**Pierre Rémond de Montmort** was a French mathematician who wrote an important work on probability.

- His parents were François Rémond, Sieur de Breviande, and Marguerite Rallu.
- François Rémond was said to be very severe and very uncompromising.
- Tired of studying law, he left home at the age of eighteen and decided to go abroad.
- The Treaty of Ryswick, signed in September 1697, ended the Nine Years' War between France and the forces of England, Spain and the Netherlands.
- One result of this treaty was the Frenchmen could travel freely in Europe and Pierre took full advantage of this.
- He visited his cousin, M de Chamoys, in Regensburg in Germany.
- M de Chamoys was a French representative on the Diet of Regensburg.
- While living in M de Chamoys' home he found Malebranche's La Recherche de la Vérité Ⓣ(The Search for Truth) in his cousin's library and read the book.
- By the age of 21 he was back in France where he began to study under Malebranche.
- Particularly given Rémond's earlier behaviour, one might have expected him to live a life of leisure once he had the financial means to do so.
- Malebranche taught Rémond philosophy and Descartes' physics.
- Rémond went on to study the latest mathematics, in particular studying algebra and geometry with M Carré and M Guisnée.
- For three years he and another young mathematician François Nicole (1683-1758), together taught themselves about the latest mathematical developments.
- In 1700 he made a second visit to London and at this time he briefly met with Isaac Newton.
- In 1704, he used this wealth to purchase an estate at Montmort (and therefore became Pierre Rémond de Montmort).
- From this point on we shall refer to him as Montmort.
- He lived most of his life in the Château de Montmort on his estate and often invited top mathematicians to visit him.
- The Duchess of Angouleme lived at the Château Mareuil, a neighbouring property to the estate at Montmort, and Montmort had met the Duchess's niece while making a courtesy call on his neighbours.
- Before his marriage, he had given up his position as canon at Notre Dame de Paris.
- Montmort's reputation was made by his book on probability Essay d'analyse sur les jeux de hazard Ⓣ(Essay on the analysis of gambling) which appeared in 1708.
- However, we should give some background to Montmort's work by looking at various influences on him.
- The correspondence between Blaise Pascal and Pierre de Fermat in 1654 is generally taken as the beginnings of probability theory, but the first published work on the topic was by Christiaan Huygens who heard about the Pascal-Fermat correspondence but independently solved the problems they had discussed.
- Huygens published De Ratiociniis in Ludo Aleae Ⓣ(Reasoning in games of dice) in 1657 and in it stated five problems which Montmort solved in his book.
- Both Huygens' paper and knowing that Jacob Bernoulli had written an unfinished work in probability seem to be the main influences on Montmort.
- Montmort collaborated with Nicolaus (I) Bernoulli in a fascinating correspondence which began in 1710.
- They discussed many topics, particularly the probability questions that arose from Montmort's book.
- Nicolaus(I) Bernoulli spent three months at the Château de Montmort in 1712.
- In the second edition of Essay d'analyse sur les jeux de hazard Ⓣ(Essay on the analysis of gambling) published in 1713, Montmort included copies of the correspondence.
- Here is an ideas of the contents of this second edition.
- There are five sections: (1) A Treatise on Combinations; (2) Problems on Games of Chance; (3) This is called "Problem on Quinquenove:" (4) Various Problems; and (5) Correspondence.
- The third section examines games played with dice: Quinquenove, Hazard, Esperance, TricTrac, Trois Dez, Rafle, Trois Rafles, and Noyaux.
- The fourth section solves various problems including Huygens problems from De Ratiociniis in Ludo Aleae Ⓣ(Reasoning in gambling games).
- The fifth section contains Montmort's correspondence with Nicolaus (I) Bernoulli.
- However, it was not only probability that Nicolaus (I) Bernoulli and Montmort discussed in their letters.
- Such a work, if done well, could be regarded to some extent as a history of the human mind, since it is in this science, more than in anything else, that man makes known that gift of intelligence that God has given him to rise above all other creatures.
- Of course, since this present biography is part of a History of Mathematics archive, Montmort's comments are particularly important.
- It is interesting to note that Jean-Etienne Montucla, in his Histoire des mathématiques Ⓣ(History of Mathematics) (1758), claimed that this letter was his inspiration in writing his famous history of mathematics book.
- In 1715 Montmort visited England again, this time to watch the total eclipse of the sun in the company of the Astronomer Royal, Edmond Halley.
- He met a number of mathematicians on this visit including Abraham de Moivre and Brook Taylor.
- He became friendly with these mathematicians even though he suspected de Moivre of plagiarism with his De Mensura Sortis Ⓣ(The measure of Socrates) (the Latin precursor of Doctrine of Chance).
- It says a lot that they were capable of friendship despite having had a quite public scientific disagreement.
- De Moivre had made a vicious attack on Montmort's first edition of the Essay in his De Mensura Sortis Ⓣ(The measure of Socrates) (1711) and Montmort had retaliated with an attack on de Moivre when he brought out his second edition.
- However Montmort has more credit in trying to mend the quarrel, for although he wrote repeatedly to de Moivre, the latter only infrequently responded.
- After returning to France in the spring of 1715 Montmort carried out a very active correspondence with Taylor.
- In addition to those mentioned above, let us add at this point that Montmort corresponded with John Craig, Edmond Halley, Gottfried Leibniz, Jakob Hermann and Giovanni Poleni.
- At a time of high feelings in the Newton-Leibniz controversy it says a lot for Montmort that he could be close friends with followers of both camps.
- Montmort had been elected to be a Fellow of the Royal Society of London in 1715 while he was on this trip to England.
- He was elected an associate member of the Académie Royal des Sciences in 1716.
- This close friendship did not stop them carrying out a fascinating discussion regarding the merits of the physics of Descartes and that of Newton.
- We are as divided on physics as theologians, but at least we can see a bit more clearly in science than in religion.
- You deserve good proofs.
- Montmort eventually produced Dissertation on the principles of physics of M Descartes compared to those of the English philosophers which was published in October 1718 in L'Europe savante.
- Montmort constructed a carefully reasoned defence of Malbranchian physics that was rooted, in his mind, in the fundamental similarity between it and a correct reading of Newton's 'Principia'.
- This is the method of analysis used by mathematicians, and the art of pulling the unknown out of the known is what renders this science the most beautiful and the most useful production of the human mind.
- In this argument, he was precisely following Newton's approach and he went on to argue that application of Newton's ideas led directly to the theory of vortices.
- He tried to bridge the gulf between the two sides by accepting Newton's inverse square law of attraction but arguing that the mechanism was due to Descartes' vortices.
- Rather, he argued, we can never know what the real nature of bodies is, and we are thus restricted to rational descriptions of empirical phenomena.
- Smallpox was a dreaded disease at this time with around 400,000 people dying each year in Europe.
- There were frequent epidemics, the one that struck Paris in 1719 killed 14,000 of the inhabitants of the city.
- Montmort, was infected by smallpox during this 1719 epidemic and died in October of that year.
- After his death his paper on summing infinite series, De seriebus infinitis tractatus Ⓣ(A tract on infinite series), was published in the Philosophical Transactions of the Royal Society.

Born 27 October 1678, Paris, France. Died 7 October 1719, Paris, France.

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**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive