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Blaise Pascal

b. 19 June 1623 in Clermont-Ferrand, Puy-de-Dôme, Auvergne, France
d. 19 Aug 1662 in Paris, France

In 1631, Ètienne Pascal, the father of Blaise, moved to Paris with his son and two daughters. Blaise began his scientific education about 1635. According to this sister Gilberte he began to accompany this father to the meetings of the Acadèmie Parisienne which had been founded by Mersenne in 1635, but it is more likely this did not occur until 1639.

Early in 1646 he converted to the doctrine of Saint-Cyran, a Jansenist sect. He maintained contact with both the Jansenists at Port-Royal and the scientific community until his second conversion 23 November 1654. At this time he abandoned his scientific work in order to devote his energies to religious activities and joined the Port-Royal des Champs. It is perhaps worthwhile to note that Bishop Cornelius Jansen, founder of Jansenism, believed that scientific curiosity was only another form of sexual indulgence and therefore sinful.

Among his many works should be mentioned the important Treatise on the Arithmetic Triangle. This treatise was printed in 1654 but not distributed until 1665. The Provincial Letters, written with the aid of Arnauld and Nicole between 13 January 1656 and 24 March 1657, attacked the Jesuit doctrine of probabilism. These letters were published in 1657 under the pseudonym Louis de Montalte. During this same period he contributed to the famous Port-Royal Logic, L'Art de Penser or Ars Cogitandi, published anonymously in 1662. The pertinent sections are Book IV, Chapters 13-16. Finally, his unfinished Pensées or Thoughts were published postumously. This last work contains the famous Wager.

The correspondence between Pascal and Fermat indicate that in 1654 the Chevalier de Méré (1607-1684) asked Blaise Pascal about two problems in games of chance, thereby initiating his interest in probability.

The first problem concerned the minimum number of throws of a pair of dice which afforded an advantage to the thrower if he is to make his point. The second concerned the division of stakes between equally matched players if the game must be terminated prematurely. This latter problem is called the problem of points. Both of these problems apparently had been much discussed at this time. De Méré, among others including Roberval, had found the solution to the dice problem. In fact, de Méré was very much disturbed by the solution.

De Méré, while not a mathematician, did know some mathematics. He was interested in an apparent paradox with respect to the dice problem that he had observed concerning the critical number of throws required to make a point: To throw a 6 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.

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 4:6::24:36. But de Méré knew that the advantage lies with 25 throws and not 24. Is it the case that the mathematics is inconsistent? No, Cardano's Rule is incorrect. Indeed, a theorem proved by Moivre at a much later date shows why Cardano's Rule sometimes gives correct results.

However, de Méré was unable to solve the problem of points. For this reason he appealed to Pascal.

At some time in 1654 Pascal apparently sent a letter Pierre de Fermat in which he asks that Fermat confirm his reasoning concerning some problems in gaming. Follow the link to Fermat for a summary of the content of the letters.


Pascal - Fermat Correspondence. The link at left is to the translation that I myself made. Two published translations of the correspondence are available in English besides One appears in Smith's Source Book of Mathematics, the other in F.N. David's Gods, Games and Gambling.

The reader can consult a translation of the Treatise on the Arithmetic Triangle and Diverse Usages of the Arithmetic Triangle made by me. A translation of the Treatise on the Arithmetic Triangle appears in the Great Books of the Western World series.

The Wager from the Pensées. This is the Trotter translation which was included in the Harvard Classics series, Vol. 48. There are numerous other translations of the work available.