The normal distribution and the central limit theorem

In 1733 Abraham de Moivre, a French Huguenot living in London, found that the binomial probabilities for many coin tosses lie along a smooth bell-shaped curve. Carl Friedrich Gauss used the same curve in 1809 to describe errors in astronomical measurements, which is why it is often called Gaussian.

Pierre-Simon Laplace explained in 1810 why the curve keeps turning up: sums of many small independent effects tend towards it, whatever the effects look like individually. That result, the central limit theorem, is the reason most of the statistics in the next lessons works.