# Ledermann's St Andrews interview

We interviewed Walter Ledermann in St Andrews in September 2000.

Part 1: Parents and upbringing

EFR: Could you tell us something about your parents.

My father was born in Berlin, although his father came from a part which is now Polish and he was originally a schoolteacher. Because in my father's school there were both Polish and German speaking children, my father was bilingual. I never met my grandfather because he died the year I was born.

My parents, my father certainly, entirely felt himself to be German. He had a German name, and was born in Berlin. In the First World War he was called up as a doctor in the medical service, became a captain in the army, was sent to the front in Belgium and France, and so on. He was a very patriotic German, and whatever he saved as a doctor he bought German Government bonds to support the government. Then came hyperinflation in 1922 when money was completely wiped out. In the end, after one year, the new currency was introduced at the rate of 1 to $10^{12}$. One billion old marks was one new mark.

Then my father got a letter from the bank where he had been saving his assets, saying, "Dear doctor we have, of course, all your savings, your Government bonds etc, and if you would be kind enough to come here and collect them, we will be at your disposal. But we cannot send them to you by post because their total value is less than the stamps ..."

So my father, at the age of 55, was a total pauper and he had to start again. I remember I was about 11 years old and had already started violin lessons. My mother found out that one of the professors at the High School for Music in Berlin, who would normally only take professionals, would be willing to take anybody for the money. So I was introduced as a boy of eleven to this Professor - a man with a long white beard - I was terrified of this man.

When the year was over the new currency was introduced and the old one was of course totally worthless. But I collected the banknotes to play with my friends - snakes and ladders where you put money - and I still have these notes to this day. I have a whole shoebox full of these inflation banknotes of that one year. Some of them are very interesting, for example the Germans were silly, they had no sense of direction. They made elaborate designs on 500,000 mark notes with Martin Luther, or whatever picture, but by the time they had finished the design the notes had become completely worthless so they printed across in red letters 5 million marks and I have this today and this is how it went on.

After that year my father was completely impoverished. I remember we had to pay a little each year for school fees, not much - about 5 marks. My father didn't have that. He asked one of his patients, a banker, "Can you lend me 5 marks please, I have to send my boy to school and I haven't got five marks". So this man, the banker, paid my school fees.

EFR: Did you had enough to eat?

We had enough staple food which you could buy and my father got money as he went along. Sometimes my father's patients didn't have enough money to pay and they gave him a sack of flour. One day he got 5 kilos of salt which is not much use but he brought this home. Once he even got a live chicken! And that is how we lived.

Gradually he had enough income. He got a regular salary, he was engaged to look after the very poorest people, who were so poor they couldn't even pay the National Insurance stamp. So he got a small salary for being a paupers doctor. He was very popular, everybody knew him and as he went along the streets everyone said "Good morning, doctor."

We benefited to some extent from his popularity. One of his patients was a taxi driver, who had his taxi nearby and took this taxi to the centre of Berlin on business in the morning. But it so happened that going to the centre passed my school, so he picked me up at 8 o'clock in the morning and he dropped me off at the school which was only one mile away, I could easily have walked. All my school mates were terribly envious because Ledermann comes in a taxi! It was a school in a rather poor district and nobody had a car, of course. My father never owned a car, he did his round with a coach and horse.

EFR: Was this where your first interest in mathematics came, at that school?

Yes, at that school when I was then about 10 or 11, it was 1920-21. That was the time for us to have our first lesson in mathematics. Latin started at age 9, then Greek came later on but mathematics at age 11. But there were no teachers to teach us mathematics for they were caught up in the First World War and had not been dismissed, and so the mathematics teaching was undertaken by the arts master, who taught us drawing but, of course, he was not a mathematician. But he read up a little bit of Euclid from the textbook so that he could tell us about triangles and whatever that he had learnt himself. Then he came to this theorem, that the sum of the angles of the triangle is exactly 180 degrees, and this should be true for any triangle at any time in the future. I was so impressed by this universal truth, which wasn't in itself absolutely world shaking, but it was something which was absolutely true and at that time, at age about 11, I thought I would be a mathematician! Something that was absolutely true, not like a religion or something you have to believe.

EFR: Mathematics didn't come from your parents then?

No, my parents were not at all mathematical. My father was like me, educated in the classical tradition. His Latin was so good. In those days doctors would use Latin phrases when conversing with other doctors so that patients would not understand. They would meet, two doctors, and discuss a case and speak in Latin.

JJO'C: Even until comparatively recent times they would write prescriptions in Latin.

When my father went to the war in 1915/16, and I was already starting school, he wrote me letters in Latin. They were delivered by the Red Cross from where he was working at the front in a military hospital. He was very fluent with his Latin. So, at age 9 we started 6 lessons a week in Latin. I remember one day the Latin teacher couldn't come and we were taken by the deputy headmaster, who was an old professor, and he said he would not teach us anymore but he would tell us some fairy tales, the seven dwarfs or that type of thing, but he would tell us them in Latin. He told us these fairy tales, which we knew, Cinderella etc in Latin.

Then came Greek and French but I couldn't manage French very well. I was sent to France once as a schoolboy - this was also quite ironical. In those days the League of Nations quite rightly tried to make peace between the German and French nations, who had been fighting each other for centuries. They thought, probably quite rightly, one of the ways would be to change the children from each nation. So they sent circulars round for people volunteering to go on the exchange. Ironically they decided that I was a typical German boy and they selected me to go to France on this peace mission; I was 15 then, it was 1926. I was sent to the home of a French chemist, they couldn't find a doctor like my father, but the nearest they could find was a pharmacist and I went to Châlons-sur-Marne, one of the cities in the eastern part of France, and I stayed with that family and even went to school there because their school holidays started later than ours. I went to school with Pierre, my exchange student of my age, I went to mathematics lessons in French and even to the German lesson. Finding I could speak German fluently, I was very popular with the teacher who taught German!

EFR: How long were you there for?

About 5 or 6 weeks. We would cycle together in this part of France; this part was devastated by the First World War. We saw the Marne, the city, and the military cemeteries which were kept very well by the government. It was absolutely shattering; we went with our bicycles to the cemeteries and there would be 20,000 or 30,000 graves of allied soldiers with white crosses, sometimes with consecutive numbers, New Zealanders, British, Canadians. Then there was a hedge and behind it black crosses, these were the German soldiers that had been killed.

EFR: Of course this is what Aitken had gone through.

That's right. And when I saw this, I was only 15, I formed the opinion that France would never be able to fight again. It was a broken nation, physically and mentally broken by this experience. When Hitler came, so many German Jews very stupidly went to France because that was the cultural centre of Europe. I said I will go anywhere but not to France -they were a broken people and would not stand up to Hitler.

You asked about my parents. Yes, my father was a very busy doctor. My mother was brought up in a very German household. She was Jewish but did not go to the Synagogue because she was an orthodox Jew and in the Synagogue men and women had to sit separately, and she said she would not do this, she protested about this. Even her father, a well to do business man in Berlin - quite a wealthy man - remained Jewish but completely assimilated and when my mother was sent to school, a girls school of course, the Jewish girls there had special instruction with a Hebrew teacher to teach them Hebrew prayers. Her father wrote a letter to the headmistress saying "I do not want my daughter to be sent to the Hebrew class - if she wants to pray to God she can pray in German." She remained very German and was well versed in German literature and used to recite long poems to us in German, Goethe etc, everything in German.

EFR: So, when you were at school you became interested in mathematics, and then you trained as a schoolteacher?

Yes, that's right. I was good at mathematics and also good at Latin, so good at Latin that I skipped a whole semester and when I left school, with my certificate of maturity, I was only 17.

Part 2: Undergraduate university career

Throughout my first semester at University I had still not reached my 18th birthday. I was very lucky because I had finished before Hitler made it impossible. Anyway, I was good at classics but I was even better at mathematics and I was enthusiastic about going to be a mathematics student in Berlin with Erhardt Schmidt and so on. There were two ways open to me. Either to take a PhD, which was not then a postgraduate degree, you could go straight for a PhD on entering University, or you could go to be a school teacher and do the state diploma, which was to be the scientific part of it, later to be followed by teachers training which was completely independent. My father, quite rightly, said "You are only 17, you don't know whether you will ever be able to write an original research paper on mathematics or a dissertation and you must have a profession, you must have a living. You can't be sure you can make a living as a University Don. So, you will become a schoolmaster." Therefore I entered university to become a schoolmaster. However, the academic side was almost exactly the same as that for a PhD candidate, worse even. For a schoolteacher you had to do two subjects to be fully trained, in my case mathematics and physics, whereas a candidate for a doctorate would only do mathematics. A PhD candidate could do physics if he wanted to but for me it was compulsory - I was forced to do physics. I had no knowledge of physics because at the school where I was taught we had virtually no science.

EFR: And this is where you were taught by Planck.

Yes and Nernst. Nernst taught experimental physics and Planck theoretical physics, and later Schrödinger, and there was another physics lecturer who was a good teacher but not a famous researcher.

EFR: These were very famous physicists.

Wielandt was great company. He would be always dreaming about something. He would be walking along dreaming that one day he would prove Herr Fermat's theorem, or this or that other conjecture. He was also a very good mathematician. He worked with Schur and he was a doctoral candidate, but the lectures we attended together, Wielandt and I. He was a German of course and stayed behind when I left. He was drafted into the German army and I believe he had a very bad experience. I think he went to Russia and I believe he suffered a nervous breakdown. When he came back after the war, he visited Britain and America quite frequently and one year he went to Warwick. Maybe you were even there then. (EFR: Yes I was there at the time.)

They put him up in Warwick at a hostel which was adjacent to the Students Union and he could not bear the all night concerts/ discotheques. He was very musical and he played the violin very well. The loud music drove him mad. He turned up at our home in Brighton in Sussex. He said, "I am staying in Warwick but at the weekend I just cannot bear to be there!" He asked if he could stay with us! We put him up, we had a large house. We went on Sunday to the sea front in Brighton and exchanged memories and so on. My wife would talk of her psychiatric work (she was a Jungian psychoanalyst) and she talked a little bit about her work but Wielandt stopped her because of his own personal experience. I think he spent some time in a mental hospital. He had a breakdown. He said, "You don't have to tell me, I know from inside this sort of thing." That's why he couldn't bear the noise from the Union. He was very nervous and highly strung. He stayed with us and he gave us a nice present, I still have it - a Mozart string quintet record.

EFR: Schur had the biggest influence on you?

By far, I was absolutely captivated by Schur. I wrote about 300 lectures in fair copy in cloth bound books which I had until quite recently, running to something like 2000 pages of Schur's lectures. Only two years ago, when we had the International Congress in Berlin, they were very kind to me there, I donated them because nobody could read them. Not only were they written in German, they were written in Gothic script, which even Germans can't read now. I can even now and it was quite useful. Have you come across the book by Charlie Curtis about the pioneers of representation theory? I transcribed the letters of Emmy Noether who wrote to Richard Brauer, postcards, even letters about their work. They were written not only in German but in Gothic script and nobody could decipher them in America because the German émigrés they had there were younger people, and Charlie sent them all to me and I translated all the letters. Some were very interesting, so I gave these letters to the Library in Berlin, the Humboldt University.

Only the other day I found that I still have the set of exercises which Schur gave us for his course on determinants and matrices which may be of interest to you for your linear algebra. I picked them up only yesterday. He gave exercise classes, which were compulsory, once a week. He came in, he wrote on the board maybe six problems in his own handwriting and sometimes when it was a difficult problem he said, "This is quite a difficult problem" and made one sloping line against it. Very rarely, perhaps once a year, he would set a problem which was really difficult and he gave it two sloping lines!! Those of us who were ambitious, we worked there the whole week and we to hand them in. Exercises were never done on the spot, we had time to do them at home and then hand them in. He did not mark the exercises or discuss them, this was done by Alfred Brauer. So when Schur had given the exercises, after 20 minutes or so, he left the classroom and Alfred Brauer took over. He went over the problems from the previous week and very seldom, when somebody had given a really good solution, he was called on to go to the blackboard and show it to the other people. It was a frightening experience, standing there in front of 200 to 300 people. I owe a lot to Brauer, he was very careful, meticulous, and I still have the remarks he made. Some are standard problems on determinants, but others are quite tricky things, about matrices and so on. This is how I learnt this from Schur, and other topics like invariants and other things.

Every year Schur gave two courses, one elementary and one more advanced. There would be determinants and matrices, he did not use the term linear algebra, and also the theory of ideals, algebraic numbers and so on, or invariants, or some advanced work on algebraic numbers and ideal theory. Then there was Galois theory, group theory, and so on. Covering the whole field from the most elementary bits about matrices and determinants right up to quite difficult things. Then, in my very last year (1932), just before the Nazis came to power, he gave a course for the first time on representation theory, and group characters, which at that time were not at all part of the syllabus. I wrote this out as well. This was quite valuable and I gave this to Charlie Curtis when he wrote his book The pioneers of representation theory.

He had in front of him my set of notes and I remember Schur saying that this theory of group characters, originally purely an algebraic theory due to Frobenius and Burnside, nowadays has become even the object of some interest to applied mathematicians even to so called chemistry, using the symmetry of molecules! I believe they used even character theory. This was 1932 and I finished the course when Hitler came.

Part 3: The Nazis and escape

EFR: After the Nazis came to power, what did it feel like?

It was terrible. Of course, I had seen it coming. For me it was not a surprise. I had been sufficiently well versed in the history of German anti-Semitism, going back to Martin Luther who already advocated something like genocide. He said the Jews should all be locked up in their synagogues and the synagogues set alight. That was about 1520. And then Richard Wagner who wrote this notorious pamphlet about the Jews where he tears Mendelssohn's music to pieces saying that it has no value, it is for insects. All this I knew perfectly well. The only time I was away from Berlin was to do my chemistry lab in Marburg (1931, I think). Nobody spoke to me except one boy whose father was a general in the army. He was very nationalistic but because he was an aristocrat he didn't like the Nazis who were plebeian to him. He would sometimes go for a drink with me. Everybody else was Nazi and wouldn't talk to me at all. When Hitler finally came to power, all the Jewish faculty were dismissed instantly, including Schur who was not allowed to come even to the library any more.

However Erhardt Schmidt, who was the decent sort of German, found that in the regulations of the Nazis there was a clause to say that these dismissals would not apply to two types of non-Aryan:

1) those who had fought in the First World War in the German army on the front, and

2) those who had during the First World War held a position making them German/Prussian civil servants.

The first of these applied to Alfred Brauer who had been a soldier (EFR: He was wounded), and yes, he was badly wounded, and the second applied to Schur because in 1916 he was an extraordinary professor at Bonn, so had effectively become a Prussian civil servant.

So, Schmidt applied this clause. He went to Goebbels and said, "You must abide by your own law and reinstate Schur for this reason", and he was reinstated. He could then come to the University but he was not allowed to lecture. For supervision of my dissertation, I had to go to his house. It was nice to meet with him, he lived in a suburb of Berlin, to see him and his wife and talk not only about mathematics but also about the Jews. He said, "I can read the English Times which is still allowed", all the other papers were taken over by the Nazis. I cannot bear this. And then the time came for me to have my exam, the oral, and he was allowed to come to take this examination in mathematics for one hour. Also, a co-examiner was expected to come. They did not normally ask questions but would take a record, more like a secretary. This co-examiner was, unfortunately, none other than Bieberbach, who appeared in Nazi uniform, brown shirt and swastika. He came and sat down to take notes about what Schur was asking me. But I must say he was quite fair. He didn't interfere and I got a very good result.

There was no Faculty of Science in Berlin at that time, so anybody who was not a Divinity or Jurisprudence or Medical student or Chemist had to pass an examination in Philosophy. This was a half hour oral exam, which was a big problem for me because I was told that all the professors of Philosophy had become Nazis, or sympathisers of the Nazis. There was one professor at the Technical University who was also an examiner, a man called Meltser, who was a Roman Catholic so probably not a Nazi. At the beginning the Roman Catholics had their own party, called the Centre party, who were not directly connected with the Nazis, and in fact some of them even opposed them. So, I went to Prof Meltser and asked if he would take me on as a candidate. He said, "You're a mathematician, all right, you have to read certain books on philosophy, then I will take you on". I did read the books of course, and he came at the set date six months later, in November 1933, to examine me. For some reason he was held up by traffic, he was late and very nervous. I was the first candidate and he apologised for being late. He said, "Yes, I remember you, you are a mathematician, and now this mathematical logic, which you are studying, would you say because of this, the traditional logic of Aristotle is now invalid?" Now I knew what he meant. Being a Roman Catholic, his church's theology was partly based on Aristotle's foundation of logical theory, and he was afraid that we had undermined his beliefs. I said to him "No, the philosophy of Aristotle is different from ours, but it is not invalid, it is similar." He said, " I've always said that -- I'll give you Grade 1, next please!"

So, I got through my Philosophy using psychology rather than my knowledge of Philosophy, which I'm afraid was very meagre, but I knew what he meant, so I got through.

By this time it was November 1933 and I was desperate to leave, and within a few weeks, fortunately, I got this scholarship from St Andrews. I had never heard of St Andrews. I took a big atlas and thought where is this place that I have never heard of and how do I get there. I knew they spoke English there, so I rapidly took some lessons from a friend of my mother who was an English teacher.

[At this point we have inserted a description of events which took place at this time which Walter told us about during his visit to St Andrews in September 2000 but was not part of the taped interview.]

It was Walter's brother who was studying medicine in Edinburgh who heard about the St Andrews scholarships. There were two scholarships, one for a Jewish student from Germany and the other one for a political refugee. Walter's brother quickly wrote to Walter telling him about the scholarships. They were administered by the International Student Service in Geneva and Walter applied. These were scholarships for any subject at St Andrews University and Walter won the scholarship for a Jewish student from Germany.

On the last night before he left Berlin Walter said to his father that he would like to attend the opera. The performance did not begin on time, a most unusual thing to happen. Then Walter found why there was a delay. Hitler came in and sat down. Still the performance did not begin and it was not until Goebbels and Göring also came in that the opera began. They did not know that one of the main parts was sung by a Jewish singer!

On the following day Walter took a train to leave Germany. The journey was certainly not uneventful. Two men in the same carriage as Walter had been overheard by a Nazi as speaking against the regime. They were removed from the train by SS men who told the others in the compartment, including Walter, to throw the men's luggage through the window. There was no further conversation in the carriage for the rest of the journey. Walter heaved a huge sigh of relief when the train reached the Dutch border.

[At this point we return to the transcript of the taped interview.]

My father stayed behind and then more and more his life became impossible. He was not allowed to practice medicine anymore, except for Jewish patients, but soon there weren't any, and then one day he had an accident and he was knocked down in the street by a car. He didn't drive -- he was a pedestrian -- but the car broke both legs and he was taken to hospital. My mother, who was quite a bit younger, took the opportunity to get everything packed together in a transporter. You were not allowed to take money, but you could take furniture and books and personal belongings, and she got the transporter to take all these things to the ship and they sailed from Hamburg , and eventually arrived in Southampton.

Unfortunately the ship was a bit late, so they had to spend the night in Southampton in a bed and breakfast. They were allowed to take ten shillings out, everything else was confiscated. So, they arrived with their ten shillings in Southampton. Their B and B was 7/6d and they arrived at Waterloo station with half a crown - that was all they had. Fortunately I was already a lecturer here at St Andrews, in 1938, and my brother was a doctor in a medical practice in London. We were able to get our parents a little flat in North London where they were accommodated until the war became so bad that they were evacuated to Oxford during the bombing. My father survived and they returned to London. Not only that but at that time, during the war, there was a shortage of British doctors. The young doctors who were medically qualified had all been called up to the army. The British Government relaxed the conditions on foreign doctors, who until that time were obliged to take medical examinations, even although they could do them all in one year. My brother had to do this. For the time being, during the war they were allowed to practice if they wanted to, and my father did. There were a lot of German Jews in the Hampstead area, there still are, and in some parts German was spoken more often than English, so he had a few people who consulted him, until his health broke down, and he died in 1949.

So he survived the war but he was never really at home here - his English was not good enough. He did read a newspaper, with a dictionary, I saw him every morning sitting there looking up every other word. Also the currency, there were 12 pennies in the shilling -- he couldn't understand that! I remember when he got his British citizenship his neighbour, an Englishman, said "Well, aren't you happy now you're British?" He replied, "I'm very glad, but I can't be happy, how can you be happy when half of ten is six!" He would think of sixpence as half a mark.

My mother spoke English quite well, but when my father died, she decided to go and join my two sisters in Israel. They had family, and she wanted to be a useful grandmother, so she lived there for the next 35 years. She lived until she was 97, but never spoke any Hebrew, only English and German. We visited, every other year. We went to Israel. She was in good health until almost the end. I remember visiting her near Haifa, where she lived, and I wanted to go and see Haifa, and she told me there was a bus. I said, "Yes, but how do I ask for a ticket, I don't know any Hebrew." "Don't worry", she said, "the man who drives the bus is a lawyer from Frankfurt!" So we still go to Israel, unfortunately my sisters have died, but we go to see their children, and grandchildren.

Part 4: In St Andrews

EFR: So, that was you in St Andrews in 1934.

When I arrived in St Andrews in 1934, I was completely bewildered. I was 22. I had never been to Britain before. I had virtually no English although I had taken a few lessons. I could just about read but I very soon made friends very soon with the Scottish students, some of whom studied German as a subject. So we practiced on our walks - on the way out, towards the river Eden, we would talk in German and on the way back we spoke English. I was taught by the students.

Turnbull, who was English, not Scottish, was very keen that I would not pick up any Scoticisms and every now and again I would say a Scottish phrase I had picked up from the students. He would be very severe and said, "You mustn't say that". I felt very soon at home. The faculty would invite me to tea; some were going on holidays and wanted to pick up on their German and we would do a little bit of conversation. I did this quite often. Turnbull, a very able and experienced mountaineer, at that time went to Switzerland almost every year. Even on one occasion he climbed the Matterhorn, which is one of the most difficult climbs, with a guide of course. But he never spoke a word of German. He was not a linguist at all.

EFR: It was quite fortunate for you then that Turnbull was working in an area which was reasonably close to yours.

Yes, Schur knew about Turnbull. When I told Schur that I was fortunate to obtain a scholarship to St Andrews he said, "Oh yes, there is Turnbull there". He knew about his work on determinants and also especially on invariants. Yes, that was very fortunate, and I was able to carry on with algebra. The way it came about was that this book by Turnbull and Aitken had just appeared and I went through it very carefully. There were one or two places where there were gaps or possibly things that could be elaborated. One of these things I picked on, it had something to do with tensors of matrices, quite a complicated problem which was not entirely correct, so I did my thesis on this Turnbull and Aitken book. It went alright -- took two years, I think. Yes, I was very fortunate. He tried me on invariants first, but I didn't fancy invariants. I don't know why.

EFR: So what was the system of examining PhD's? Was there somebody from outside St Andrews?

Yes, I don't know who my examiner was. It could possibly have been Aitken, I don't know. There was no oral examination. Is there now?

JJO'C: Yes

There was no oral exam for PhD's in Scottish Universities so I never met the external. Copson said one day "Your thesis was highly recommended, it's a pity we couldn't give you something else." Apparently it was well received, possibly by Aitken, I don't know, because there was no oral. I was given the diploma and I graduated. Then he said go to Edinburgh, Professor Whittaker might help you - and he did - I was so lucky. Every time I had a piece of luck. Whittaker advised me to broaden my mathematical interests and to attend lectures by Aitken on statistics. When that finished, Godfrey Thomson came along, introduced by Aitken, and then came this meeting in 1938, where one of Turnbull's staff left and he was in a fix. He appointed me; I was really lucky all the way through.

[Another insert of details given by Walter, but not during the taped interview.]

When Walter returned to St Andrews in 1938 he was appointed during the summer by Turnbull who now had a vacancy since a member of the St Andrews department had left. The appointment was not welcomed by everyone however and one member of Senate objected to the appointment of a foreigner. Turnbull had to go to the lengths of saying that he would resign if Walter's post was not confirmed before the protest at the appointment of a foreigner was ended. He attended the Edinburgh Mathematical Society Colloquium of 1938 in St Andrews (the last for a number of years due to the war). The previous Edinburgh Mathematical Society Colloquium had been held in St Andrews in the summer of 1934. Walter, arriving in St Andrews in January 1934, had helped with the organisation. Walter gave us lots of details of the participants of these two conferences as we sat examining the conference photographs.

It was while he was at St Andrews that Walter suggested a cheap series of books for undergraduates. His idea was taken up and the Oliver & Boyd series of mathematical texts was born. Despite being the one to come up with the idea Walter could not become an editor since it was felt impossible to have a foreigner take such a role.