This article outlines some of the mistakes made in the calculus of probability, especially when the discipline was being developed. Such is the character of the doctrine of chances that simple-looking problems can deceive even the sharpest minds. In his celebrated Essai Philosophique sur les Probabilités (Laplace 1814, p. 273) the eminent French mathematician Pierre-Simon Laplace (1749–1827) said:

<abstract><p>We prove the uniqueness property for a class of entire solutions to equation</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} \left\{ \begin{array}{ll} -{\rm div}\, \mathcal{A}(x,\nabla u) = \sigma, \quad u\geq 0 {\text{in }} \mathbb{R}^n, \\ {\liminf\limits_{|x|\rightarrow \infty}}\, u 0, \end{array} \...