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No one "invented" it; it occurs naturally in a wide variety of real world situations. As for who discovered it and described it mathematically, that's another story.

The normal distribution is also known as the Gaussian distribution, after Johann Carl Friedrich Gauss (30 April 1777 to 23 February 1855). It was he first discovered the equations governing the distribution (in 1809) but saw it only as a tool for analysis of measurements. In 1810, Pierre-Simon, marquis de Laplace (23 March 1749 - 5 March 1827) proved its theoretical importance in math. But is was James Clerk Maxwell (13 June 1831 - 5 November 1879) who, decades later showed that the distribution also directly describes certain natural phenomena.

It is worth noting that Gauss, Laplace, and Maxwell each made numerous other contributions to mathematics and science, so one tends to see their names all over the place.

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Q: Who invented the normal distribution?
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