Jürgen K. Moser 1928–1999 A Biographical Memoir by Paul H. Rabinowitz ©2015 National Academy of Sciences. Any opinions expressed in this memoir are those of the author and do not necessarily reflect the views of the National Academy of Sciences. J Ü RGEN KURT MOSER July 4, 1928–December 17, 1999 Elected to the NAS, 1971 After the death of Jürgen Moser, one of the world’s great mathematicians, the American Mathematical Society published a memorial article about his research. It is well worth beginning here with a lightly edited version of the brief introductory remarks I wrote then: One of those rare people with a gift for seeing mathematics as a whole, Moser was very much aware of its connections to other branches of science. His research had a profound effect on mathematics as well as on astronomy and physics. He made deep and important contributions to an extremely broad range of questions in dynamical systems and celestial mechanics, partial differen- By Paul H. Rabinowitz tial equations, nonlinear functional analysis, differ- ential and complex geometry, and the calculus of variations. To those who knew him, Moser exemplified both a creative scientist and a human being. His standards were high and his taste impeccable. His papers were elegantly written. Not merely focused on his own path- breaking research, he worked successfully for the well-being of math- ematics in many ways. He stimulated several generations of younger people by his penetrating insights into their problems, scientific and otherwise, and his warm and wise counsel, concern, and encouragement. My own experience as his student was typical: then and afterwards I was made to feel like a member of his family. He had an important influence in his role as director of the Courant Institute of Mathematical Sciences (1967–70), as director of the Mathematics Research Institute of the ETH (Swiss Technical University) (1984–95), as president of the International Mathematical Union (1983–86), and through his active membership on numerous advisory bodies. 2 JÜRGEN MOSER Moser was a lifelong music lover—he played the cello—and amateur astronomer. He enjoyed biking, swimming, and hiking. At the age of 60, he took up paragliding. With his untimely death at the age of 71, many of us in the mathematics community lost a hero, friend, and mentor (Mather et al. 2000). Moser was born in Königsberg, Germany, at the time a beautiful old city located on the Baltic Sea not far from the border with the then Soviet Union. Königsberg is well known to mathematicians as the site of the seven bridge problem of Euler. Totally destroyed during the Second World War, the city was rebuilt, renamed Kaliningrad, and is now part of Russia. Moser’s father was a neurologist and the family—parents, older brother Friedrich, and Jürgen—lived comfortably in a large apartment that also contained his father’s practice. A second brother, Klaus, was born in 1939. The family loved music. There was a Bechstein grand piano in the living room that mother and grandmother played, and father played the violin. Jürgen and Friedrich took piano lessons. Many evenings were devoted to chamber music. Later, at age 12, being somewhat bored by piano lessons, Jürgen began to study the cello, an instrument whose sound he was taken by. His affinity for the cello continued for the rest of his life. An aunt owned a large estate near town and Jürgen had happy boyhood memories of biking there during summer holidays with Friedrich, of fun-filled days of horseback riding, of picking mushrooms, and of working with the farm animals. In 1933, the Nazis came to power in Germany. This did not affect Moser’s life much until 1938, when he was 10 years old and pushed to go to a distant elite training school. His parents recognized the possible consequences of such training, and they managed to avoid it. Instead, he entered the Wilhelmsgymnasium, where the famous mathematician David Hilbert had also been a student. World War II began in 1939 and four years later, at the age of 15, Moser’s entire class was drafted into the army. The boys were trained to use anti-aircraft guns to defend Königsberg from air attacks. These guns were very large, and being one of the smallest boys in his class, Moser could not lift the heavy shells. So he was assigned the task of computing the paths of the attacking aircraft. These feeble defenses proved to be for nought; in two nights of concentrated bombing, the city was destroyed, and a period of trials and hardships 3 JÜRGEN MOSER followed for most of its residents. “For more than Planning to enter West two years Moser lived at the edge, always hungry Germany illegally during the and often in mortal danger, surviving by sheer will night, train delays led to his and wit” (Nasar 1999). Over 90 percent of his reaching the border area at classmates were killed in the war, as was his brother dawn. Another hazardous Friedrich. crossing resulted in which shots were fired, but he put When the war ended, Moser was in the British his running ability to good occupied zone, and even though 16 years old he use. looked like an undernourished child. Having managed to obtain some civilian clothing and in that way avoiding the prisoner-of-war camps, he registered as a refugee and found a job repairing roads. After several months of searching for his parents, Moser finally found that they were living in a small town, Greifswald, in the Russian-occupied zone. He decided to visit them by illegally crossing the border but was captured by Russian soldiers and held without food in a water-flooded basement for six days. He barely escaped starvation, with only a stolen turnip to sustain himself. On a dozen later occasions he crossed the border again—still illegally but at better chosen times and places, and was never caught again. Upon his release by the Russians, he was was able to reunite with his parents. Returning to school, Moser completed his high-school education in April 1947 and sought admission to a university in the Russian zone. But both of his applications were turned down, given the requirement in those days that his father had to be a farmer or a worker. Furious, he decided to try to study at the University of Göttingen, located in West Germany and the first German university allowed to reopen after the war. Moser’s high-school mathematics teacher supplied him with a letter of recommendation to Franz Rellich, director of the Mathematics Institute at Göttingen. Planning to enter West Germany illegally during the night, train delays led to his reaching the border area at dawn. Another hazardous crossing resulted in which shots were fired, but he put his running ability to good use. After arriving in Göttingen, he reached Rellich. In an interview with mathematics writer Constance Reid many years later, Moser recalled his amazement at Rellich’s friendliness and interest. Göttingen was extremely crowded; and lodging, though crucial, was elusive. “One could not register as a student,” said Moser, “without having a place to live; and one couldn’t get a place to live unless he was 4 JÜRGEN MOSER a student.” But Rellich helped him find a room. Indeed, Rellich was quite generous toward all of the In a letter to Courant 10 days students, many of whom were older [and needier] after the American occu- than usual because their lives had been disrupted by pation of Göttingen, Rellich the war. “And then there was the matter of food,” wrote: “The Mathematics Moser said. “We students were literally starving, Institute sleeps like Sleeping and Rellich managed somehow to get CARE Beauty and obviously awaits packages and distribute food to us” (Reid 1976). the kiss of the prince. It would be wonderful if you felt like So began Moser’s six years of mathematics study playing the role of the prince.” at Göttingen. Although historic and famous, the university had suffered severe losses of personnel, first because of the Nazis’ policies and then from the effects of the war. In particular Richard Courant, who had been director of the Mathematics Institute at Göttingen, had been forced out of his position and compelled to emigrate from Germany because he was Jewish. Rellich had been his student. In a letter to Courant 10 days after the American occupation of Göttingen, Rellich wrote: “The Mathematics Institute sleeps like Sleeping Beauty and obviously awaits the kiss of the prince. It would be wonderful if you felt like playing the role of the prince” (Reid 1976). Moser chose mathematics for his studies because he had always liked the subject, though he did not have much formal training. However, during his military service and its aftermath, he had developed an effective way to distance himself from his surroundings. He would make up a mathematical problem and focus on solving it in his head. In an email to his grandson, Moser later observed: “[This process] was very soothing. The officers could yell as much as they wanted; they could not reach me. That is how I learned to think and concentrate.” While living in Greifswald—in a small attic room with his parents and younger brother, Klaus, often with no light—Jürgen would put a tea cozy over his head as a signal that he wanted to study and be focused on his mathematics. This too led to his development of great powers of concentration. Moser studied at Göttingen from 1947 to 1953, together with some classmates—Erhard Heinz, Konrad Jorgens, Johannes Nitsche—who later became well-known mathemati- cians.