Ilias Tsoumas

Did you know that people tried to prove central limit theorem for over two centuries, first starting with de Moivre (1733), then almost a century after by Laplace who both used binomial distribution. Then it was Poisson who worked on this theorem, and Chebyshev (1890–1891) who gave a rigorous demonstration of it in the middle of the nineteenth century. At the beginning of the twentieth century, the Russian mathematician Liapounov, Aleksandr Mikhailovich (1901) created the generally recognized form of the central limit theorem by introducing its characteristic functions.  Markov, Andrei Andreevich(1908) also worked on it and was the first to generalize the theorem to the case of independent variables. In 1924 Kolmogorov started to become interested in research in Probability Theory and in 1928 he was able for the first time to formulate necessary and sufficient conditions of the Law of Large Numbers that escaped other best mathematicians of the time for many decades. It has taken the best mathematicians almost two centuries to prove conditions for LLN and prove CLT. In fact there is almost 500 (!) pages book describing the history of CLT. medicine.mcgill.ca/epidemiol… #statistics #machinelearning #gaussian