# How could I have discovered the normal distribution?

What was the first derivation of the normal distribution, can you reproduce that derivation and also explain it within its historical context?

I mean, if humanity forgot about the normal distribution, what is the most likely way I would rediscover it and what would be the most likely derivation? I would guess the first derivations must have come as a byproduct from trying to find fast ways to compute basic discrete probability distributions, such as binomials. Is that correct?

I would guess the first derivations must have come as a byproduct from trying to find fast ways to compute basic discrete probability distributions, such as binomials. Is that correct?

Yes.

The normal curve was developed mathematically in 1733 by DeMoivre as
an approximation to the binomial distribution
. His paper was not
discovered until 1924 by Karl Pearson. Laplace used the normal curve
in 1783 to describe the distribution of errors. Subsequently, Gauss
used the normal curve to analyze astronomical data in 1809.

Source : NORMAL DISTRIBUTION

Other sources with historical context:

Nowadays the fact that the Normal distribution is an approximation for Binomials for large $n$ is considered as a special case of the Central Limit Theorem. It can be found in most text books and is considered as elementary. You can find a proof on Wikipedia. The exponential just shows up as $e^x=\lim(1+\frac{x}{n})^n$ after some Taylor expansion of the characteristic function that yield $-\frac{t^2}{2}$. Sometimes you still find special proofs for Binomials in textbooks and this is known as DeMoivre-Laplace theorem.