The mathematical systems of statistics surfaced from probability theory, which dates back to the communication between Pierre de Fermat and Blaise Pascal in 1654. In 1657 Christiaan Huygens gave the first known scientific handling of the subject. In 1713 Jakob Bernoulli's, Ars Conjectandi and Abraham de Moivre's Doctrine of Chances (1718) handled the subject as a section of mathematics. The studies of Kolmogorov, in present day have has been influential in creating the underlying model of Probability Theory, which plays a major role in statistics.
The theories on errors are traceable to the 1722 Opera Miscellanea and Roger Cotes, but a journal arranged by Thomas Simpson in 1755 initially applied the theory to the discussion of errors of observation. In 1757 it was reprinted and then the memoir notes the axioms that positive and negative errors are evenly probable, and specific assignable limits within which every error may be intended to drop; continual errors are reviewed and a probability arch is set.