Bayes' Theorem

Chapter 11: Bayes’ Theorem History

Bayes’ Theorem has a spectacular 200-year history, and there are a number of fantastic books that delve deeply into it. For this website, we’ll include an abbreviated look at the highlights.

The Discovery of Bayes’ Theorem

1740’s, Edinburgh, Scotland

Thomas Bayes was born in London, England in 1702. Bayes studied logic and theology at the University of Edinburgh and served as a minister at a Presbyterian church in Tunbridge, Wells (35 miles from London). He retired in 1752 and passed away in 1762.

Apart from his faith, Bayes had a deep love and interest in mathematics and was considered an amateur mathematician. In his later years, he became fascinated with probability, specifically inverse probability. No one knows why for sure, but one thing is clear: Bayes became consumed with figuring out …the approximate probability of a future event he knew nothing about except its past, that is, the number of times it had occurred or failed to occur.

Sometime in the 1740’s Bayes’ figured out a solution that can be summed up as follows: An Initial Belief + New Evidence = A New, Updated Belief. But, for reasons unknown, he never did anything with it and instead, it sat on the solution until his death in 1762. After he passed away his friend Richard Price discovered the theorem, saw its importance, and for two years worked on it. Price then submitted it to The Royal Society and it was published a year later.

Across the English Channel in 1774 a French mathematician named Pierre-Simon Laplace recreated Bayes’ solution. At the time he was completely unaware of Bayes’ discovery and had come to it on his own merit. For almost 40 years he worked on the theorem, and sometime between 1810 and 1814 he put the final touches on it, eventually (more or less) creating the formula that is known today as Bayes’ Theorem. Laplace did most of the work, but Bayes name stuck with theorem for some reason.

However, Bayes’ Theorem was generally not accepted and had few advocates until recently in modern history. From Laplace’s final touches on the theorem until the mid-1960’s, Bayes’ Theorem was criticized as being subjective due to the formula’s prior. Most mathematicians considered the formula taboo and would not touch it.

During World War 2 it was used by Alan Turing (a brilliant mathematician and played by Benedict Cumberbatch in The Imitation Game) to break the German’s Enigma Code, but that information was classified for a long time after the war. It wasn’t until the 1980’s and the introduction of personal computing that Bayes’ Theorem became widely accepted. It is now used across many sectors and likely touches your life on a daily basis.

Continue on to Chapter 12: Books on Bayes’ Theorem.