Kaczynski graduated from Harvard in 1962 and subsequently attended the University of Michigan, where he earned a PhD in mathematics. Kaczynski's specialty was a branch of complex analysis known as geometric function theory. He earned his PhD with his thesis entitled "Boundary Functions" by solving, in less than a year, a math problem that was unsolved by one of his professors at Michigan, George Piranian, who later commented on Kaczynski by saying, "It is not enough to say he was smart." Maxwell Reade, a retired math professor who served on Kaczynski's dissertation committee, also commented on his thesis by noting, "I would guess that maybe 10 or 12 men in the country understood or appreciated it." In 1967, Kaczynski won the University of Michigan's $100 Sumner B. Myers Prize, which recognized his dissertation as the school's best in mathematics that year. While a graduate student at Michigan, he held a National Science Foundation fellowship and taught undergraduates for three years. He also published two articles related to his dissertation in mathematical journals, and four more after leaving Michigan later.
Kaczynski became an assistant professor of mathematics at the University of California, Berkeley in Fall 1967, teaching undergraduate courses in geometry and calculus. He was also noted as the youngest professor ever hired by the university. This was short-lived however, as Kaczynski received numerous complaints and low ratings from the undergraduates he taught. Many students noted that he seemed quite uncomfortable in a teaching environment, often stuttering and mumbling during lectures, becoming excessively nervous in front of a classroom, and ignoring students during designated office hours. He resigned from his position without explanation in 1969 at age 26. The chairman of the mathematics department, J. W. Addison, called this a "sudden and unexpected" resignation, while vice chairman Calvin Moore said that given Kaczynski's "impressive" thesis and record of publications, "he could have advanced up the ranks and been a senior member of the faculty today."