Born in Budapest, Hungary, Kemeny attended the Rácz private primary school in Budapest and was a classmate of Nandor Balazs. In 1938 his father left for the United States alone. In 1940, he took the whole Kemeny family to the United States when the adoption of the second anti-Jewish law in Hungary became imminent. His grandfather, however, refused to leave and perished in the Holocaust, along with an aunt and uncle. Kemeny's family settled in New York City where he attended George Washington High School. He graduated with the best results in his class three years later. In 1943 Kemeny entered Princeton University where he studied mathematics and philosophy, but he took a year off during his studies to work on the Manhattan Project in Los Alamos National Laboratory. His boss there was Richard Feynman. He also worked there with John von Neumann. Returning to Princeton, Kemeny graduated with his BA in 1947, then worked for his Doctorate under Alonzo Church, also at Princeton. He worked as Albert Einstein's mathematical assistant during graduate school. At 23 years old, Kemeny was awarded his doctorate in 1949 for a dissertation entitled "Type-Theory vs. Set-Theory."