Bayes' theorem

Thomas Bayes, an English Presbyterian minister with a taste for mathematics, died in 1761 without publishing his work on chance. His friend Richard Price found the manuscript among his papers and sent it to the Royal Society, which printed it in 1763 as “An Essay towards solving a Problem in the Doctrine of Chances”.

The problem it tackled is the one every doctor, spam filter and fraud system faces: we know how likely the evidence is if a cause is present, and we want to know how likely the cause is now that we have seen the evidence. Those two numbers are not the same, and confusing them is one of the most expensive mistakes in applied reasoning.