Statisticians make inferences from observed data. Just as scientists and engineers, statisticians rely upon mathematical models. While for the scientist or engineer differential equations is commonly the area of mathematics of most utility, and while these tools are not unimportant for the statistician, the statistician's primary mathematical tool is probability.
Some facts from probability of most value to the area of statistics have only been established in the last hundred years or so. Whether they are considered results from probability or from statistics and whether their authors are considered statisticians or probabilists, the application of these facts has been primarily important to the practice of statistics. In many cases the results were motivated by statistical problems. Among the primary contributors to the development of statistics are Francis Galton , generally credited with development of the ideas of regression and correlation, Karl Pearson , inventor of the chi-square test of fit, , W. S. Gosset who is credited with the t-distribution and paving the way for small sample inference, R. A. Fisher super star in the development of statistics known perhaps primarily for the analysis of variance, and J. Neyman whose work demonstrated that the commonly used methods of statistical inference based upon these probabilistic results were in some sense optimal.
More historical information is available.