Ars Conjectandi

work by Bernoulli

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June 18, 2026

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Ars Conjectandi, published posthumously in 1713, is a seminal work by Swiss mathematician Jakob Bernoulli. This groundbreaking text introduced fundamental concepts in probability theory, including the first principles of permutations and combinations. It also presented Bernoulli numbers and laid out what is now known as the Bernoulli law of large numbers, a cornerstone of modern sampling theory. Bernoulli's work aimed to provide a formal structure for reasoning from observed data to infer underlying causes, suggesting that observed proportions converge to true probabilities as the number of trials increases.12

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Jakob Bernoulli
Jakob Bernoulli’s pioneering work Ars Conjectandi (published posthumously, 1713; “The Art of Conjecturing”) contained many of his finest concepts: his theory of permutations and combinations; the so-called Bernoulli numbers, by which he derived the exponential series; his treatment of mathematical and moral predictability; and the subject of probability—containing what…
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Jakob Bernoulli’s pioneering work Ars Conjectandi (published posthumously, 1713; “The Art of Conjecturing”) contained many of his finest concepts: his theory of permutations and combinations; the so-called Bernoulli numbers, by which he derived the exponential series; his treatment of mathematical and moral predictability; and the subject of probability—containing what…
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probability and statistics
The probability of causes
…1713 from a manuscript, the Ars conjectandi, left behind at his death in 1705. There he showed that the observed proportion of, say, tosses of heads or of male births will converge as the number of trials increases to the true probability p, supposing that it is uniform. His theorem…
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…1713 from a manuscript, the Ars conjectandi, left behind at his death in 1705. There he showed that the observed proportion of, say, tosses of heads or of male births will converge as the number of trials increases to the true probability p, supposing that it is uniform. His theorem…
Read More