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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.
In 1956, Thomas Watson, Jr. took over as CEO of IBM from his father who had led the company for 42 years. He kept the key slogan - THINK.
In 1957, the IBM 305 Random Access Method of Accounting and Control contained the first computer disk storage system.