The Fractalist Read online

  Mother was the kind of person who witnessed her world collapse around her six times, regained her composure in no time, and soon resumed full steam. Only in old age did she mention having nightmares of what she had experienced but kept to herself in her prime. Szolem repeatedly said that “she had a bad character … but that is often said of someone with a strong personality.”

  At twenty, during the time of the failed 1905 revolution in Russia, she forsook politics for study. She had a gift for languages; her Yiddish was near German, her Polish, Russian, and German were flawless, and—more important—her French became very good.

  She beat the hated quota system of the Imperial University of Warsaw Medical School. In fact, she came out first, part of a brilliant generation of pathbreakers—and proud of it. She had to study the high school curriculum all by herself. The New Testament was a compulsory subject, and the textbook’s binding incorporated a big cross—hence, before being smuggled into her parents’ home, it was hidden in plain brown wrapping. When terminal illness was making her lose her dignity, that was the part of her life she clung to the longest.

  (Illustration Credit 1.4)

  She chose dentistry, the medical specialty most compatible with motherhood: no night calls and fewer nasty bugs in an epidemic-prone part of the world. Before generalized anesthesia, a dentist’s reputation depended greatly on speed in pulling teeth, and I recall Mother’s strong right hand and powerful biceps.

  This photo shows me in Świder in 1930 with my brother, Léon, fifteen months younger than I. As children, we were seldom separated, and of course we argued endlessly. To have him as a worthy sparring partner was one of the best things in my life. Small differences grew in time, and he took some turns he could not help and I could not help reverse. Sad to say, being my brother may have been one of the worst burdens in his own life.

  This street scene, photographed at roughly the same time as the momentous dinner party, shows Mother to the left, holding my hand. Until I became old, bald, and fat, I did not change that much. After all these years, I can still squeeze my mind into the skin of that little boy. Unhurried, not a poet, but attentive, careful, and taking the world head-on.

  The same street scene also introduces Mother’s inseparable younger sister, Raya, holding the hand of Léon. Raya lived a few safe blocks away, so we could walk there alone. Having no children of her own, she was our always free and eager “deputy mother.” For example, being herself a dentist, she took care of her nephews’ teeth. For their offices’ waiting rooms, the sisters chose the same furniture, except that the finish was black for one and tan for the other. Raya was essential to our happy and carefree childhood in a large extended family. We adored her, but her fate was to stay behind when we left Warsaw. She perished in the Holocaust.

  Mother had two brothers. Her younger brother was a charming wastrel. Her older brother had moved from Lithuania to Sweden, but then came back. A fateful return! Had he stayed, he might have brought us to his new country, and our lives would have been altogether different. He reached France in 1939, but did not live long. His wife and daughter followed, then moved to the United States.

  Parents, Continued

  Among those with a tragic view of life who trust hard work and don’t accept that anything is impossible, my parents—taken singly or together—were of championship class. Father was bold and Mother was cautious. They never shouted at each other but argued constantly about strategy, and they taught me very early that before taking big risks, one must carefully figure the odds.

  (Illustration Credit 1.5)

  Their families were of comparable social standing, Father’s being higher intellectually. They met when they were children. Father was a classmate of Mother’s older brother. Until both were established in a profession, they remained engaged. When Father was traveling, his daily postcard to Mother was addressed to “Szanowna [esteemed, honored]” Miss Lurie. Through endless moves, Mother managed to preserve those cards as a private treasure. But at one point, Léon and I found the package and tore the cards to keep the rare stamps. Mother sobbed and I am still ashamed.

  They finally married just after World War I. Photographs show their first son as quite handsome, and everyone recalled him as extraordinarily gifted. He died in an epidemic of meningitis. Mother was so distraught that Aunt Helena had to hold the dying child. Until close to her own death, whenever she thought of him, Mother cried. Two sons born after that loss diminished her grief, but increased her expectations. All of that contributed to the ferocity of my parents’ love for their two children.

  My high level of self-confidence had its roots at home. It was nurtured at an early age. Both parents worshiped individual achievement, but because of the Depression and the war, they never achieved what they wanted and deserved. So their ambition and high expectations were transferred to me. Actual achievement came later. It took a long time for me to evolve into the image they implanted in me—and perhaps to even fulfill their expectations.

  When World War I erupted, my parents and their first son were living in Warsaw. In their families, Germany was an admired beacon of civilization, Russia (except its musicians and writers) was despised, and France and Britain were thought too far away. But Father’s business was ruined, so my parents moved to Kharkov. They lived there during the gory civil war that followed the Communist takeover in Russia, during which control alternated between equally ruthless Reds and Whites. Ruined once again, they managed in 1919 an acrobatic escape—south to Sevastopol in Crimea, then west by sea to Constança in Romania, and north back home to Warsaw. They reestablished themselves, only to be ruined a third time by the Depression, a fourth by World War II, and a fifth and final time by a nonpolitical event, Father’s cancer.

  Nuances of my parents’ Lithuanian roots mattered in many ways, important or simply pesky. For example, in 1919, the newly reunited Poland tried to rebuild the old dynastic union. It was rebuffed, yet annexed southeastern Lithuania around Vilnius, the historical capital—but not Mother’s birthplace. An armistice was in force but peace was never signed. Letters from Mother’s older brother in Lithuania had to go through a business partner in Danzig (today’s Gdańsk), which was then a free city. Far more serious was the fact that the armistice made Mother an “enemy alien” in Poland—an illegal immigrant. Appropriate bribes saved her from being expelled back to a country she did not remember and away from her family and friends. But our later move to Paris brought an incidental minor delight. To have been born in Šiauliai rather than Warsaw became safe. Between the wars, Jews of Lithuanian descent residing in Poland were citizens in theory but in fact were viewed as foreigners in two undesirable ways. Moving to France replaced both ways of being a foreigner with a third and far less undesirable one, and moving on to America brought a fourth, again a very different one.

  In my case, things were much better in France and America than in Poland, but the onus of remaining a foreigner persisted, expanding from countries to fields of science. This did not prevent me from functioning well enough. But even for an accomplished foreigner, repetition does not make uprooting any easier. It carries a heavy price.

  Uncle Szolem

  Recall this book’s dedication. Along with my parents and my wife, Aliette, Uncle Szolem is one of the four people who had the deepest and broadest influence on my life. The love of his mind was mathematics.

  As a teenager, he started attending university courses and became familiar with “modern” concepts that were about to be organized into the Polish mathematics movement. During the civil war that followed the Russian Revolution, he spent a short time in Kharkov, which had an immense effect on the rest of his life—and mine. Attending the university lectures of the mathematician Sergei Bernstein (1880–1968), a fresh Ph.D. from Paris, he fell in love for life with the works of Poincaré and his intellectual heirs who dominated the scene in Paris. Returning to Warsaw, Szolem witnessed Polish mathematics arise as a militantly abstract field, was repelled, and went to France—a r
efugee driven by an ideology that was almost purely intellectual.

  The fact that my parents, as economic and political refugees, joined Szolem in France saved our lives.

  Years later, on a kind of “wall of honor” in his Paris study, Szolem hung a photograph that his mentor, Jacques Hadamard, had dedicated to him as his “spiritual son.” Hadamard had spent most of his working life as professor at the Collège de France, an ancient and famed postgraduate institution. In 1937, Szolem succeeded him in that chair. In 1973, Szolem was elected to the Académie des Sciences to a chair held by the great scientist Henri Poincaré, then for a long time by Hadamard, followed briefly by Paul Lévy (to be introduced in due time).

  A record of Szolem’s brilliance and the reasons for his being quickly and widely accepted is found in a letter dated August 28, 1924, from Paul Jouhandeau to Max Jacob—one very well-known French literary figure to another. The words that follow fit the look of a more or less contemporary photograph.

  [I met a] mathematician of genius who revealed mathematics to me. He says that they are the same thing as poetry, that one invents mathematical beauty, and that true mathematicians never do arithmetic. Those who invent formulas that are important and revolutionary renew science and bear no resemblance to calculators. This man is a Pole and a genius; he walks around with letters of recommendation from the world’s greatest scientists and shows them with childish pride. He is in love, blond, brutal, and has the most beautiful eyes. He draws with equal genius and has never learned to draw. Sometimes he becomes madly gay and describes people with admirable satirical ferocity. He is a Pole but with something from the Tirol (la la la-iou) and makes me think of officers who fight duels in the Caucasus … I think he is an immensely good person and capable of unheard violence if forced, but it may be that only the language is “violent.”

  (Illustration Credit 1.6)

  The last words suggest that Jouhandeau was a fine judge of people. He might have added that Szolem carefully insulated mathematics from pictures. I made them work together for wide benefit. This difference was fated to become a bone of contention between us throughout my life.

  Szolem’s timing was perfect as mine was a generation later during IBM’s heyday as a scientific powerhouse. After the carnage of World War I, Hadamard and Paul Montel recognized that fresh blood was desperately needed, and were delighted to find themselves a successor who closely shared their interests. Therefore, Szolem encountered open arms rather than competition or discrimination. Later, many foreigners flocked to Paris. Competition revived and discrimination returned. Like Poincaré and Hadamard, and Isaac Newton long before them, Szolem viewed mathematics as almost real, but with a crucial difference. They were fascinated by profound issues of physics and the actual world, but Szolem was not.

  He befriended a brilliant and driven younger man, André Weil (1906–98), soon to become the founder and forceful leader of a new generation of French mathematicians who emerged just after World War I. Szolem was invited to join Weil’s circle, and they cofounded a mathematical “secret” cult that called itself Nicolas Bourbaki. The original title of their book—The Fundamental Structures of Mathematical Analysis signaled their expectation that analysis would remain among the topics “approved” by Bourbaki.

  But this did not happen. After spending World War II in the United States, Szolem returned to Paris. Bourbaki was coming to power, and had narrowed and hardened, putting Uncle in an incongruous and uncomfortable situation. He had survived by fleeing the Polish ivory tower, only to fall into the French one. When pressed, he tried to distinguish between abstraction for its own sake and abstraction for the sake of the future—a distinction that was lost on me. He remained personally grateful for his Bourbaki friends’ early welcome and help, and he deferred to their taste when his vote was needed. But the conflict between true love and friendships persisted to the end of his life. He belonged in the old ivory tower—a fact that will matter greatly to me.

  One last comment: although deeply devoted to mathematics, Szolem found enough leisure time to join several literary and political avant-garde groups of Roaring Twenties Paris. He befriended other brilliant immigrants who kept the inner fires started in Eastern Europe burning, but he adopted French ways very quickly and soon sharply diverged from the immigrant group. Those friends published short-lived periodicals with timeless titles such as Philosophies and L’Esprit, but also La Revue Marxiste. He and I never discussed Marxism, and he recalled horror stories about the USSR. Several of his friends, however, were serious about radical politics and perished during the war: Georges Politzer became a pro-Soviet Communist leader; Paul Nizan later moved in the orbit of Jean-Paul Sartre (1905–80). Another friend was philosopher Jean Wahl (1888–1974), a pillar of the Sorbonne. Szolem’s literary friends were the precursors of a group centered on Sartre that became far better known after 1945, the existentialists. Periods of intellectual ferment mix aristocrats and penniless immigrants.

  Intellectual Dynasties

  When Hadamard took Szolem as his young protégé, his daughter Jacqueline was of compatible age and unmarried. Therefore, Szolem’s marriage to Gladys Grunwald countered a well-established custom.

  Szolem’s Ph.D. committee chairman, Émile Picard (1856–1941), had married the daughter of his mentor, the brilliant Charles Hermite (1822–1901), who in turn married into the family of his mentor, Joseph Bertrand (1822–1900). Helped by family connections, those individuals of varying levels of achievement lorded for generations over the politics of French mathematics. Orphaned when still very young, Gladys became accustomed to being asked about her father’s health and responding that Monsieur Hadamard was fine or perhaps had the flu.

  The social custom in question persisted. Peeking ahead, it led some to expect that I would marry Hadamard’s granddaughter or perhaps Paul Lévy’s grandniece. Also, the alumni of the school I was to attend held regular dances to introduce their daughters to up-and-coming recruits. I went to that “market” once but chose to follow Szolem’s example of “exogamy” and married Aliette. Like many social customs, it could be defied, but at a cost: not being part of a system of patronage that is pervasive in intellectual and professional groups. Hadamard remained Szolem’s patron, but my “disobedience” surely contributed to my never acquiring one.

  2

  Child in Warsaw, 1924–36

  NOW THAT I HAVE INTRODUCED the key actors around Grandfather’s dinner table in 1930, let me turn to my story. A tree’s roots are important, but less important than its fruit, and describing them is slippery territory. With age, even half-successful people favor family and social friends over truly formative events. I shall try to be fair to both.

  Large Family and a Carefree Childhood

  The only apartment I recall from Warsaw was at Ulica Ogrodowa 7 (Garden Street), a treeless, straight, and charmless side street off Ulica Solna (Salt Street). The neighborhood, close to the Jewish area, was quiet, with one exception. Warsaw was often crossed by processions of people carrying banners proclaiming support for one cause or another. For some reason, the police pushed protesters into the block where we lived, then rushed toward them with truncheons. We watched from the safety of our balconies, rarely knowing what was happening—but clearly seeing that the political situation was unstable and ominous.

  A fourth-floor walk-up, U.S. style, was the farthest up a moderately high-class dentist’s patients would climb. Mother was a dental surgeon, and the elegant street side was reserved for her surgery and a nice waiting room, both heated by one large through-the-wall stove lined with white and blue porcelain tiles, like in Old Dutch paintings.

  (Illustration Credit 2.1)

  The living quarters facing the back courtyard were more austere. The kitchen was as far removed as possible to lessen the smell of boiling cabbage. The ceilings were high, a valuable luxury in the heat of summer, and the kitchen had a mezzanine for our old cook and maid, Boniusiowa. We wore custom-made shoes—a sign of prosperity, but only relat
ive to the cobblers’ notorious poverty. Later, when Father left to find us a place to live in Paris, Boniusiowa had to go, and the off-the-street half of the apartment was sublet. Mother and sons moved into the former waiting room; the patients who had to wait were relocated to the rearranged entrance hall.

  The fairly large bathroom was very important. Warsaw’s polluting horses, dust, and dirt were not up to Mother’s health standards. So Léon and I were constantly washing our hands. Each time we returned from the park during the hot summer, we stripped down and took a freezing cold shower.

  During the Depression—long before any medical insurance—Mother’s dental practice was excruciatingly slow. Patients came only when the pain was unbearable—with one memorable exception. One morning at seven, the doorbell rang and a young man stepped in, accompanied by an overwhelming stench of manure. He apologized for coming straight from the slaughterhouse, where he had taken his charges, and explained that his beloved would not kiss him because all his teeth were rotten and his mouth smelled. He wanted this fixed, had enough money to pay, and also brought along some fresh meat. The apartment had to be thoroughly aired after his visits. But times were tough. For a while, the demands of one patient’s beloved paid many bills.

  Few early childhood recollections can be dated precisely. I still see myself in my mind’s eye endlessly walking through Warsaw and playing in one of its beautiful parks. The Saxon Garden (Ogród Saski) was a memorial to Augustus the Strong, hereditary king of Saxony and elected king of Poland.

  I remember my initiation to the mystery of the value of money. I observed, or was told—by reports of the truth or subtle pedagogy—that a one-kilogram chunk of farmer cheese cost one zloty, a silver coin, then and now the name of the basic unit of Polish currency. But one kilogram of butter cost far more. Also, the price of fruit varied as the quality ranged from perfect to rotten. That is, long before I heard of the gold standard, I had relied on the farmer cheese standard. Cheese and butter were basically well-defined concepts. When we moved to Paris, I vividly recall Mother being flabbergasted by the variety of foods available even in the slum where we lived. The “thousand” different kinds of French cheese were a cliché, but butter! All the way from economy to premium and then superpremium: Isigny butter.