Thomas Bayes was a British mathematician and Presbyterian minister, known for having formulated a special case of Bayes' theorem. Bayes was elected Fellow of the Royal Society in 1742.
Bayes is known to have published two works in his lifetime: Divine Benevolence, or an Attempt to Prove That the Principal End of the Divine Providence and Government is the Happiness of His Creatures (1731), and An Introduction to the Doctrine of Fluxions, and a Defence of the Mathematicians Against the Objections of the Author of the Analyst (published anonymously in 1736), in which he defended the logical foundation of Isaac Newton's calculus against the criticism of George Berkeley, author of The Analyst. It is speculated that Bayes was elected to the Royal Society on the strength of the Introduction to the Doctrine of Fluxions, as he is not known to have published any other mathematical works during his lifetime.
Bayes' solution to a problem of "inverse probability" was presented in the Essay Towards Solving a Problem in the Doctrine of Chances (1763), published posthumously by his friend Richard Price in the Philosophical Transactions of the Royal Society of London. This essay contains a statement of a special case of Bayes' theorem.
In the first decades of the eighteenth century, many problems concerning the probability of certain events, given specified conditions, were solved. For example, given a specified number of white and black balls in an urn, what is the probability of drawing a black ball? These are sometimes called "forward probability" problems. Attention soon turned to the converse of such a problem: given that one or more balls has been drawn, what can be said about the number of white and black balls in the urn? The Essay of Bayes contains his solution to a similar problem, posed by Abraham de Moivre, author of The Doctrine of Chances (1733).