2020Unpublished venueOpen access

Blaise Pascal Versus Pierre de Fermat

Kenneth Binmore

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Abstract

Pascal and Fermat are credited with being the fathers of probability theory as a consequence of a sequence of letters they exchanged about how to solve a famous gambling problem raised by the Chevalier de Méré. Their method consists of counting the number of equally likely ways that something can happen. Méré’s problem is much more complicated, but their approach is no different from Fermat’s earlier proof that Méré will win more often at rolling a six in four throws of a dice than at rolling a double-six in twenty-four throws of two dice. We would nowadays say that the probability of winning is greater in the first case, but the concept of probability had not been invented in 1654.

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Pascal and Fermat are credited with being the fathers of probability theory as a consequence of a sequence of letters they exchanged about how to solve a famous gambling problem raised by the Chevalier de Méré. Their method consists of counting the number of equally likely ways that something can happen. Méré’s problem is much more complicated, but their approach is no different from Fermat’s earlier proof that Méré will win more often at rolling a six in four throws of a dice than at rolling a double-six in twenty-four throws of two dice. We would nowadays say that the probability of winning is greater in the first case, but the concept of probability had not been invented in 1654.

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Available abstract

Pascal and Fermat are credited with being the fathers of probability theory as a consequence of a sequence of letters they exchanged about how to solve a famous gambling problem raised by the Chevalier de Méré. Their method consists of counting the number of equally likely ways that something can happen. Méré’s problem is much more complicated, but their approach is no different from Fermat’s earlier proof that Méré will win more often at rolling a six in four throws of a dice than at rolling a double-six in twenty-four throws of two dice. We would nowadays say that the probability of winning is greater in the first case, but the concept of probability had not been invented in 1654.

Key concepts: Fermat's Last Theorem, Dice, Pascal (unit), Sequence (biology), Mathematics, Fermat number, Calculus (dental), Mathematical economics

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