alt Hacker NewsRight, and Cauchy is the person we have to thank for Bayes’ Theorem, and of course Euler, De Moivre, Poisson and Gauss for the Gaussian integral[1]. You can’t really get figures more central to mathematics than that.
[1] Athough Gauss apparently credited it to Laplace.
Most of the names you mention belong to the next (18th) century.
Gauss worked out some sort of probability distribution too.