Ars Conjectandi

Ars Conjectandi (Latin for "The Art of Conjecturing") is a book on combinatorics and mathematical probability written by Jacob Bernoulli and published in 1713, eight years after his death, by his nephew, Niklaus Bernoulli. The seminal work consolidated, apart from many combinatorial topics, many central ideas in probability theory, such as the very first version of the law of large numbers: indeed, it is widely regarded as the founding work of that subject. It also addressed problems that today are classified in the twelvefold way and added to the subjects; consequently, it has been dubbed an important historical landmark in not only probability but all combinatorics by a plethora of mathematical historians. The importance of this early work had a large impact on both contemporary and later mathematicians; for example, Abraham de Moivre. Bernoulli wrote the text between 1684 and 1689, including the work of mathematicians such as Christiaan Huygens, Gerolamo Cardano, Pierre de Fermat, and Blaise Pascal. He incorporated fundamental combinatorial topics such as his theory of permutations and combinations (the aforementioned problems from the twelvefold way) as well as those more distantly connected to the burgeoning subject: the derivation and properties of the eponymous Bernoulli numbers, for instance. Core topics from probability, such as expected value, were also a significant portion of this important work. In Europe, the subject of probability was first formally developed in the 16th century with the work of Gerolamo Cardano, whose interest in the branch of mathematics was largely due to his habit of gambling. He formalized what is now called the classical definition of probability: if an event has a possible outcomes and we select any b of those such that b ≤ a, the probability of any of the b occurring is . However, his actual influence on mathematical scene was not great; he wrote only one light tome on the subject in 1525 titled Liber de ludo aleae (Book on Games of Chance), which was published posthumously in 1663.