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Antoine Bombaud,
Chevalier de Méré

b. 1607
d. 29 December 1684

De Méré was a prominent figure in the court of Louis XIV where he acted as an advisor and arbiter. De Méré, while not a mathematician, did know some mathematics. However, he apparently did have a somewhat inflated opinion of his abilities. In Letter XIX to Pascal (Lettres de Monsieur le Chevalier de Méré, 1682) he writes:

"Vous sçavez que j'ay découvert dans les Mathematiques des choses si rares que les plus sçavans des anciens n'en ont jamais rien dit, & desquelles les meilleurs Mathematiciens de l'Europe ont esté surpris; Vous avez écrit sur mes inventions aussi-bien que Monsieur Huguens, Monsieur de Fermac & tant dautres qui les ont admirées."

"You know that I have discovered in Mathematics some things so rare that the most scholarly of the ancients have never said anything of them, and of which the better Mathematicians of Europe have been surprised; you have written on my inventions as well as Mr. Huygens, Mr. Fermat and so many others who have admired them."

Extracts from this letter are included in a lengthy article on Zenon, the Epicurean philosopher, in Bayles Dictionary. The subject of the letter was a disagreement between de Méré and Pascal regarding the composition of the line. It possesses a somewhat nasty tone. De Méré first argued that relying solely on mathematical proof prevented Pascal from seeing the true nature of things and that those involving infinity in particular led him into error. Unfortunately, de Méré was unable to express himself clearly and in the remainder of the letter, his discussion is obscure. It is safe to say, however, that his difficulty seemed to lie in the distinction between reality and the mathematical model: matter must consist of indivisibles finite in number, but the mathematical model of bodies is of a continuum and hence infinitely divisible. 

We infer from the correspondence between Pascal and Fermat that he was very much interested in an apparent paradox he observed while gambling. This paradox involved the critical number of throws required to make a point.

To throw a six with one die, the advantage lies with 4 throws. That is, it is more likely to observe at least one 6 in four throws of a die than to not observe a 6. In fact, the odds are 671 to 625. This means that a gambler, who wagers that he will throw at least one six in four throws, has the advantage or greater chance of winning over one who would wager against him.

Now de Méré knew Cardano's rule which asserts that the ratio of the critical number of throws to the number of outcomes is constant. Therefore, in order to throw two 6's with a pair of dice, the advantage should lie with 24 throws since there are 36 outcomes in this case and 4 is to 6 as 24 is to 36.

But de Méré knew too that the advantage actually lies with 25 throws and not 24. Both he and Roberval had found the solution to the problem. The critical number of throws could be determined quite easily and it was not the number given by Cardano's rule.

Therefore, de Méré believed mathematics to be inconsistent.

De Méré was unable to solve the so-called problem of points. This problem concerned the division of the stakes in a prematurely terminated game of chance. For this reason he appealed to Pascal for a resolution of the difficulty.