchestra played superbly and there was a first class cast of soloists. The role of King Marke was sang by the excellent bass Emmanuel List, who was Jewish (perhaps this was kept from Hitler so as not to spoil his enjoyment). For me it was an ideal way to be granted this musical treat on my last evening in Germany, although I had to share it with Hitler, Goebbels and Goering.

I left the next morning. My parents could not see me off, as it was a working day for my father. But my sister Káte came with me to the Bahnhof Friederichstrasse and waved good-bye to me as the train left for Holland. I was destined not to see her again for almost twenty years. My plan was to go first to Edinburgh, where my brother Erich was working in order to obtain the British medical qualification and then to go on to St Andrews two days later. The third class compartment in which was travelling was fully occupied. Nobody spoke to me. The first stop was Hanover. I was horrified when two SS soldiers in black uniform stormed into our compartment and seized two middle aged men and pulled them out of the train. As the train was beginning to move out of the station we threw the men's suitcases out of the window. I have no idea why these men were arrested. Perhaps they were trying to smuggle money out of Germany. The frightening thought occurred to me that one of the passengers in our compartment was a Nazi spy who communicated with the police and had informed them of the men's location. Not another word was spoken until we had crossed the Dutch border. Everybody's face brightened up with relief that at last we had reached freedom. The train took us to Hoek-van-Holland, where I boarded the boat to Harwich. On arrival at Harwich I saw several trains at the quay-side; one was clearly marked: Edinburgh. I quickly got into it with my luggage. The train left and a few minutes later the ticket collector came. When he looked at my ticket, it became clear that I was in the wrong train. I should have gone to London and then taken the "Flying Scotsman" from Kings Cross Station to Edinburgh. My heart sank because I felt sure that I should have to buy the correct ticket for this train. To my surprise the collector just waved his hand and said: "Never mind! It is the wrong ticket; but continue your journey to Edinburgh." It was my first encounter with a pleasant British characteristic: absence of rigid bureaucracy and sense of humour. Having travelled throughout the night I was hungry and sat down in the attractive dining car and studied the menu. A nice Dutch gentleman sat at the same table; he spoke English and German and he explained to me that full English breakfast includes bacon and eggs. This was new to me. I ordered it and I enjoyed it: the second encounter with a pleasant British custom. When I arrived in Edinburgh I was very pleased to see Erich at the platform. Luckily he had made enquiries and been told that the "wrong" train I had taken was the official boat train. I spent two pleasant days in Edinburgh and then continued my journey.

On my arrival at St Andrews I was received by William (Bill) McC. Stewart who was the local representative of the International Student Service. Stewart was the Head of the French Department at St Andrews. Bill was a lively and cultured Ulsterman. Apart from a fluency in French he had an excellent command of German so that I had no difficulty in communicating with him. He had recently married a Jewish lawyer from Munich. So I felt very much at home with the Stewart's, who lived in one of the few modern houses of St Andrews. Bill Stewart remained my mentor and friend for many years to come, and I was most grateful to him.

He introduced me to D. E. (Dan) Rutherford who was one of the three lecturers in the Mathematics Department. Dan spoke some German, as he had spent one semester at Göttingen as a postgraduate student.

My friendship with Dan was most precious to me. Coming as he did, from a background very different from my own, he greatly enriched my life. He also helped me in a practical way to settle down in the new surroundings.

I could read English fairly well, but the spoken language caused considerable difficulty. I tried to improve my vocabulary. One method was to walk through the streets of St Andrews in order to learn words from inscriptions on shops and notice boards. I had no problem about "Tobacconist" or "Newsagent." I understood the meaning of "Fishmonger" after looking up the second part of the word in a dictionary; but "Family Butcher" was to my mind an outrageously cruel occupation. However, I settled down fairly rapidly in these very strange surroundings. The terms of the scholarship laid it down that I should receive a sum of money (if I remember rightly £5 per week) to cover the cost of lodgings and breakfast.

My landlady was a simple-minded elderly woman who was sometimes slightly worse for drink. She had four male students in her flat which was part of an old house in the centre of St Andrews. There was no electricity in the house. We were each given a box containing three matches with which we could use to turn the gas light on when we came home after dark. She explained that she was unwilling to give us a full mach box as we might use the matches to light our cigarettes or pipes. But she was prepared to issue thee more matches when asked to do so. The lack of electricity puzzled me, especially when I discovered that there were some quite modern cottages without this service. Then it was explained to me that the chairman of the local gas company (which at that time was privately owned) was also an influential member of the town council and he used his influence to withhold planning permission from any building that was planning to have electricity installed.

I was the guest of the Students Union for lunch at their dining room. For the evening meal I joined the students at St Salvator's Hall. This was the main Hall of Residence for male students. It was a spacious and fairly modern building. The rules of conduct were in the Oxford and Cambridge style. Dinner was "formal", that is, the Warden and other members of faculty sat at the High Table; they wore black gowns. The students sat at long tables below the High Table. They had to wear the scarlet gown which was characteristic for St Andrews. Fortunately, Erich knew a lady in Edinburgh who had been a student at St Andrews and kindly passed her scarlet gown on to me.

These arrangements made it easy for me to mix with other students; most of them were from Scotland, a few from England but only a small number from other countries. Some of the students I met were studying German as a foreign language. We helped each other with our linguistic endeavours by going for walks along the beach speaking German on the way out and English on the way back or vice versa. There also some faculty members, rather more often their wives, who wanted to brush up their conversational German. Usually they invited me for tea and we had a conversation in German afterwards.

Another way to meet people was through music. I had my violin and viola with me. Soon I found pianists who played sonatas with me and I took part in the annual performance of The Messiah by a capable amateur choir and orchestra. As in most universities, St Andrews students had their "hop" on Saturday evenings. Regrettably, I had never succeeded in learning ball room or folk dancing. But I offered to bring my violin and to play Scottish Reels and Strathspeys while the rest of the company enjoyed itself on the dance floor. Another social occasion to play music were the meetings of the Franco-Scottish Society which was founded to commemorate the alliance in former times between France and Scotland in their fight against England. At these meetings only French was spoken and French music was performed. I was invited as a guest and to play pieces by Couperin and Raneau.

Initially, there was uncertainty about my status at the University. It was my hope that I should be allowed to work for a doctorate. But since this is a higher degree, candidates must have a first degree before being admitted. The question was whether the State Examination from Berlin could be regarded as equivalent to a British B.Sc. degree. This problem had never occurred in the five hundred years history of St Andrews University. Fortunately, it was discovered that a similar case had recently been considered in Edinburgh. A refugee had arrived with a complete teaching qualification and she was given permission to register for the Ph.D. degree. (In fact, she was Charlotte Auerbach who became an eminent geneticist in Edinburgh and was one of the few women to be elected to a Fellowship of the Royal Society of London.)

I was very pleased that Professor H. W. Turnbull, the (only) Professor of Mathematics at that time, accepted me as one of his research students. He was a well-known authority on classical algebra, which had been my favourite subject as an undergraduate. I was particularly interested in his joint book with A. C. Aitken on Canonical Matrices, a brilliant work that suggested areas for further research.

Professor Turnbull was a patient and understanding supervisor. Before being appointed to the Regius Chair of Mathematics at St Andrews he had spent several years in China and had acquired some knowledge of the Chinese language. During one of our early sessions, Professor Turnbull noticed that I was struggling with words and he kindly said to me: "Walter, I see that you have difficulties in expressing yourself; would it help you if I spoke to you in Chinese?" I politely declined adding that I would prefer to stick to English, however imperfect on my part.

It is hard to imagine a greater difference than between Berlin and St Andrews. Life in a large city can be impersonal and may lead to a sense of isolation. But in a small town like St Andrews I soon got to know almost everybody -- at least by sight. I constantly got invited, usually for tea, and I was always received with warm hospitality. Professor and Mrs Turnbull were particularly caring and helpful. In the warm season they often asked me to join them for a picnic. (It is unlikely that a German professor would do this with one of his doctoral candidates.)

I observed that generally religion played a more prominent part in the lives of the British people than was the case in comparable continental communities. Both Professor Turnbull and Dan Rutherford were devout Christians. Indeed Professor Turnbull usually began his lecture with a prayer. He and Mrs Turnbull belonged to the Oxford Group, a religious movement which had gained some influence in the 1930's. Occasionally they held meetings at their house for members of this group. After partaking of an enjoyable afternoon tea, the participants would sit in a circle and "with perfect honesty" would publicly confess their misdeeds or sinful thoughts. I had been invited to several of these meetings but felt increasingly uncomfortable. Eventually, I appealed to the principle of "perfect honesty" and confessed that I would prefer not to be asked to attend any more meetings of the Oxford Group.

Both Professor and Mrs Turnbull were excellent pianists. Quite often, after a delicious tea they played to me works on two pianos; for example the St Anthony Variations by Brahms and the work better known as Piano Quintet by Brahms, but originally scored for two pianos. Much later my memory of these splendid pieces of music was revived when Rushi played them with our friends; for although at the beginning of our marriage we had rather modest houses, we made sure that there was always enough room for two pianos in our music room.

Mountaineering was another of Professor Turnbull's hobbies. I was told that one tricky route to the top of a particular mountain in the Scottish Highlands was named after him, because he was the first to have reached the peak in this way. He had frequently undertaken major mountaineering expeditions in Switzerland, including an ascent of the Matterhorn with the aid of a professional guide. Surprisingly, St Andrews offered opportunities for practicing one's mountaineering skill albeit on a small scale. Turnbull was particularly fond of a rock formation called the Rock and Spindle. It was situated on the Eastern shore of St Andrews. Turnbull would take his students to this place and give them some experience in rock climbing. One day he took me to this impressive place. At low tide the rock could be reached dry-footed; but at high tide it was completely surrounded by the sea. We started our climb at low tide under his guidance I managed to reach the top albeit rather slowly. I was rather worried lest the tide might come back before I got down and I said: "Professor Turnbull, what shall I do if the tide has come in before I have completed the descent?" He answered rather typically: "Then you will just have to pray." Fortunately, this was not necessary, as I got down in time.

The rest on Sunday (or the "Sabbath Day" as some Scots say) was strictly observed and even enforced by law. There were no trains or buses operating at St Andrews on a Sunday. Cinemas were closed, and restaurants were open only for a few hours. Most students attended University Chapel. One Sunday after the other lodgers had left and I stayed behind, the landlady said to me; "why don't you go to church"? I replied: "Because I am Jewish." "This does not matter" she said. "We have churches for Presbyterians, Anglicans, Methodists and others; surely, one of them will suit you." After Chapel, the students, wearing their bright scarlet gowns would walk in a procession down to the harbour and along the ancient pier. In fine weather this was a picturesque sight. Despite my denial to the landlady I sometimes joined the students at the Chapel -- not entirely out of boredom, because there were occasionally interesting guest preachers whom I wanted to hear.

The climate was a minor stumbling block on the road to assimilation. It rained very frequently. I suppose that "showers and bright intervals" is the most accurate weather forecast for much of the British Isles throughout the year. I just made a habit of never leaving the house without wearing my raincoat, however blue the sky; I knew that sooner or later there would be a heavy downpour. Only a British poet could have written the line "The rain -- it raineth every day."

However, I soon got used to the North Sea climate and indeed, enjoyed its bracing effect. Moreover, I fell in love with the majestic beauty of the Scottish Highlands to which Dan Rutherford introduced me by inviting me to join him and some friends in most delightful walking and climbing expeditions.

At the end of a summer term all St Andrews students had to vacate their lodgings because the landladies could let the accommodation more profitably to the visitors who flocked to St Andrews for the golf season. I was therefore in a dilemma as I did not know where to go. It would have been disastrous for me to return to Germany for the vacation, although my parents still lived there until 1938.

Unexpectedly, it was the Glasgow mathematicians who came to my rescue in this predicament. They invited me to move to Glasgow where suitable lodgings were found for me. Although I was not a student at Glasgow University, the Librarian provided me with a writing desk in a quiet corner of the library, where I continued to work on my thesis.

In their kindness my hosts even thought of some recreations and holidays for me. In the 1930's Glasgow had been badly hit by the recession and there was a great deal of unemployment especially among the Clyde ship workers. Some of the men had not had a holiday for many years. So the Glasgow students put up a camp on a small island, known as Inchcalliach, in Loch Lomond near its Eastern shore. They invited a group of unemployed men to spend a week's holiday there. The camp consisted of several large tents, each housing six men and one student whose task it was to entertain the men. I was put in charge of one of the tents. Initially, there was some difficulty in communication: their strong Glaswegian accent did not blend well with my foreign intonation. But we soon got on well with one another and engaged in friendly chats. The men were grateful for the hospitality and the opportunity of a holiday. But soon I noticed signs of unrest and frustration; the landowner who controlled the Eastern shore of Loch Lomond had refused to grant licences for alcoholic drinks in the region and there was no chance of having a pint of beer in the vicinity. The nearest place where these invigorating beverages could be obtained was at Luss, a village on the West shore of Loch Lomond, at some distance from our camp. I borrowed a large rowing boat from a group of boy scouts who were camping near us on the same little island. Then I selected three of the most needy and thirsty men from my tent who could handle oars, and we rowed across the lake. I had hardly finished fastening the boat at the pier in Luss, when the men made a dash for the nearest pub and disappeared. They were not seen again until it was time to start on our return journey. When they finally came out of the pub it was plain that they were in no condition to hold an oar, let alone share in the rowing. Instead they slumped on to the floor of the boat and remained there motionless. So I had no option but to row the heavily laden craft single-handedly back to our camp. Needless to say I made no further excursions to Luss.

While I was grappling with the Glaswegian accent of my companions, I worked assiduously at improving my knowledge of standard English. It was my intention to obtain the Certificate of Proficiency in English awarded under the auspices of the University of Cambridge. I must have used my leisure on the camp to good effect, because I passed the examination "with merit" later during the summer.

On my return to St Andrews I felt increasingly at home in this captivating little town. To some extent St Andrews had preserved the authority and dignity of the ecclesiastical centre that it possessed in mediaeval times. The magnificent cathedral was destroyed in the Reformation. But the ruins of its walls and those of the castle and other monuments afford an awe-inspiring reminder of its glory, as numerous impressive ancient buildings which are still being used. Even in 1934, when I arrived, the ecclesiastical character of St Andrews was reflected in the composition of the teaching staff of the University: there were six Full Professors in the Faculty of Divinity, but only one Professor of Mathematics and none of French or German.

The character of the town was maintained by the absence of heavy motor traffic: there were no traffic lights in the town. The nearest point on the main railway line was a place called Leuchars, a few miles distant from St Andrews to which it was linked by a branch line. The railway station at St Andrews was closed each Saturday evening and not opened again until Monday morning. Some years ago this rail link was abandoned for economic reasons and replaced by a bus service.

The academic community at St Andrews was small, but very friendly and sociable. Although I was but an insignificant post-graduate student I soon got to know most members of the teaching staff, including the Heads of other Departments. With one of these my encounter had a mathematical aspect. Sir d'Arcy Thompson was the Professor of Zoology. He was a man of impressive appearance: a white beard, a strong voice and the bearing of a "real" professor, he was admired for the remarkable breadth and variety of his knowledge. He had a sonorous voice and was a fluent and powerful speaker. Trained at Trinity College Cambridge he remained attached to his alma mater throughout his life. Even as an old man he would make the journey from St Andrews to Cambridge in order to take part in a "Feast". On one of these occasions I asked him after his return to St Andrews if he had liked the excursion. He replied: "The company was delightful. But the meal was abysmal; when I was at Trinity, the College could boast of some of the finest kitchens in England. But now they buy their provisions at the Co-operative Stores. I would willingly spit upon their graves."

Apart from his own subject of biology, he was a highly competent classical scholar and he was fond of exercising his skills as an amateur of mathematics. His master piece Growth and Form was a classic; in it he used quite sophisticated mathematical methods to elucidate the shapes that occur in the living world and bearing witness to his linguistic prowess the book is replete with long quotations in French, German, Latin and classical Greek (with no English translation). When I met him, he was engaged in writing a new and revised version of his book. One of the topics he was interested in required the use of differential equations, a subject which evidently lay outside d'Arcy Thompson's fields of knowledge at that time. So one day when he saw me in the University Library he said: "Do you know anything about differential equations?" When I replied that I was familiar with the usual facts in this subject, he put his arm on my shoulders and said: "Here is a good boy. Come along with me to my house and tell me all about it." So I went to his house with him, sat down at his desk and wrote out the answer to his question.

When I moved from Berlin to St Andrews, the strangeness of language, society and climate was to be expected. But I was surprised and, initially embarrassed, to find that the attitude to mathematics and the topics taught at St Andrews were markedly different from the experiences I had as a student in Berlin. For example, I had learned the precise conditions under which a certain type of differential equation would have a unique solution; but when I was confronted with the problem of finding the solution of a particular equation, I needed some time to carry out the task. As was the custom at many British universities, research students at St Andrews were asked to help with exercise classes given to undergraduates. In the 1930's there were few duplicating machines available. So, the professor or lecturer who took the exercise class wrote a number of problems on the black board at the beginning of the hour. Then, together with his assistants he would walk through the class room and help the students to write out the solutions. The ability to solve unseen problems rapidly was the principal aim of the undergraduate's mathematical education. Indeed, the final assessment for the award of a degree consists almost entirely such problems about the various branches of mathematics that had been taught; some questions contained a small amount of 'book work', that is the request to recall certain definitions or standard results; but as a rule only a small number of marks could be gained for book work. Exceptionally, in the examination paper for second year students, there were questions about the history of mathematics. For Turnbull always gave a course of lectures on this subject to young students. The questions in the examination paper were quite impressive; for example: "Give an account either of the Pythagoreans and their work or of the Alexandrian School."

In fact, Turnbull had a keen interest in the history of mathematics. He was the author of the charming little book The Great Mathematicians and he had made some major contributions to the history of mathematics, notably through his work on the life of James Gregory and the Correspondence of Isaac Newton.

Since the examination paper had to be written in a limited time, normally three hours, speed was of the essence and a good memory was essential, because no access to notes or reference books was allowed.

To be sure, as an undergraduate in Berlin I also attended exercise classes, at which problems were written on the blackboard. But the solutions were not to be attempted during the hour; they were left to us to do in our time at home. The note books containing our work was handed in within a few days and returned the following week with corrections and comments. I have never, to this day, been locked up in a room and was expected to solve a number of unseen problems within a specified time.

In the meantime I submitted my doctoral dissertation. It was accepted and, to my relief, it was decided to dispense with an oral examination. In the summer of 1936, little more than two years after my arrival, I was awarded the degree at the colourful ceremony which, I was told, was an ancient tradition at St Andrews.

However, my pleasure of having received the title of a Doctor of Philosophy was soon overshadowed by thread of an uncertain future. It was made clear to me that there was no prospect of employment for me at St Andrews. So Professor Turnbull suggested that I might have a better chance at Edinburgh and he suggested that I should seek an interview with Professor Edmund Whittaker, and this was the beginning of the next chapter in my professional life.


Previous chapter
(The formative years: Berlin 1928-33 )
Contents Next chapter
(Edinburgh: 1936-8 and thereafter)

JOC/EFR May 2009