The idea of using machines to solve mathematical problems can be traced at least as far as the early 17th century. Mathematicians who designed and implemented calculators that were capable of addition, subtraction, multiplication, and division included Wilhelm Schick hard, Blaise Pascal, and Gottfried Leibnitz.
The first multi-purpose, i.e. programmable, computing device was probably Charles Babbage's Difference Engine, which was begun in 1823 but never completed. A more ambitious machine was the Analytical Engine. It was designed in 1842, but unfortunately it also was only partially completed by Babbage. Babbage was truly a man ahead of his time: many historians think the major reason he was unable to complete these projects was the fact that the technology of the day was not reliable enough. In spite of never building a complete working machine, Babbage and his colleagues, most notably Ada, Countess of Lovelace, recognized several important programming techniques, including conditional branches, iterative loops and index variables.
A machine inspired by Babbage's design was arguably the first to be used in computational science. George Scheutz read of the difference engine in 1833, and along with his son Edvard Scheutz began work on a smaller version. By 1853 they had constructed a machine that could process 15-digit numbers and calculate fourth-order differences. Their machine won a gold medal at the Exhibition of Paris in 1855, and later they sold it to the Dudley Observatory in Albany, New York, which used it to calculate the orbit of Mars. One of the first commercial uses of mechanical computers was by the US Census Bureau, which used punch-card equipment designed by Herman Hollerith to tabulate data for the 1890 census. In 1911 Hollerith's company merged with a competitor to found the corporation which in 1924 became International Business Machines.
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