Tercentennial Anniversary of Bernoulli’s Law of Large Numbers

The importance and value of Jacob Bernoulli’s work was eloquently stated by Andrĕı Andreyevich Markov during a speech presented to the Russian Academy of Science on December 1, 1913. Marking the bicentennial anniversary of the Law of Large Numbers, Markov’s words remain pertinent one hundred years later: In concluding this speech, I return to Jacob Bernoulli. His biographers recall that, following the example of Archimedes he requested that on his tombstone the logarithmic spiral be inscribed with the epitaph Eadem mutata resurgo. This inscription refers, of course, to properties of the curve that he had found. But it also has a second meaning. It also expresses Bernoulli’s hope for resurrection and eternal life. We can say that this hope is being realized. More than two hundred years have passed since Bernoulli’s death but he lives and will live in his theorem. Indeed, the ideas contained in Bernoulli’s Ars Conjectandi have impacted many mathematicians since its posthumous publication in 1713. The twentieth century, in particular, has seen numerous advances in probability that can in some way be traced back to Bernoulli. It is impossible to survey the scope of Bernoulli’s influence in the last one hundred years, let alone the preceding two hundred. It is perhaps more instructive to highlight a few beautiful results and avenues of research that demonstrate the lasting effect of his work.