Thomas Bayes (1701–1761) is one of the most consequential figures in the history of probability and statistics, yet remarkably little is known about his life. Born in London to a prominent Nonconformist minister, Bayes was educated privately—likely at the University of Edinburgh—and spent most of his career as a Presbyterian minister in Tunbridge Wells, Kent. His fame rests almost entirely on a single essay, published two years after his death by his friend Richard Price, which introduced the theorem that now bears his name.
Early Life and Education
Bayes was the eldest son of Joshua Bayes, one of the first Nonconformist ministers to be publicly ordained in England. Because Dissenters were barred from attending Oxford and Cambridge, Thomas likely received his education at Dissenting academies or in Scotland. Evidence suggests he studied logic and theology at the University of Edinburgh around 1719. He was ordained as a minister and eventually succeeded his father in the Presbyterian meeting house in Tunbridge Wells, where he served from about 1734 until his retirement.
Mathematical Interests
Although Bayes published little during his lifetime, he was clearly engaged with the mathematical debates of his era. In 1736, he anonymously published An Introduction to the Doctrine of Fluxions, and a Defence of the Mathematicians Against the Objections of the Author of The Analyst, a defense of Isaac Newton's calculus against the criticisms of Bishop George Berkeley. This work was sufficiently impressive that Bayes was elected a Fellow of the Royal Society in 1742, despite having no other known mathematical publications at the time.
The Essay and Bayes' Theorem
Bayes' central contribution is contained in An Essay towards solving a Problem in the Doctrine of Chances, read to the Royal Society by Richard Price in 1763. The problem Bayes addressed was an inverse probability question: given that an event has occurred a certain number of times, what can we infer about the probability of its occurrence on the next trial? He framed this using a thought experiment involving balls thrown onto a table, reasoning from observed outcomes back to underlying causes.
Price edited and extended the essay, adding a philosophical preface arguing that Bayes' result provided evidence for the existence of God by demonstrating that order in nature could be inferred from observation. While this theological motivation is often overlooked today, it was central to the original context of the work.
Bayes imagined a ball tossed onto a perfectly level table, landing at an unknown position. Subsequent balls are then thrown, and an observer is told only whether each lands to the left or right of the first. From this limited information, the observer must infer the position of the original ball—a canonical example of reasoning from evidence to hypothesis.
Legacy and Rediscovery
Bayes' essay attracted some attention in the late eighteenth century but was largely overshadowed by Laplace's independent and more general treatment of inverse probability. It was not until the twentieth-century revival of Bayesian methods that Bayes' name became synonymous with an entire paradigm of statistical reasoning. Today, Bayesian statistics encompasses fields from machine learning to clinical trials, all tracing their conceptual lineage to a quiet minister in Kent.
Born in London, eldest son of Nonconformist minister Joshua Bayes.
Studied at the University of Edinburgh.
Became minister of the Presbyterian chapel in Tunbridge Wells.
Published anonymous defense of Newton's calculus against Berkeley.
Elected Fellow of the Royal Society.
Died in Tunbridge Wells on 7 April.
Richard Price presented Bayes' Essay to the Royal Society posthumously.
The Man Behind the Theorem
Perhaps the deepest irony of Bayes' legacy is how little we know about the man himself. No authenticated portrait exists. His mathematical notebooks have not survived. The theorem that made him immortal was published only because a friend thought it worthy of preservation. Yet Bayes' insight—that we can and should update our beliefs in light of new evidence—has become one of the most powerful ideas in all of science.