Walter Ledermann: Encounters of a Mathematician


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Start of my academic career

Every four years, except for a rather long interruption caused by the war, the Edinburgh Mathematical Society organized a Mathematical Colloquium to be held for several days in the summer. The venue is St Andrews, where it is attractive to stay in the summer; also since the students have gone home, the spacious residential homes afford comfortable accommodation for the participants. Members of their families were welcome to join them, various entertainments and excursions are provided for those who do not wish to take part in the mathematical proceedings. The standard of the mathematical offerings is high. Usually some eminent British or foreign mathematicians are invited to give one or more lectures as part of the varied and stimulating programme. But the organizers do not neglect the social aspect of the conference. There are plenty of opportunities of meeting other participants and their families. In the evenings there are enjoyable performances of chamber music by members of the conference. The quality of string quartet playing rivals that of the mathematical lectures offered earlier that day. On one occasion a complete Bach Cantata was presented in which Edge sang the solo part and Schlapp played the double bass instead of the cello, which was his usual instrument.

One such colloquium took place in July 1938. Dan Rutherford had been appointed local secretary. He invited me to be an assistant secretary, which I was very willing to do. The invitation to the foreign visitors and most of the programme had already been arranged by the senior members of the organizing committee. I was mainly concerned with the social and domestic aspects of the conference. But the experience was valuable to me

Shortly before the Colloquium started, Professor Turnbull unexpectedly asked me to see him. He told me that a member of his staff had decided to leave at rather short notice and he invited me to fill the vacancy. Of course, I was delighted to receive this offer; but then he added: "I have to tell you that the post is in applied mathematics; so most of your teaching will be in applied mathematics." My heart sank and I replied meekly: "But I do not know any applied mathematics." With the greatest regret I thought I ought to decline this highly tempting offer. However, Turnbull consoled me: "This does not matter, Walter. We are now at the beginning of July and term does not start until October. So you have plenty of time to prepare your lectures on applied mathematics." With his encouragement I accepted the offer most gratefully. A few days later Professor Turnbull confirmed the appointment in a hand-written letter covering two full pages. I should like to quote some passages from this letter, as it was characteristic of Turnbull's kindness and caring attitude towards young members of the profession.

The University
St Andrews
16.7.38
W. Ledermann Esq Ph.D.

My dear Walter,
Following our talk the other day I have much pleasure in formally offering you the post of Assistant in the Mathematics Department here for the coming year from October 1938 at the salary of £ 325. The position is for one year in the first instance, & is capable of renewal. It will involve from 8 to 10 lectures or tutorials a week in mathematics pure and applied ... .
I naturally look back on my start at lecturing in thinking of your present position. My first post outside Cambridge (where I gave one course a term) was at Liverpool & involved at least 3 sets of new lectures to be prepared, & in one term 4 sets ... .
I hope you will have a good holiday in Wales with your brother. Please give him my kind regards. Llanfairfechen on the coast is a good centre for combining sea & hill walking ... .

With best wishes
Yours very sincerely.
H. W. Turnbull

It was courageous of Turnbull to offer me the appointment, In 1938 I was still a foreigner -- and a "German" to boot. My situation as a refugee was not generally understood. I remember that, shortly after I obtained the Ph.D. degree, the Professor of Philosophy, who was a kindly gentlemen, said to me: "You were welcome to take the doctorate here; but now we expect you to go home." I was told later that, when the Senate of the University met again after the summer vacation, Turnbull was severely criticized by some of his colleagues who insisted that "we want our own people." There was even a rumour that at one point Turnbull indicated that he would resign from the Regius Chair of Mathematics at St Andrews. Fortunately, no action was taken although I sensed a coolness towards me on the part of some senior members on the University. In fact, my appointment was renewed each year until 1945 when it was made permanent.

During the next two months I immersed myself in the large text-book literature on Mechanics in order to prepare the required lectures and tutorials in applied mathematics. I was familiar with the general principles of mechanics, which I had learned from lectures by R. von Mises in Berlin. But I had no experience of solving complicated problems involving various objects sliding down an inclined plane or elastic spheres being in collision. By looking at examination papers of previous years I realized that this was precisely what I had to teach my students. It became clear to me that there was a fundamental difference in the training of students of mathematics in Britain and on the Continent. To put it succinctly, perhaps with some bias and exaggeration, I am tempted to say: German students are taught to talk about mathematics; but British students are trained to do mathematics.

I hope I discharged my duties as a teacher of applied mathematics in a satisfactory manner. I liked my students and enjoyed the friendly atmosphere in the mathematics department. But I have reservations of the subject, to my mind, mechanics, which is what applied mathematics is really about, forms a very important part of physics, a study of the laws that govern the motion of material objects. To be sure, these laws are expressed in the language of mathematics. But we must guard against confounding form and content. Mathematics is used in many other disciplines. The modelling of market risks requires quite sophisticated mathematics; yet, our students are not taught the principles of financial management. It is true that there have been persons, the outstanding example being Isaac Newton, who were masters of both mathematics and physics. But this does not justify the demand that every mathematician must be proficient in physics or even in parts of it. My view is that while physics has a great deal to do with mathematics, mathematics has nothing to do with physics. Many treatises on psychology are written in English. But this does not mean that students of English literature have to master psychology.

Although the bulk of my teaching was in applied mathematics, as I was told at the time of my appointment, I was pleased that occasionally Professor Turnbull allowed me to give a course on pure mathematics, which I enjoyed very much more. In 1938 the Department consisted of five persons: Turnbull, the only Professor, E. T. Copson, who later succeeded Turnbull in the Chair, Dan Rutherford, Geoffrey Timms as Lectures or Senior Lecturers and myself. Timms was a quiet man who was very reserved. He was a geometer of the classical school Dan was the senior member responsible for applied mathematics, although his doctoral dissertation, like mine, was on an algebraic topic. I once heard a colleague in another University mock St Andrews as the place where applied mathematics is represented by two algebraists. The teaching load for the five faculty members was heavy because the degree course at a Scottish University extended over four years. The four stages are referred to as General Class, Special Class, Junior Honours Class and Senior Honours Class, each having separate lectures, exercise classes and examination papers. With so much effort expended on teaching and examining it is not surprising that research did not flourish as much as one might have hoped. There were only few post-graduate students and we had no regular research seminars. Occasionally members of the faculty reported about their research: Timms and Turnbull speaking about topics in geometry. Regrettably, I derived no stimulation for original work from my colleagues at St Andrews. Perhaps I was too much occupied with my teaching duties. Also, just over one year after my appointment war broke out and I was engaged in some war work (to be described in the next chapter), which I carried out in addition to my university duties.

I enjoyed lecturing and I was always pleased to meet my students and to get to know them individually and to help them in the exercise classes.

My mind went back to the time when I was a student in Berlin. I remembered how much I benefited from reading the pocket-sized (10cm by 15cm) books of the Göschen Sammlung, each of about 180 pages bound in dark-yellow cloth. They contain some excellent volumes, e.g. two by H. Hasse on Algebra and two by K. Knopp on Complex Analysis. I always carried one of these booklets in my pocket and read it during the dreary railway journey from my parents' home to the University. It occurred to me that there did not seem to be a similar set of mathematics text-books in English (the Methuen Monographs were mostly about Physics). I made this observation to my friend Dan Rutherford. He was interested in the idea and discussed it with the Edinburgh publishers Oliver & Boyd and it was agreed to launch the blue series University Mathematical Texts. On reporting to me the successful outcome of his negotiations Dan added: "Although it was your idea, Walter, you will understand that we will not put your name on these books. People will not like to see a German name on them. I have therefore asked Alec Aitken to be one of the editors. (However after the war I was asked to contribute a book on Group Theory to the series.)

My time at St Andrews, 1938-46, included the whole period of the Second World War and was therefore dominated by the terrible events that happened here and elsewhere. Initially, at a personal level my anxiety was increased by the fear for the safety of my parents who were still living in Berlin until September 1938 when they were able to join my brother and me in Britain.

Despite the deep shadow which the war cast over all of us, I also had happy experiences and, generally, was content with my life at St Andrews. Quite frequently, Dan invited me and other friends to make excursions into the Scottish Highlands. We stayed at Youth Hostels and mingled with young people. I was greatly impressed by the beautiful scenery and I enjoyed exhilarating hill walks. Later on Dan rented a cottage in Glen Lyon in a remote part of Perthshire. It was a cosy little house with accommodation for four persons. It was only on rare occasions that Norah (Dan's wife) stayed at the cottage. Usually, Dan invited two or three friends to make up an all male mathematical party. The main room, which served as kitchen and dining room, was fitted with a "black board" consisting of a large piece of dark linoleum nailed to the wall. After dinner we sometimes had a mathematical session in which we discussed special problems or read together a text book on a less familiar topic. But for the main part a stay at the cottage was intended as a holiday with walks and other recreations. Although food was rationed during the war, we had enough to eat. Nevertheless, some supplements were welcome. Dan was a skilful angler. He had permission to fish in the nearby river and often brought back some sizeable trout which made a delicious dinner. One day, unwisely, I asked for the loan of a fishing rod and went down to the river to try my luck at the sport. But my attempt at casting was so clumsy that the line rebounded and the barbed hook got embedded in my finger. Dan had to call on the gamekeeper in the neighbouring estate, who came to the cottage and freed my hand from the painful injury.

One morning, all of us who stayed at the cottage went for a stroll in a nearby wood. I noticed a large cluster of yellow mushrooms under a tree. I am not an expert on mushrooms; but I knew that this particular kind, called chanterelle, was edible and in fact very tasty. It is quite popular on the Continent though rarely seen in British shops, as it is widely believed that all mushrooms, except the white meadow mushroom, are poisonous. As we were filling a hat with the yellow chanterelles, the farmer observed us from the other side of the river and shouted across: "What are you doing?" Dan answered: "We are picking mushrooms for our dinner." The farmer asked: "How many are you at the cottage?" Dan said: "Four." And we received the decisive answer: "I shall send four coffins to the cottage to-morrow." When we got back to the cottage with our harvest, Dan was a little skeptical. Perhaps he thought the farmer has a point after all. So he said: "Let us fry the mushrooms. Walter will have some for his tea. If he is still alive, we shall all eat the rest for our supper."

There was a flourishing musical life at St Andrews with numerous participants from both the "town" and the "gown" sections of the community. Being a small town and outside the main line of communication, St Andrews was not visited by professional orchestras or operatic companies. So music lovers were all the more encouraged to make their own music. There was an annual amateur performance of the Messiah, in which I played the viola. I met several good pianists with whom I played violin sonatas. But my greatest pleasure was to play chamber music, usually as second violin, with a group of competent amateurs. On a few occasions the Music Department of the University arranged visits from celebrated artists. I remember a recital by Myra Hess. It was my duty to provide her with a piano stool; she was not easy to please and rejected my first offer of what I thought was a suitable piece of furniture. A visit from the Griller Quartet was a great joy. It was one of the finest performances of chamber music I have ever heard.

In 1939 the University of St Andrews decided to establish a department of astronomy. A modern observatory was to be built near the University with facilities for teaching and research. The person who was to be in charge of these developments was Erwin Freundlich. At the time of his appointment to the post at St Andrews he was already in his mid-fifties and had a world-wide reputation as an astronomer. Freundlich was not Jewish. His father was a German business man. His mother was British; her maiden name was Finlayson. When he settled in St Andrews, he added "Finlay" to his name, which is a Scottish name and he was henceforth called Erwin Finlay Freundlich. However his wife was Jewish. Moreover, when his wife's sister died in 1933, they adopted her children.

It was therefore to be expected that his wife and the children would suffer racial persecution under the Nazis. Freundlich decided to leave Germany and like a number of other senior German academics who were affected by the racial laws of the Nazis, he accepted a position at the University of Istambul, where one of his tasks was to supervise the building of a modern observatory. Although he was well paid, he found the conditions uncongenial. It seems that professors were treated in some ways like servants. At the end of the semester he had to fill in a form giving an account of his work. One of the questions was: "How often have you been late for your lecture?" to which he replied proudly: "I cannot be late for my lecture, because my lecture begins with me." Evidently, a sense of humour was not a strong point with the administrators of the University: he was ordered to appear before the Principal and apologize for the insulting the authorities,

Not surprisingly, Freundlich was pleased to accept an invitation from the Charles University of Prague, where he was asked to help with the construction of an observatory. However, his stay was cut short by Hitler's invasion of Czechoslovakia. He fled with his family to Holland where he received the offer to come to St Andrews and, for the third time, was asked to help with the construction of an observatory.

Although Freundlich was twenty-six years my senior, I felt close to him from the beginning. The fact that we were the only two persons with a continental background brought us naturally together in the first place. He was a fatherly friend. I often visited him and his wife in their attractive house on the outskirts of St Andrews, which was adorned by a striking oil painting of Freundlich by Max Pechstein. On one occasion Freundlich and I went for a holiday to an island on the West coast of Scotland, when his wife was unable to go with him. He was a tall impressive looking man. When we walked from the observatory back to the centre of the city, people would say: "Here comes the Sun and the Moon."

Freundlich was a keen and able cellist. We played piano trios in his house with an excellent young pianist. But our greatest joy was to play string quartets or sometimes string quintets in the house of a Scottish clergyman, who played the viola. The quartet was led by Mary Lakeman, a student at the University. She was an excellent violist, very charming and much admired.

Freudlich had a remarkable academic career. After obtaining his doctorate in pure mathematics at the University of Göttingen he was engaged as an assistant to Einstein at the Observatory near Berlin. Contrary to popular belief Einstein was not a strong mathematician. His genius lay in having a profound intuitive understanding of laws of physics that had not previously been thought of; but he required the services of a mathematician ("my tame mathematician", as he called him) in order to express his ideas in rigorous mathematical terms. Freundlich told me that one day Einstein came to his office and expounded some of the ideas of his General Relativity theory, on which he was working at that time. Einstein suggested that geometrical relations in space would not follow the Euclidean pattern and that, for example the shortest distance between two points would not be the straight line joining them but a certain curve. Freundlich said: "Professor Einstein, what you have described is known to mathematicians as Riemannian geometry. It was discovered more than fifty years ago by Bernhard Riemann and developed by him." Einstein was so flabbergasted by this revelation that he blurted out: "Freundlich, you are a liar." But Freundlich made his point by going to the Library and producing a copy of Riemann's original paper. Ever since then, it has been accepted that the General Theory of Relativity is formulated in term of Riemannian geometry.

Freundlich's main interest throughout his life was to test the predictions of General Relativity by direct observation. One of the effects predicted by the Theory is the Light Deflection: if light from a star passes near the sun, then its beam will be deflected by 1.75 seconds of arc. Of course, normally a star near the sun cannot be observed during the day, because its light will be obliterated by the much brighter sun. But such an observation will be possible during an eclipse of the sun. In 1929 Freundlich led a well equipped and carefully planned expedition to the Indonesian island of Sumatra where a suitable eclipse of the sun was due to occur. However, to his surprise and embarrassment, the observed light deflection was equal to 2.2 seconds and thus substantially larger than the value predicted by the Theory. Unfortunately, several attempts to determine the correct value by repeating the observation elsewhere were frustrated by bad weather. As far as I know the matter remained undecided during Freundlich's life. The evaluation of the observed data requires a fair amount of mathematical manipulation, which Freundlich explained to me. I was able to offer some technical contributions. These were published in our joint paper The problem of an accurate determination of the relativistic light deflection -- my only modest foray into the field of astronomy. Whatever are the academic merits of this paper, it was of the utmost importance in my personal life, as I shall relate later.

The experiences I had while I lived in St Andrews 1938 - 46, were very precious to me. I am grateful for the friendship and kindness I received and I enjoyed my work at the University. My attachment to Scotland has remained undiminished throughout my life.


Previous chapter
(Edinburgh: 1936-8 and thereafter)
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(War experiences and marriage )

JOC/EFR May 2009