After receiving her Ph.D. in mathematics at Yale, Hopper worked as an associate professor at Vassar College before joining the U.S. Naval Reserve in 1943. She went on to work as a researcher and mathematician at the Eckert-Mauchly Computer Corp. and the Sperry Corporation. Having retired from the Navy after World War II, she returned
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in 1967 to work at the Naval Data Automation Command. Later, the U.S. Navy was to name a new destroyer after her: the U.S.S Grace Hopper, DDG-70.
At Eckerd-Mauchly, Hopper developed programs for the first large-scale digital computer, the Mark I. She also developed the first compiler, the A-O. She published the first paper on compilers in 1952. The successor to the the A-O, named FLOW-MATIC, lead to the development of the COBOL programming language. Until then programming was done using assembler language. Admiral Hopper's idea was to make a programming language closer to ordinary language so that it could be used by non-technical people, thus opening the practice of programming to the business world and freeing it from the rarefied environments of science and engineering.
Admiral Hopper remained in the Navy until 1986 and then worked as a senior consultant for DEC until shortly before her death. She was highly sought after as an enthusiastic and entertaining public speaker and educator of young programmers. Hopper was an early advocate of the use of shared code libraries and developed compiler verification software and compiler standards.
Hopper is also credited with applying the engineering term bug to computing when her team found a moth trapped in a relay of the Mark II computer. This particular "bug" was removed, taped to the log book, and now resides at the Smithsonian Institute.