central limit theorem

— Laplace continued his research throughout France’s political upheavals. In 1810 he announced the central limit theorem, one of the great scientific and statistical discoveries of all time. It asserts that, with some exceptions, any average of a large number of similar terms will have a normal, bell-shaped distribution. Suddenly, the easy-to-use bell curve was a real mathematical construct. Laplace’s probability of causes had limited him to binomial problems, but his final proof of the central limit theorem let him deal with almost any kind of data. In providing the mathematical justification for taking the mean of many data points, the central limit theorem had a profound effect on the future of Bayes’ rule. At the age of 62, Laplace, its chief creator and proponent, made a remarkable about-face. He switched allegiances to an alternate, frequency-based approach he had also developed. From 1811 until his death 16 years later Laplace relied primarily on this approach, which twentieth-century theoreticians would use to almost obliterate Bayes’ rule.