He became interested in mathematics at the age of 10, struck, as he wrote in his short memoir, "by the charm and unusual beauty of negative numbers", which his father, a PhD in chemical engineering, showed him.
His winning paper[3][4] contained a solution to the problem of the French analyst Raphaël Salem on sets of uniqueness of trigonometric series.
His contact with Shafarevich, who was a professor at the Steklov Institute, broadened Piatetski-Shapiro's mathematical outlook and directed his attention to modern number theory and algebraic geometry.
In 1966, Piatetski-Shapiro was again invited to the ICM in Moscow [7] where he presented a 1-hour lecture on Automorphic Functions and arithmetic groups (Автоморфные функции и арифметические группы).
Ilya gave his famous answer: “The membership in the Communist Party will distract me from my work.” During the span of his career Piatetski-Shapiro was influenced greatly by Israel Gelfand.
[citation needed] Piatetski-Shapiro lost his part-time position at mathematics department of Moscow State University in 1973, after he signed a letter asking Soviet authorities to release a dissident mathematician Alexander Esenin-Volpin from a mental institution.
[citation needed] After his ex-wife and son left the Soviet Union in 1974, Piatetski-Shapiro also applied for an exit visa to Israel and was refused.
[citation needed] As a prominent refusenik with connections to an international scientific community, Piatetski-Shapiro was followed around by a KGB car and his apartment was under electronic surveillance.
[citation needed] In 1976, a presentation was made to the Council of the National Academy of Sciences urging the use of their good offices to get Piatetski-Shapiro an exit visa.
One of his major works at Yale dealt with the converse theorem which establishes a link between automorphic forms on n by n matrix groups and zeta functions.
His condition worsened in the last 10 years to the point where he was barely able to move and speak, but thanks to the support of his wife Edith, he was still able to travel to mathematical conferences.
[citation needed] He was married three times and had a son, Gregory I. Piatetsky-Shapiro and daughters, Vera Lipkin and Shelly Shapiro Baldwin.
[citation needed] Piatetski-Shapiro was elected to the Israel Academy of Sciences and Humanities in 1978,[9] was a Guggenheim Fellow for the academic year 1992–1993,[14] and was the recipient of numerous prizes, including: He was invited to address the quadrennial International Mathematical Congress — one of the highest mathematical honors — 4 times: 1962, 1966 (gave plenary address), 1978 (presented 45 minute talk), and 2002.