Hartmanis was born in Latvia on July 5, 1928. He was a son of Mārtiņš Hartmanis [lv], a general in the Latvian Army, and brother of the poet Astrid Ivask. After the Soviet Union occupied Latvia in 1940, Mārtiņš Hartmanis was arrested by the Soviets and died in a prison. Later in World War II, the wife and children of Mārtiņš Hartmanis left Latvia in 1944 as refugees, fearing for their safety if the Soviet Union took over Latvia again.
They first moved to Germany, where Juris Hartmanis received the equivalent of a master's degree in physics from the University of Marburg. He then moved to the United States, where in 1951 he received a master's degree in applied mathematics at the University of Kansas City (now known as the University of Missouri–Kansas City) and in 1955 a Ph.D. in mathematics from Caltech under the supervision of Robert P. Dilworth. The University of Missouri–Kansas City honored him with an Honorary Doctor of Humane Letters in May 1999.
After teaching mathematics at Cornell University and Ohio State University, Hartmanis joined the General Electric Research Laboratory in 1958. While at General Electric, he developed many principles of computational complexity theory. In 1965, he became a professor at Cornell University. He was one of the founders and the first chair of its computer science department (which was one of the first computer science departments in the world).
Hartmanis contributed to national efforts to advance computer science and engineering (CS&E) in many ways. Most significantly, he chaired the National Research Council study that resulted in the 1992 publication Computing the Future – A Broad Agenda for Computer Science and Engineering, which made recommendations based on its priorities to sustain the core effort in CS&E, to broaden the field, and to improve undergrad education in CS&E. He was assistant director of the National Science Foundation (NSF) Directorate of Computer and Information Science and Engineering (CISE) from 1996 to 1998.
In 1993, Hartmanis and R.E. Stearns received
the highest prize in computer science, the Turing Award. The citation reads,
"In recognition of their seminal paper which established the foundations for the field
of computational complexity theory."
defined the foundational notion of a Complexity class, a way of
classifying computational problems according to the time required to solve them.
They went on to prove a number of fundamental results such as the
Time hierarchy theorem. In his own Turing Award lecture, Richard M. Karp remarks that "[I]t is the 1965 paper by Juris Hartmanis and Richard Stearns that marks the beginning of the modern era of
With P.M. Lewis II, Hartmanis and Stearns also defined complexity classes based on space usage and proved
the first space hierarchy theorem. In the same year they
also proved that every context-free language has deterministic
space complexity (log n)2, which contained the essential idea that led
to Savitch's theorem on space complexity.
Hartmanis continued to make significant contributions to the field of computational complexity for decades. With Leonard Berman, he proved that all natural NP-complete languages are polynomial-time isomorphic and conjectured
that this holds for all NP-complete sets. Although
the conjecture itself remains open, it has led to
a large body of research on the structure of NP-complete sets, culminating
in Mahaney's theorem on the nonexistence of sparse NP-complete sets. He and his coauthors also
defined the Boolean hierarchy.
Hartmanis's 1981 article  gives a personal account of developments in this area and in automata theory and discusses
the underlying beliefs and philosophy that guided his research. The book
written in honor of his 60th birthday, in particular, the chapter by Stearns, is a valuable resource on computational complexity.
In the late 1980's, Hartmanis's exposition on a newly discovered letter dated 20 March 1956
from Gödel to von Neumann brought fresh insight
into the early history of computational complexity before his landmark paper with Stearns,
touching on interactions among Turing, Gödel,
Church, Post, and Kleene.
Gödel, in this letter, was the first to question whether a problem equivalent to an NP-complete
problem could be solved in quadratic or linear time, presaging the P = NP? question.
^In the Baltic languages, own-names are not lexical constants, but have different grammatical forms. Hartmanis must be understood as Hartman-is, whereby Hartman is the stem of the own-name, whereas the suffix -is indicates a masculine grammatical form in the Latvian language. In a similar manner, for example, the philosopher Kant is known as Kantas in the Lithuanian language.
^ abHartmanis, Juris (July 26, 2009). "Dr. Juris Hartmanis Interview" (text). Interviewed by William Aspray. Ithaca, New York: ACM Oral History interviews. doi:10.1145/1141880.1775727.
^ In two of the interviews cited in section #Interviews, Hartmanis talks in detail of this period of his life, in which his father was given an estate, Lestene; the Russians occupied Latvia, took his father away, and confiscated Lestene; the Germans took over once more and restored part of Lestene to his family; and the family left Latvia for Germany before the Russians invaded Latvia again.
^ ab—; Lewis, P.M.; Stearns, R.E. (May 24, 1963). Wayne A. Kalenich (ed.). Classifications of computations by time and memory requirements. Proc. IFIP Congress 65. New York City: Spartan Books, Inc., Washington, D.C. pp. 31–35. doi:10.2307/2272795. JSTOR2272795.
^ abc—; Lewis, P.M.; Stearns, R.E. (October 6, 1965). Hierarchies of memory limited computations. FOCS 65: Proc. Sixth Ann. Symp Switching Circuit Theory and Logical Design. New York: IEEE. pp. 179–190. doi:10.1109/FOCS.1965.11.
^These early papers developed many principles of computational complexity theory. Hartmanis's 1981 survey paper provides extensive information on the work in computational complexity theory.
^ ab"Lielā medaļa" [Grand Medal]. www.lza.lv (in Latvian). Latvian Academy of Sciences. Archived from the original on January 6, 2022. Retrieved August 4, 2022. 2001 ... Juris Hartmanis, par izcilu ieguldījumu datorzinātņu attīstībā. [2001 ... Juris Hartmanis, for his outstanding contribution to the development of computer science.]
^新智元 [Xin Zhi Yuan] (July 31, 2022). "图灵奖得主，"计算复杂性"理论奠基人Juris Hartmanis逝世，享年94岁" [Turing Award winner and founder of "computational complexity" theory, Juris Hartmanis, dies at 94]. 新浪 finance.sina.com.cn (in Simplified Chinese). Retrieved August 4, 2022.
^Mahaney, Stephen R. (October 1982). "Sparse complete sets for NP: Solution of a conjecture of Berman and Hartmanis". Journal of Computer and System Sciences. 25 (2): 130–143. doi:10.1016/0022-0000(82)90002-2. hdl:1813/6257.