## In Memoriam - Ilya Piatetski-Shapiro

Ilya Piatetski-Shapiro, an extraordinary scientist from the Soviet Union, died on February 21, 2009 in Tel Aviv Israel after a long debilitating illness. During a career that spanned 60 years he made major contributions to applied science as well as theoretical mathematics. These contributions range from cell biology, geophysics, automata, and homogeneous networks, to digital computers. In the last forty years his research focused on pure mathematics; in particular, analytic number theory, group representations and algebraic geometry. His main contribution and impact was in the area of automorphic forms and L-functions. Ilya Piatetski-Shapiro was the recipient of a number of prestigious honors and prizes, including the Wolf Prize.The most striking fact about Piatetski-Shapiro’s career is that he continued to perform research at the highest level until the end of his life in spite of a deteriorating condition that left him severely handicapped and often deprived him of speech. Even when he could barely move, he traveled the world, attending conferences in order to exchange thoughts with colleagues about their latest researches. His wife Edith, herself a PhD in mathematics, assisted him in his travels and communication with others.Ilya was born on March 30, 1929 in Moscow, Russia. Both of his parents were from traditional Jewish families. His father was a PhD in chemical engineering from Berdichev, a small city in the Ukraine, with a largely Jewish population. His mother was from Gomel, a similar small city in Belorussia. Both parents' families were middle-class, but they sank into poverty after the October revolution of 1917.In 1952, while still an undergraduate at Moscow University, Piatetski-Shapiro won the Moscow Mathematical Society Prize for a Young Mathematician. His winning paper contained a solution to the problem posed by the French analyst Raphael Salem on sets of uniqueness of trigonometric series. Piatetski-Shapiro was surprised by the award, which was announced one week before Stalin's death, because of the surge in anti-Jewish activities sanctioned by the authorities at that time.Indeed, his application to enter a graduate program at Moscow University was rejected by the University Communist Party Committee, despite a very strong recommendation by his mentor Alexander O. Gelfond, who was a professor of mathematics at Moscow University and a prestigious party member; in fact, Gelfond's father had been a friend of Lenin's. It was only by Gelfond's persistence that Ilya was ultimately admitted to the Moscow Pedagogical Institute, where he received his PhD in 1954, and his Doctor of Sciences in 1958.Ilya attended lectures at the Moscow Steklov Institute. His contact with Igor Shafarevich, who was a professor at the Steklov Institute, broadened Ilya's mathematical outlook and directed his attention to modern number theory and algebraic geometry. This led, after a while, to a joint paper on algebraic surfaces that has influenced many mathematicians. Ilya valued Shafarevich's friendship, even when years later Shafarevich published anti-Jewish essays.Ilya's career was on the rise, and in 1958 he was made a professor of mathematics at the Moscow Institute of Applied Mathematics. By the 1960's he was recognized as a star mathematician. In 1965 he was appointed to an additional professorship at the prestigious Moscow State University. At advanced seminars, he made contact with Gregory Margulis (now at Yale) and David Kazhdan (now at Hebrew University).Ilya's reputation spread internationally; in 1962, he was invited to address the quadrennial International Mathematical Congress in Stockholm. But despite his fame, Ilya was not allowed to travel abroad to attend meetings or visit colleagues except for one short trip to Hungary. Ilya was advised that his chances of traveling abroad would be improved if he would join the Communist Party. His reply is famous in his family: “Membership in the Communist Party will distract me from my work.”During the span of his career Piatetski-Shapiro was influenced greatly by Israel M. Gelfand. The aim of their collaboration was to introduce novel representation theory into classical modular forms and number theory. These efforts stand among Ilya’s most important works. His research then and later was marked by brilliance, originality, and deep insight.During the early 1970s, a growing number of Soviet Jews were permitted to emigrate to Israel. The anti-Jewish behavior in the Soviet Union, however, was not enough to make Ilya want to leave his country. What shook him to the core was the difficulty of maintaining a Jewish identity and the enforced conformity to communism around him in the scientific community. He didn’t wish this future for his son, sixteen at the time. After his wife and son left the Soviet Union, Ilya was fired from his Moscow State University professorship. In 1974 Ilya applied for an exit visa to Israel and as a result, he also lost his research position at the Moscow Institute of Applied Mathematics. Authorities also refused to grant Ilya an exit visa, claiming that he was too valuable a scientist to be allowed to leave. As a refusenik, he lost access to mathematical libraries and other academic resources. He continued his researches nevertheless, and colleagues took books from the library for him.As a prominent refusenik with connections to an international scientific community, Ilya was followed around by a KGB car and his apartment was “bugged.” He conducted his meetings with friends and colleagues by writing on a plastic board, especially when he needed to communicate about his situation. His plight as a mathematician, with serious restrictions on his researches and without means for survival, attracted much attention in the U.S. and Europe.In 1976, a presentation was made to the Council of the National Academy of Sciences urging the use of their good offices to get Ilya an exit visa. Later that year, Ilya obtained an exit visa. He visited colleagues all over the world who had signed petitions and fought for his freedom before going to Israel. He was welcomed warmly upon arrival in Israel and accepted a professorship at Tel Aviv University.Starting in 1977, Ilya divided his time between Tel-Aviv University and Yale, directing doctoral dissertations in both places. One of his major works at Yale dealt with the "Converse Theorem" which establishes a key link between automorphic forms on n by n matrix groups and zeta functions.For n=1 this theorem is classical. The assertion for n=2 was proved by Andre Weil, and the unexpected and novel version for n=3 was conceived by Piatetski-Shapiro while he was still a refusenik in the Soviet Union. It took another 25 years and works with other collaborators, in particular his student James Cogdell, before the suitably flexible and powerful general case was completed. The converse theorem has played a crucial role in many of the most striking results known towards the "principle of functoriality" of Langlands, which is the holy grail of modern number theory.Ilya had a wide circle of friends. He was down-to-earth, practical, and generous. All of his adult life, Ilya was a devoted hiker and camper and nothing pleased him more than combining a hiking trip with mathematical conversation.In later years James Cogdell was the only person outside Ilya's immediate family who could understand Ilya's speech, and Ilya continued to work with Cogdell until 2009. Ilya's wife Edith took care of him to the end, traveling with him wherever he wished to go, and helping him to maintain warm connections with a wide variety of friends in the mathematical community.Ilya is survived by his wife Edith, his children Gregory, Niki and Shelley, and two grandsons, Peter and Matthew. He was buried in Israel on February 24, 2009.See also the New York Times obituary and a longer discussion of Ilya's mathematics from the Math department at Tel Aviv.