Johannes Kepler* helped invent calculus while calculating the volume of wine kegs. In 1612, wine came in kegs, not 750 ml bottles, and Kepler was concerned because the method used to estimate the volume of these kegs was inaccurate.
The volume of a cylinder is simply the area of the base times the height. (V = πrrh)** This formula can’t be used to determine the volume of a keg because of the bulgy parts on the sides. Kepler imagined slicing the kegs into infinitely thin sections. He calculated the volumes of the sections and added them up. Not only did he get a pretty good answer, he devised the precursor to taking an integral.
This story and many others about the history of mathematics can be found in Zero: the biography of a dangerous idea by Charles Seife. (Penguin Books, 2000)
*In case you think Kepler was just an old sot, he also figured out that the planets move in elliptical paths.
** I couldn't make the "r squared" notation with a superscript 2 in Blogger.
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