Sigma story [2]: Mathematician with no diploma

France 1685: King Luis XIV revokes the edict of Nantes. The edict, issued by Henry IV, 87 years earlier after a series of five civil wars, kept an uneasy peace between the Catholics and the Protestants. Hundreds of thousands flee to neighboring Protestant countries; Abraham de Moivre, age eighteen, settles in England.

London 1738: a Fellow of the Royal Society, buddy-buddy with Isaac Newton and Edmund Halley, Moivre publishes his second edition of The Doctrine of Chances. Near the end, Moivre expands on his earlier paper, in which the concept of normal distribution was introduced for the first time, although it was not called that explicitly.

It does take a mathematician with lots of patience to read something titled as:

A Method of approximating the Sum of the Terms of the Binomial (a + b)n
expanded into a Series, from whence are deduced some practical Rules to estimate the
Degree of Assent which is to be given to Experiments.

Laplace later expands on his result and today we have the de Moivre-Laplace theorem. The following paragraph (from the Doctrine of Chances) is particularly interesting:

Again, as it is thus demonstrable that there are, in the constitution of things,
certain Laws according to which Events happen, it is no less evident from Observation,
that those Laws serve to wise, useful and beneficent purposes; to preserve
the stedfast Order of the Universe, to propagate the several Species of Beings, and
furnish to the sentient Kind such degrees of happiness as are suited to their State.
But such Laws, as well as the original Design and Purpose of their Establishment,
must all be from without; the Inertia of matter, and the nature of all created
Beings, rendering it impossible that any thing should modify its own essence, or
give to itself, or to any thing else, an original determination or propensity. And
hence, if we blind not ourselves with metaphysical dust, we shall be led, by a short
and obvious way, to the acknowledgment of the great Maker and Governour of
all; Himself all-wise, all-powerful and good.

Whoa, it seems he had a clear understanding that the laws governing games of chance are somehow present “in the constitution of things” and “preserve the order of the universe”. All this two hundred years before quantum mechanics. Not bad for a guy who never actually had a college degree; another dropout success story.

To get a feeling for the theorem check out the bean machine (Galton board).

To be continued.