The origins of modern combinatorics
The origins of modern combinatorics
In 1654 Fermat and Pascal used combinatorial and other means to solve theoretical questions arising from games of chance; indeed, Pascal’s treatise on the arithmetical triangle might be called the first modern treatise on combinatorics. Leibniz was also deeply interested in this subject, but nearly all of his contributions to symmetric functions, partitions, and determinants remained unpublished until recently. Frénicle de Bessy’s contributions to combinatorics were also published posthumously. Jacob Bernoulli’s posthumously published Ars Conjectandi presented an exhaustive treatment of early modern combinatorics. Soon after Bernoulli’s death, Pierre Rémond de Montmort and Abraham de Moivre mathematically analysed card games and games of dice in terms of derangements. James Stirling’s contributions to combinatorics were motivated by algebraic studies.
Keywords: Fermat, Pascal, Leibniz, Frénicle de Bessy, Jacob Bernoulli, Pierre Rémond de Montmort, Abraham de Moivre, James Stirling
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