One Hundred Twenty-One Days

by Michèle Audin

  We must confess that we have learned more about mathematics over the course of observing this patient’s behavior than we did at school.

  We should add that G.’s skill as a mathematician is recognized among the experts in the field. He summarizes the results of his research in articles that he then sends to specialized journals, which publish them. His articles appear to be read and used, because they are cited by several mathematicians in other articles that G. has showed us. In one of these articles, his name is associated with a theorem, “G.’s theorem”; another uses “G.’s constant.” Students have even defended dissertations in which they have answered questions raised by G. in his work. He keeps us informed on the day-to-day progress of his research and mathematics in general.

  We asked him if he would like to meet his mathematician correspondents—which we would have considered beneficial for this patient who has no real contact with the world—but he calmly refused, asserting his desire for peace and quiet.

  THE PROBLEM OF THE TWO RACES

  BY R. VON MISES, ISTANBUL

  (Matematicheskii Sbornik, Moscow, 1934)

  The example that follows is, by its very subject, of particular interest.

  In a country in Europe whose inhabitants number around 65 million, the population is composed of two races A and B, with respective figures of 0.9% and 99.1%. A very small number of these inhabitants perform scientific research in physics or chemistry. No absolute scale to measure scientific capacity exists. It is generally accepted that the winners of the Nobel Prize form a set of the highest values with this capacity. The list of winners from the years 1901 to 1933 includes 27 names from said county, of which 5 belong to race A.

  We will now address these figures with established formulas.

  […]

  From these calculations, we can conclude that there is a probability of about 85% that, among the individuals of race A, the probability of there being an eminent talent in physics or chemistry is at least 20 times and at most 42 times greater than in race B.

  EXERCISES IN MULTIPLICATION AND DIVISION

  (Matematisches Arbeits- und Lehrbuch, Neuenheim-Verlag, 1937)

  -The construction of an insane asylum costs 6 million Reichsmarks. How many detached houses at 15,000 Reichsmarks each could have been built for that sum?

  -The care of a mentally ill patient costs 8 Reichsmarks a day. How many Reichsmarks will this mentally ill patient cost after 40 years?

  PIERRE MEYER (interview, December 18, 2006, cont.). I’m the one who saved these two articles. But like me, Mortaufs was interested in what was happening in Germany. Bernadette told me about the little German girls with blond braids whom the family hosted during the International Exposition in 1937. There were also grand receptions in Chatou, with members of the French Academy, friends from the France-Germany Committee, sometimes foreign guests as well. Marguerite had a notebook in which she wrote down the menus for the dinners she gave. As for Mortaufs, he had been going to Germany since the early ’30s—he had some scientific contacts and many friends there. He traveled a lot, I think. Marguerite didn’t go with him, but with that whole household, what would you expect?

  CARMO’S CONJECTURE IN THE FINITE CASE

  NOTE BY A. SILBERBERG, PRESENTED BY C. MORTAUFS

  (Reports from the Academy of Sciences, Meeting of March 27, 1939)

  We prove, for Galois fields, a conjecture similar to the one proposed by Carmo in the complex field. From this we deduce a few corollaries and a few questions to which we hope to return in a future paper.

  PIERRE MEYER (interview, December 18, 2006, cont.). This is André Silberberg’s very first article. It may well also be the very first note Mortaufs presented at the Academy of Sciences. He was elected at the beginning of 1939. This article was found among Mireille Duvivier’s papers. The ones on Gorenstein, too. She must have gotten them from her mother.

  ASSESSMENT OF THE G. CASE

  BY J. MEYERBEER, PSYCHIATRIC DOCTOR, SAINT-MAURICE HOSPITAL

  (Gazette of the Association of Psychiatric Doctors of France, Vol. 47, 1939)

  In our previous articles (Gaz. Assoc. Psy. Doc. Fr. 28, 1920, Fr. Rev. Psy. Med. 11, 1930), we mentioned G.’s interest in current events. Here we will be content to make a list of the subjects on which he has commented for us over the years.

  TOPICS FROM CURRENT EVENTS ADDRESSED BY THE PATIENT

  Among these, the Paris Colonial Exposition of 1931, the choice of Hitler as German chancellor, the death of Paul Painlevé (a mathematician who didn’t retreat from our times, he commented), the riots of February 1934, the victory of the Popular Front, the start of the war in Spain, and the Olympic Games in Berlin.

  He was particularly taken aback by the interviews with Hitler published by certain newspapers. “Look, Doctor Meyerbeer, the journalist even had that fraud autograph a photo for him,” he showed us one day.

  In mathematics, the important step taken by a Russian mathematician towards demonstrating Goldbach’s conjecture was worth several explanations. “Doctor Meyerbeer, you know what a prime number is, right?” he asked us. Of course, and the patient knows that his therapist knows what a prime number is.

  MANICO-MELANCHOLICUS

  The patient shifts easily, unexpectedly, and rapidly from a dejected mood to one of happy restlessness, often while speaking on the same topic. This disorder, which is rather mild, seems to particularly manifest during our conversations. The racist politics of the ruling Nazi Party in Germany seem to depress him profoundly.

  “They’re going to exterminate us, Doctor Meyerbeer, you and me both. You won’t be able to escape,” he tells us regularly in a bleak voice. And sometimes, almost without taking another breath, he bursts into laughter while showing us a mathematics article in which a Jewish German scholar calculates the probability (which is very high) of a Jewish German being better in physics than an “Aryan” German.

  “But can’t you see it’s a joke, Doctor Meyerbeer? Don’t you know I can prove the same thing about psychiatrists for you?”

  We must admit that we do not always understand what makes him laugh (especially in mathematics). We considered giving him a lithium treatment, but the mildness of his disorder does not seem to hinder him, especially as we are certain that mathematics, and the fact that he can either find the subject funny or work on it seriously, is enough to bring him back to the side of euphoria.

  SAID AND UNSAID

  As the list above shows, for twenty years already, the patient has addressed a wide variety of subjects with us. However, it must be noted that G. has never spoken about the triple murder or his time in the war, either spontaneously or at our request. Every question concerning one of these subjects causes a brilliant and slightly exalted discourse to emerge on quite unrelated subjects.

  Apart from prime numbers, sardine fishing, the scientific dispositions of Jewish Germans, current politics, and, as always, succubi and other demons with blue eyes, here are a few examples of his assertions collected over the course of the years:

  “Doctor Meyerbeer, I am your Robert le Diable. Did you know that the real Robert the Devil passed himself off as a madman?”

  “My mother slept with the devil.”

  “There is a butterfly with my name—no, not G., Robert-le-Diable.”

  “My sister was the one born from my mother’s hideous adultery.”

  “I hate dogs. Because I loved a woman who preferred cats.”

  “I should write about you, Doctor. I would study the way you say ‘perfect’ every time I say something absurd.”

  In a feature article, currently in progress, we reveal in this case specifically (but also in several others) the connection between the murder of one’s father and the phobia of dogs.

  We will add that, since G. is an educated patient, he politely and carefully read our previous articles dedicated to his case. Although we thought we saw him hold back a smile, he did not make the slightest comment. Concerning an earlier version of the present article,
which we had hoped would draw him out of his shell, he corrected a past participle and made this single comment: “Excuse me, but I have things to do. I have to try to answer an arithmetic problem that a mathematics student asked me about. A brilliant boy, that Silberberg! You’ll hear more from him!”

  Thus ends the last of the articles saved by Pierre Meyer in the large manila envelope.

  CHAPTER IV

  Strasbourg, 1939

  (TRANSCRIPTION OF AN INTERVIEW WITH PIERRE MEYER, NOVEMBER 2006)

  In the large manila envelope, I had arranged—well, you may not find it very well arranged… I had saved articles from before the war that one person or another had given to me. You’re handling the chronology, right? One day, if you’d like, I could relate some of the things my wife told me about that period.

  But you wanted me to talk to you about Silberberg.

  Yes, I knew him well. We were students at Strasbourg together, until 1939. Yes, both in mathematics. André had passed the exam for his teaching degree in 1938. Then he had started working on a dissertation. After a few months, he had already obtained his first result, which Henri Pariset, his professor, had called “very important.” Pariset sent it to Professor Motfraus, in Paris. And Motfraus presented it to the Academy of Sciences.

  No, André didn’t know Motfraus personally, and for that matter, neither did I at the time. But if you don’t mind, I’ll speak about Motfraus at some other point.

  Where was I? Oh yes, André Silberberg’s note. We were both so happy! The Silberberg family even organized a little party when it was published. André’s parents weren’t scientists or even academics. You see, they were business owners, but their two children were in college. Yes, André did have a sister, named Clara. She died not long after the war.

  No one in the family, neither Clara nor her parents, understood mathematics, but you don’t need to know what a number field is to understand the honor of having an article published in a journal with your name printed underneath. I think André’s father had been rather disappointed that his son hadn’t tried to get into the École Polytechnique. At the party, he declared how relieved he was. And we all drank white wine on the balcony of the family apartment, overlooking the Ill River.

  André was brilliant, good at everything. Very athletic. He was the goalie on our soccer team at the university. He also won the silver medal in the 800 meters at the university track championship. In 1938, I believe. He trained almost every morning at the Vauban stadium. At that time, you couldn’t just go running out on the street. And he was a musician. He played the piano. You know Mozart’s Fantasia? He really liked Mozart.

  Yes, I was a student, too. Not as brilliant. And I had to work to pay for my schooling. Pariset suggested I work at the library of the Mathematics Institute. That way, I would earn a little money while being surrounded with books.

  Here’s what I wanted to tell you about. André, a few other students, and I formed a defense group. Yes, against the anti-Semites. In those years, signs that said “Forbidden to dogs and Jews” were appearing in the windows of more and more cafés and restaurants in Strasbourg. In French or German. You’re a historian, you must speak German. “Juden unerwünscht,” Jews are unwanted, it’s more elegant… They tried, a little more each day, to apply the bans that affected Jews on the other side of the Rhine to this side as well. Since Jews were the enemies of Hitler, they were called “warmongers.” A few months earlier, at the time of the Munich Agreement, there was even the start of a real pogrom against Jewish business owners. Fortunately, the shop André’s parents owned (and his parents themselves) had been spared. The atmosphere was terrible. We don’t have the right words to talk about that time. I’m not going to tell you the atmosphere was, I don’t know, “deleterious.” It seems to me that it’s up to people like you to invent words. Are you recording this?

  But I wanted to tell you about our “actions.” We ripped down more than one of those nauseating signs. Of course, this generally led to fights. But we were well trained. André even tried to teach me French kickboxing. We took a few serious blows now and again. One evening, we attacked the headquarters of a party pretending to be “Alsatian separatists”… needless to say, their autonomy was simply an allegiance to Nazi Germany. A real brawl followed.

  But we took the most serious beating during the attack on the bookstore. Does that surprise you? It was clearly a Nazi bookstore, the Volksbuchhandlung. We broke some glass, nothing major, but that time we had a little trouble getting away. The guards were pretty burly. André got a bit scratched up. Well, I say scratched up, but it was serious enough for him to need a doctor. We called Doctor Sonntag, who was the doctor for the Silberberg family, but also a professor at the school of medicine and a personal friend of Pariset’s. Have you heard of Sonntag? Sonntag sewed up what needed to be, at the hospital, but in a discreet manner. André, with his right hand bandaged up, couldn’t write anything for two weeks. He was quite pleased to find piano études for the left hand.

  Since I was telling you about that bookstore… I’m going to show you something. A book I snuck out with me, or rather confiscated, that day, and which by some miracle I still have. Since you read German, look at how they taught addition and subtraction in German primary schools in 1939.

  You see: they added the areas of the territories “we” had confiscated in the “Versailler Diktat.” That’s what Hitler called the Treaty of Versailles. Yes, of course, you know that already. Alsace-Moselle was part of it, for 14,521.8 square kilometers. Note the “point 8.” There are other square kilometers, with decimal points, in Belgium, Denmark, Lithuania, Czechoslovakia, without forgetting Danzig, and especially Poland. It’s very instructive: a big sum, with decimal points. And look at this one: subtraction, now. Before the war, the Reich’s territory was 542,622 square kilometers. You have to find the total area before 1938. Yes, they stop in 1938 because, by then, the conquest had already started, thanks to the Anschluss and the Sudetes. The book dates from 1939. Ah! The blue notebook. No, don’t take notes, it’s not worth it: if you want to look at the textbook in more detail, I’ll let you borrow it. There’s a whole series of exercises like this.

  But I was talking to you about André Silberberg. Didn’t you say you did some research in the Heinrich Kürz archives at the University of N.? Did you know that he came to Strasbourg, precisely in 1939? Yes, Kürz. And that he had a discussion with André Silberberg? Let me tell you about that. He came to speak at Pariset’s seminar. He was an important guest; Pariset had promoted the talk in his class and invited all the students to come listen. So I went along with André. Kürz had just proven, I can no longer remember what exactly, but it was something very important in number theory. It was actually Motfraus who had invited him to give a series of lectures in Paris, and Kürz was stopping in Strasbourg on his way back. He was the Vice-Rektor of his university, you know, and for us there was no doubt he was a Nazi. Otherwise he wouldn’t have been appointed Vice-Rektor. I suppose Pariset went to pick him up at the station. What I remember perfectly is that they arrived together. I can still see them climbing up the monumental stairs at the entrance to the university. And I can still hear them, especially Kürz, who was speaking very loudly, and in German. Pariset was content to nod in agreement.

  André and I, in fact our whole generation, learned French at school. German was our mother tongue, the language we spoke at home. A lecture in German was no problem. Besides, I should say that Kürz was an excellent speaker and his lecture was fascinating. Even so, let’s just say he was perhaps a little too smug. At the end, there was applause, one or two questions, and then people started standing up and speaking amongst themselves. Pariset introduced André to Kürz: “As you may know, this is the brilliant young man who proved that…” But Kürz knew: “Ah! It’s you! Excellent work! They told me about you at the Academy of Sciences, where I was invited last week.” The professors then went to have a beer in a nearby brasserie. Pariset kindly invited André to come along with
them. Of course, the other students weren’t invited. So I didn’t go. But the very next afternoon, André came to tell me what happened.

  It was a Tuesday; the seminar was always on Tuesdays. At the end of the month of May, if I remember correctly. I should be able to find the exact date for you, if you’re interested. It was a beautiful late afternoon, almost a summer evening, that I can remember. So they went in the café, where there was another group of professors, historians, already sitting at a table with their steins of beer. It was the closest café to the Palais Universitaire, you always saw lots of professors there. I think it still exists. How well do you know Strasbourg?

  In any case, this café wasn’t displaying the notorious “Forbidden to Jews” sign. They all ordered beers. André told me that Kürz had mainly talked about his life, with a bit of complacency and not much tact. He said he had enlisted in the navy at age seventeen and had been very happy to wage war. This was the war of ’14. That experience had been beneficial for his health and had taught him a lot. To say this to a group of Frenchmen, in Strasbourg, in 1939, was rather provocative. André found it all very tiresome. Kürz told them about his trip to Paris, and how there had been lots of people who came to listen to his lectures. He spoke of the way peace and Franco-German friendship had been celebrated in a walk with Professor Motfraus in the Jardin des Tuileries. Kürz even went as far as to proclaim how happy he was, as a German, to find himself here in Strasbourg. While gesturing to the Palais Universitaire, a Wilhelminian building, through the café windows, he said, “You French cannot understand—this is the true German spirit.” And he added: “We will return.” The atmosphere was tense, André told me. At the table next to them, the historians went quiet. The mathematicians didn’t say a word, out of politeness or embarrassment, and that had irritated André a little. But, as a student invited to a table of professors, what could he do?