Remembering Ilya Piatetski-Shapiro, by Stephen D. Miller, Associate professor of mathematics, Rutgers U.
To me, and probably everyone else who got to know him well, Ilya Piatetski-Shapiro was a true hero both mathematically and personally. He never shied from a challenge, even alone, and often defeated them spectacularly. He was a strong man of integrity who had visionary and laudable goals. Though his life was marked by terrible treatment in the Soviet Union followed by a devastating disease, he outlived that regime and fought through over three decades of Parkinson's, while still producing breakthrough and influential work.
Just earlier today I was reading my colleague Simon Gindikin's beautiful account of life in Moscow as Ilya's student. I was so moved by recalling this extraordinary person that I decided I had to write Ilya and Edith an e-mail telling them how special they are, and wishing them well. Instead, my inbox brought me the news of his passing earlier today. I was gearing up for his 80th birthday in a few weeks, a milestone which would have seemed improbable years ago. But Ilya's stubbornness to allow Parkinson's to defeat him was legendary, and he almost made it despite a body that would have kept almost anyone else from dreaming of it.
Unfortunately, I only met Ilya in 1996 while a graduate student at Princeton (though we had corresponded via my advisor Peter Sarnak a year earlier). Thus I can only reconstruct him through this shadow of himself, as he was quite ill at the time. I remember how excited I was when Bill Duke introduced me to him. He was such a modest and unpretentious man, not afraid to ask basic questions. At the time I also met his phenomenal wife Edith. I was thrilled to have the opportunity to come to Yale the following year, as it turns out to be, as his last post-doc. The Yale department is very friendly and close-knit, and Edith and Ilya were really like family. I was frequently at their house, and was impressed by how they had such close relationships with a large spectrum of mathematicians even more impressed to see their constant admiration of Ilya. Their Passover seder guests could include graduate students one year and Mikhail Gromov the next. They treated me like their son.
Though we attempted a number of projects, we were not able to write any papers together. Usually Ilya could only dictate, though occasionally when I wasn't looking he would grab the pencil and try to scribble something out. It should be pointed out that Ilya's mathematics was heavily based on calculations, and hence it's extraordinary that he could produce any ideas at all without writing. I never could figure out how he did it, but fruitful discussions with Jim Cogdell (and to an extent with his student Beth Samuels) proved that he was still able to come up with novel ideas about automorphic forms even into his mid-70s. He would still attend numerous talks and conferences, and in his better moments respond via Edith to some points raised in them. Somehow Edith, Jim, and Beth had a magic way of communicating with him I was always in awe of this.
In our abortive attempts in automorphic forms Ilya still taught me some very important folklore lessons, including many of which have been crucial in my work with Wilfried Schmid, such as dimension count heuristics. In many ways Ilya is the influence behind today's analytic approach to automorphic forms. His work with Gelfand in the 1960s is nowadays so basic that it is impossible to study them without their viewpoints. While in Russia he developed modern approaches to classical groups and converse theorems, which exploded into the successful theory for GL(n) he developed together with Herve Jacquet, Joseph Shalika, and Jim Cogdell. Aside from Galois representations, almost every known example of Langlands functorial lifting heavily uses his work. In his prime, he was the engine behind the theory of integral representations of L-functions.
Once I got to Yale I was very struck by manuscripts and lecture notes in his office about the Weyl law and other clever ideas he had in the analytic theory of automorphic forms. It is a shame he was not healthy enough to pursue these ideas further, and that they did not become well-known. His work on moment estimates with Peter Sarnak, while not resulting in a joint paper, became very influential to a host of researchers who have chosen to continue research into their connection with automorphic forms. A perusal of Ilya's publication list demonstrates that he made contributions to a very wide range of topics in algebra, analysis, and number theory and even mathematical biology! As Peter Sarnak remarked to me upon the publication of his Selected Works, "It's hard to believe this is the work of one man."
Ilya was a very deep man who was hard to defeat. He taught at all hours of the day during his temporary banishment to Kaluga, and was a proud refusenik. He was emotional about finally reaching Israel, and his revival there, especially meeting his soulmate Edith. It is fitting that he will be buried in the land he fought to live in, and which he gave so much to. He had convincing taste in recognizing important goals, and was an influential educator to his students and postdocs. I really wish I could have seen more than an echo of his peak personality and sense of humor, but his great mathematics endures regardless. His articles display refreshing expositional sensibilities in a subject which is notorious for its sloppy literature. The areas he developed remain at the forefront of research and owe much to his influence. He was a tough man working for the right cause, and anybody who knew him well was proud to be on the same team.