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During World War II, IBM and Harvard University developed the the first automatic digital calculator in the U.S. called the Automatic Sequence Controlled Calculator or Mark 1. It was 58-feet long and 8-feet high. It could add, subtract, multipy and divide numbers up to 23 digits long.
IBM charged ahead in the computing industry in the 1950s with the IBM 701 which operated from vacuum tubes instead of switches used in its earlier computers. This led to the use of computers in business applications. Transistors replaced the vacuum tubes in 1959 with the IBM 7090 mainframe being of one the first.
Here is Thomas Watson at the desk of an IBM 701.
IBM made a splash in 1957 with the introduction of FORTRAN, a computer language based on algebra, grammar and syntax rules.
Here's a PDF of original instructions for FORTRAN.