"This hypothesis has been called the law of errors. It cannot be derived by rigorous deduction; more than one attempted proof of it is crude […]. Yet everyone believes in it […] because experimentalists imagine it is a mathematical theorem, while mathematicians imagine it is an experimental fact."
These are Henri Poincaré's words from his 1896 course on Calcul des probabilités. But what is this famous "law of errors" in which everyone believes? To find out, let us turn to Pierre-Simon Laplace, who revisited the question several times, notably in 1774, 1778 and 1810.
Henri Poincaré (1854–1912).
The "probability midpoint"
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