An outline (algorithm) for what would have been the first piece of software was written by Ada Lovelace in the 19th century, for the planned Analytical Engine. She created proofs to show how the engine would calculate Bernoulli Numbers. Because of the proofs and the algorithm, she is considered the first computer programmer.
The first theory about software—prior to creation of computers as we know them today—was proposed by Alan Turing in his 1935 essay On Computable Numbers, with an Application to the Entscheidungsproblem (decision problem).
This eventually led to the creation of the academic fields of computer science and software engineering; Both fields study software and its creation. Computer science is the theoretical study of computer and software (Turing's essay is an example of computer science), whereas software engineering is the application of engineering and development of software.
However, prior to 1946, software was not yet the programs stored in the memory of stored-program digital computers, as we now understand it. The first electronic computing devices were instead rewired in order to "reprogram" them.
In 2000, Fred Shapiro, a librarian at the Yale Law School, published a letter revealing that John Wilder Tukey's 1958 paper "The Teaching of Concrete Mathematics" contained the earliest known usage of the term "software" found in a search of JSTOR's electronic archives, predating the OED's citation by two years. This led many to credit Tukey with coining the term, particularly in obituaries published that same year, although Tukey never claimed credit for any such coinage. In 1995, Paul Niquette claimed he had originally coined the term in October 1953, although he could not find any documents supporting his claim. The earliest known publication of the term "software" in an engineering context was in August 1953 by Richard R. Carhart, in a Rand Corporation Research Memorandum.