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  As cover, Léon and I were advised to become apprentice toolmakers down the river from Tulle, in Périgueux. The shop consisted of one large ground-floor room with many old-fashioned machines, a few instructors, and a dozen or so young trainees. At night, we were assigned a room in a barracks close by, across from the rail station. Common sense dictated not talking to the other residents, who might include petty criminals and informers.

  Not unlike sports, the bulk of training consisted of mastering a single but extremely arcane gesture. They gave us metal files, and from two pieces of scrap iron from a big drum we had to make a metal dovetail whose two parts would slide smoothly while allowing no light to shine through. When a part broke on a locomotive or wagon, a replacement could not be ordered from a warehouse, but instead had to be manufactured on the spot.

  To teach this kind of repair, the files were very rough, and at first a perfect dovetail seemed impossible to achieve. But—not unlike cursive handwriting—it was “merely” a matter of mastering the absolutely precise muscle control needed to move a file back and forth in an exactly horizontal position. Having firm hands and a keen sense of space, I did very well, far better than most of the other trainees—who tended to drink heavily. I acquired a lot of self-confidence, and when I became a homeowner, my experience as an apprentice toolmaker in wartime was a boon.

  Three of us—Léon and I and a mysterious fellow who came and went—stood out starkly. We did not in the least look or talk like apprentice toolmakers. But the manager knew our identities and was favorably disposed. Therefore, a routine set in for a while.

  On my fake ID card, my birthplace was declared to be Bastia, a town in Corsica. The Allies had already landed there, so nobody could check and challenge me—it was hoped. But that ID card was not entirely foolproof, so I interrupted my routine and took the train to Limoges, where a person I never met had volunteered to declare that I was living with her. The task of changing my ID card took more than one day, and the railroad station being always open and heated, I spent the night there, pretending to wait for a train. The station was otherwise empty, except for bums. One sat next to me and offered a drink from a filthy bottle. When I refused, he complained, “T’es pas un pote” (You ain’t a pal). I was frozen with fear. In exchange for police tolerance, was he assisting them by reporting what he saw? My life was filled with potentially deadly situations that called for quick reckonings of odds. It was constant anxiety.

  The next day, I visited the Second Police Precinct to pick up my “new and improved” identity card. No problem arose, but shortly afterward a person to whom I mentioned the event blanched and said, “Ain’t you a lucky bastard. In the First Precinct, the boss is so-and-so, who was recently promoted from Tulle.” Not a bad guy, but had I walked into his office, would he have arrested me? Fortunately, fate did not give him the choice.

  One morning in November 1943, two men who identified themselves as policemen, followed by a police informer, entered the machine shop where Léon and I were pretending to be apprentice toolmakers. The town was abuzz with the previous night’s big news: the occupying army’s command post had been bombed, and the police were after the perpetrator(s). The visitors zeroed in on me and ordered me to put on my overcoat and beret and to show my identification—which was of course fake. The informer said, “No question. Here is your man,” and then left with one policeman. The other stayed behind to reassure everybody not to worry. Léon and I thought this was our last day of freedom—or possibly of life.

  My overcoat was distinctive. This prewar item, long misplaced and found by Father in a warehouse, had clear virtues—the cloth was not coarse like the substitutes manufactured during wartime and it was very warm, yet it required no coupons because it was not officially registered. The downside—and the reason it had remained unsold—was that it had a terribly loud “Scottish” pattern unlike any true clan.

  Huddled together that evening after being visited by the police, with no one to consult, Léon and I wondered what to do next. The actual bomber must have been wearing a twin of my coat. The “good-cop, bad-cop” routine we had watched meant nothing, and the omens were grim. Flight was out of the question because we assumed that the police and some idle shelter neighbors were watching all the time. Long deliberation revealed no choice but to wait for the next opportunity to slip away unseen. In the meantime, we did not ask anybody about what was happening. We decided to act as if we were not concerned and stayed put with fear and clenched teeth.

  We somehow managed to get hold of our Angel, and he arranged a more appropriate setup in the Lycée du Parc in Lyon.

  Christmas at Saint-Junien

  A suitable cover for the transfer came when our training center took everybody for a Christmas break to Saint-Junien. The poor Limousin countryside produced plenty of lambskin, and dating back to the Middle Ages, this spot has been devoted to glove making. Workers were extremely specialized, skilled, independent, and well organized—medieval guilds had morphed into single-minded and powerful unions with a strong anarchist tradition.

  The street signs are all I remember of that place. In Nazi-occupied France late in 1943, one could find the boulevard Karl Marx, avenue Karl Liebknecht, allée Rosa Luxemburg, and similar homages to German Communist heroes. (Anarchists did not favor Lenin or Stalin.) Responding to my discreet surprise, a local explained that when an official foreign to Saint-Junien (for example, the prefect appointed by Vichy) was expected to visit, the signs were quickly replaced by the politically correct markers of the boulevard Marshal Pétain, avenue de Verdun, and the like. After the alert, the “rightful” signs were quickly put back.

  Oradour-sur-Glane is a little town where the Waffen SS committed a horrible massacre in 1944, herding 642 villagers into a church and setting it on fire. It happens to be near Saint-Junien. So perhaps the SS Division Das Reich did not choose it at random but reacted to evidence of fierce local independence.

  The Lycée du Parc

  Much of the world was in turmoil, but at the Lycée du Parc in Lyon, where Léon and I boarded from January to May 1944, it was almost business as usual. I was greatly relieved, almost embarrassed. Actually, the normal lycée building—which I have not visited to this day—had become a military hospital, and the part I joined had been relocated from downtown to a bland building on a steep hill called the Croix-Rousse, a very proud working-class community long famed for its silk weavers and militant anarchists.

  Practical aspects of life in hiding were not necessarily obvious. Our false ID cards were fine because providing them was a political gesture, an act of resistance. But ration cards were traded back and forth on a freewheeling black market, and inspection-proof ones carried a price tag that neither we nor our Angel could afford.

  Therefore, the prime virtue of the Lycée du Parc in Lyon was that the business manager for live-in students agreed to turn a blind eye to our obviously “touched-up” ration cards. The fact that this lycée was arguably the best in the provinces was very fortunate for me, but an accident—unless our Angel’s powers were truly supernatural.

  To avoid lapses under pressure, my forged academic papers acknowledged my being from Tulle. Therefore, when—immediately upon arrival—I cast a chance glance into the humanities classroom and recognized a former Tulle classmate, I froze with terror. Looking him straight in the eye I said, slowly, “How nice to find you here. Do you remember me?” I gave him my assumed name. No response. I repeated the phrase once again. He smiled and answered, “What a surprise. Nice to see you. Of course I remember you.” I breathed again—he would not tell on me.

  My papers cautiously downgraded my baccalaureate from its dangerously conspicuous summa to an adequate magna. One day, a student approached. “I hear that you come from Tulle. You must have known Benoit Mandelbrot.” “Of course, of course, I know him well.” “Is it true that he is un crack who got a summa at the bachot?” Back in 1944, “crack” was French slang for a high achiever. Imagine my panic. Did the student suspect
the truth? Was he testing me? Trembling and with feigned nonchalance, I started telling stories about myself, how stressful it had been for “me,” a mere future magna, to be in the same classroom as “that guy.” I did not breathe freely until it became clear that the kid was simply curious.

  My year and a half out of school was challenged. “Where have you been since high school?” “I was ill and followed the course at the École Universelle. It is a very good outfit.” This was a down-market proprietary correspondence school that advertised heavily, but in the elite Lycée du Parc, nobody had direct experience with it, so they expressed surprise that such a school would be good. That answer bought time until the kids saw me perform, guessed the truth, and stopped asking.

  Anxiety was rife. But even in the bleakest stage of the occupation, the worst horrors were never as systematic and uniform in France as in less blessed countries. They were largely localized as part of the bitter civil war between two historical sides of the country. Any one of my encounters might have led me to disaster, but none did.

  Assigned to sit next to me in the classroom, Francis Netter was—like several other classmates—of an old French Jewish family and not in hiding. Their presence never created problems—a detail about Vichy France that invariably creates disbelief. Francis lived across the road from the school. Seeing that I was quite alone, his parents wanted to invite me for a meal, but I baffled and worried them—beyond an accent they thought was from Burgundy. They agonized for several weeks, fearing that kindness could backfire, then invited me, and Francis became—and remains—a good friend.

  A Unique French Institution Nicknamed Taupe

  The Lycée du Parc may be little known, but it is the keystone of the Mandarin system that seventeenth-century Jesuits had imported from China to France. That system’s core consisted of more or less grand grandes écoles. To be admitted, one must pass certain “killer” exams. Having over time surpassed the bac in level of difficulty, those exams came to require intense preparation, and led to the development, parallel to the universities, of publicly supported classes préparatoires—cramming programs—that extend the larger lycées beyond the twelfth grade.

  Taupe is the accepted nickname and math spé is the accepted abbreviation for the fourteenth grade—mathématiques spéciales. Similarly, hypotaupe and math sup (mathématiques supérieures) both stand for the thirteenth grade. Admission to those grades is largely based on performance on the bac, and the Lycée du Parc demanded at least a summa or magna. They let me skip the hypotaupe and enter at the midpoint of the taupe. For the last of the programmed four terms, I was a taupin, linguistically an extreme form of the American “nerd.” In everyday French, taupe means “mole,” presumably because continued overwork prevented us nerds from ever seeing the light of day.

  (Illustration Credit 5.1)

  These cramming programs are found in no other country, though Japan has something like them. All preparatory classes in France teach students to pass a very difficult test, therefore molding everyone to follow what was officially declared the straightest path to the best career. They are so tough that many good students (including some on the way to becoming great scientists) fail and repeat the taupe without any stigma.

  A Geometer Meets the Love of His Mind

  The few months that followed in Lyon were a transforming period of my life. Léon and I hardly left the school grounds. Even on Sunday afternoons, we rushed out after lunch and returned well before dinner—latecomers were denied dinner, and a meal elsewhere was well beyond our means. Moreover, we lived in deep fear of the German boss of the city: his name was Klaus Barbie.

  Last but not least was a burning desire to catch up and do well. The war left no room for long-term ambition. Only the short term mattered. Bound to my desk, I worked at a rate that might not have been sustainable beyond these months, learning the ropes of the exams and honing my skills. Preparing for the exam by becoming a whiz at algebra was not a sensible goal. But, extraordinarily enough, events revealed a powerful gift of which I had been totally unaware.

  During my first two weeks as a taupin, I wandered in a dark labyrinth, in a total blur—as expected. But in the third week, something remarkable happened, with no warning. Something so melodramatic that I can best express it with words from Puccini’s opera Manon Lescaut—“Sola, perduta, abbandonata in landa desolata” (alone, lost, and abandoned in an unknown land). I too felt that way. Never mind that Manon was a Paris courtesan deported by the king to New Orleans. What matters is that utter despair was suddenly resolved—Manon’s by the appearance of her lover, and mine by the manifestation of an unknown, powerful force.

  Our math professor, Monsieur Coissard, had just joined the Lycée du Parc, where he was to spend a long and admired career. Even within the elite group of taupe professors, he was outstanding. About half of every day was spent with him, and he would go to the blackboard and describe a very long problem that—building upon generations of educators—he had deliberately contrived to require absurdly complex calculations. The problem was invariably stated in terms of algebra or analytic geometry.

  My inner voice was restating the same problem in geometric terms. During all that time in Tulle, I had relied on those outdated math books filled with many more pictures and fuller explanations and motivations than the books of the 1930s—or of today. Learning mathematics from such books made me intimately familiar with a large zoo, collected over centuries, of very specialized shapes of every kind. I could recognize them instantly, even when they were dressed up in an analytic garb that was “foreign” to me and, I thought, to their basic nature.

  I always started with a quick drawing, which I soon felt lacked something, and was aesthetically incomplete. It would, for example, improve if transformed by operations called simple projection or inversion with respect to some circle. After a few transformations of this sort, almost every shape became more harmonious. The ancient Greeks would have called the new shape “symmetric,” and in no time searching for and studying symmetry became central to my work. This playful activity transformed impossibly difficult problems into simple ones. The needed algebra could always be filled in later. Hopelessly complicated problems of integral calculus could be “reduced” to familiar shapes that made them easy to resolve. I would raise my hand and describe my findings: “Monsieur, I see an obvious geometric solution.” I quickly grasped the most abstract problem that the teacher could contrive. And then—with no effort, conscious search, or delay—I continued along a path that somehow avoided every difficulty. As the term progressed during that winter in Lyon in 1944, my freakish gift was revealed as strong and reliable.

  In a way, I was learning to cheat. But my strange performance never broke any written rule. Everyone else was training for speed and accuracy in arcane but teachable arts—algebra and the reduction of complicated integrals. I managed to be examined on the basis of speed and good taste in, first, translating algebra back into geometry, and then thinking in terms of geometric shapes. My analytic skills remained so-so, but that did not matter—the hard work was done by geometry, and it sufficed to fill in short calculations that even I could manage.

  My Lyon classmates keep in touch with one another and with me to some extent. Recently, Francis Netter wrote me that I had been the best supériorité absolue in mathematics. It was not my high aptitude for the sciences that surprised him the most, but the broader learning I possessed. One day, he recalled, we wandered around together, and I described enthusiastically a work and an author he had not previously heard of: Buddenbrooks by Thomas Mann. Where, when, and how did that book of Mann’s come into my hands? Did I praise Mann because he opposed (and fled) Hitler?

  In 1973, I visited M. Coissard near Chamonix, in the French Alps. I met his wife and his successor in Lyon, who vacationed nearby. A truly emotional reunion! Coissard told his side of the story—how deeply, during that winter of 1944, my ways had affected his own life and that of his father, a retired taupe teacher himself, who lived
with him. Both spent long evenings and weekends looking within the exams for old or new problems that I could not instantly “geometrize.” They never succeeded in stumping me.

  Where did that gift come from? One cannot unscramble nature from nurture, but there are clues. Szolem lived a double life as a weekday mathematician and a Sunday painter, and his son is a physicist and a painter. I mix mathematics and art every day. My gift for shape may have been saved by all the complications that marked my education during early childhood and the war. Learning to be fluent at manipulating formulas might have harmed this gift. And the absence of regular schooling in art may have influenced many life choices, ending up not as a handicap but as a blessing.

  Oddly, the taupe curriculum included freehand drawing. Before photography, engineers were supposed to illustrate their own work. Most students were all thumbs, but that family gene made my work extremely precise. Our subjects were mainly overused plaster casts of famous sculptures from the Louvre: the Venus de Milo (smooth and easy), the Victory of Samothrace (hard-to-draw wings), or the head of Voltaire by Houdon (a most challenging wig). The drawing master collected our efforts and returned them with grades and comments. The school had forgotten to announce the new student, so when the master exhibited my first drawing, he commented: “It seems that this is a practical joke—a drawing by a virtual student from the outside. I would love to see the students in the arts program do as well.” I stood up and introduced myself.