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!Copyright notice <!-- don't remove! -->  
 
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| This article ''Pierre R&eacute;mond de Montmort'' was adapted from an original article by E. Seneta, which appeared in ''StatProb: The Encyclopedia Sponsored by Statistics and Probability Societies''. The original article ([<nowiki>http://statprob.com/encyclopedia/PierreRemondDeMONTMORT.html</nowiki> StatProb Source], Local Files: [[Media:PierreRemondDeMONTMORT.pdf|pdf]] | [[Media:PierreRemondDeMONTMORT.tex|tex]]) is copyrighted by the author(s), the article has been donated to ''Encyclopedia of Mathematics'', and its further issues are under ''Creative Commons Attribution Share-Alike License'. All pages from StatProb are contained in the [[:Category:Statprob|Category StatProb]].
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| This article ''Pierre Rémond de Montmort'' was adapted from an original article by E. Seneta, which appeared in ''StatProb: The Encyclopedia Sponsored by Statistics and Probability Societies''. The original article ([<nowiki>http://statprob.com/encyclopedia/PierreRemondDeMONTMORT.html</nowiki> StatProb Source], Local Files: [[Media:PierreRemondDeMONTMORT.pdf|pdf]] | [[Media:PierreRemondDeMONTMORT.tex|tex]]) is copyrighted by the author(s), the article has been donated to ''Encyclopedia of Mathematics'', and its further issues are under ''Creative Commons Attribution Share-Alike License'. All pages from StatProb are contained in the [[:Category:Statprob|Category StatProb]].
 
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     \vskip 10pt  
 
     \vskip 10pt  
 
     \noindent -->
 
     \noindent -->
'''Pierre R&eacute;mond de MONTMORT'''
+
'''Pierre Rémond de MONTMORT'''
  
 
b. 27 October 1678 - d. 7 October 1719
 
b. 27 October 1678 - d. 7 October 1719
Line 21: Line 21:
 
collaboration with Nicolaus Bernoulli.
 
collaboration with Nicolaus Bernoulli.
  
The second of three sons of Fran&ccedil;ois Reymond, &Eacute;cuyer,
+
The second of three sons of François Reymond, Écuyer,
Sieur de Breviande, and Marguerite R&eacute;mond,
+
Sieur de Breviande, and Marguerite Rémond,
 
who were of the nobility,
 
who were of the nobility,
 
Pierre was born in Paris. He travelled widely in Europe in his youth after giving up the
 
Pierre was born in Paris. He travelled widely in Europe in his youth after giving up the
Line 28: Line 28:
 
of Father Nicholas de Malebranche, with whom
 
of Father Nicholas de Malebranche, with whom
 
he studied religion, philosophy, and physics. Over a period of 3 years he and
 
he studied religion, philosophy, and physics. Over a period of 3 years he and
Fran&ccedil;ois Nicole taught themselves the new mathematics. He succeeded his
+
François Nicole taught themselves the new mathematics. He succeeded his
elder brother as canon of N\^{o}tre-Dame but resigned in 1706 to marry
+
elder brother as canon of Nôtre-Dame but resigned in 1706 to marry
 
and settle down at the country estate of Montmort, which he had bought
 
and settle down at the country estate of Montmort, which he had bought
 
with the fortune his father had left him in 1699.  His marriage was a happy
 
with the fortune his father had left him in 1699.  His marriage was a happy
Line 39: Line 39:
 
Montmort was aware of, and partly motivated by, the work by the
 
Montmort was aware of, and partly motivated by, the work by the
 
Bernoullis (which had been reviewed in 1705 and 1706) on the book
 
Bernoullis (which had been reviewed in 1705 and 1706) on the book
that was to be published posthumously in 1713 as Jacob Bernoulli's (q.v.)
+
that was to be published posthumously in 1713 as [[Bernoulli, Jakob|Jacob Bernoulli]]'s  
"Ars Conjectandi'', with a preface by Jacob's nephew Nicolaus
+
"Ars Conjectandi'', with a preface by Jacob's nephew [[Bernoulli, Nicolaus|Nicolaus Bernoulli]] (1687-1759).  Nicolaus and Montmort had by then  
Bernoulli (q.v.) (1687-1759).  Nicolaus and Montmort had by then  
 
 
evolved an extensive and fruitful
 
evolved an extensive and fruitful
 
technical correspondence. Some of it is included [together with a
 
technical correspondence. Some of it is included [together with a
Line 50: Line 49:
 
mathematical influence of the Bernoullis (not to mention their
 
mathematical influence of the Bernoullis (not to mention their
 
contributions) on the second edition, was substantial.  Montmort was
 
contributions) on the second edition, was substantial.  Montmort was
piqued by De Moivre's (q.v.) ''De Mensura Sortis'' (the latin precursor of
+
piqued by [[Moivre, Abraham de|De Moivre]]'s ''De Mensura Sortis'' (the latin precursor of
 
the ''Doctrine of Chances''), which appeared in 1711 and which he
 
the ''Doctrine of Chances''), which appeared in 1711 and which he
 
regarded as plagiaristic.  It was, in fact, quite scathing in
 
regarded as plagiaristic.  It was, in fact, quite scathing in
Line 57: Line 56:
  
 
The value of Montmort's work is partly in his scholarship.  He was
 
The value of Montmort's work is partly in his scholarship.  He was
well-versed in the work of chance of his predecessors (Pascal (q.v.),
+
well-versed in the work of chance of his predecessors ([[Pascal, Blaise|Pascal]],
Fermat (q.v.), Huygens (q.v.)), met Newton on one of a number of visits to England,
+
[[Fermat, Pierre de|Fermat]], [[Huygens, Christiaan|Huygens]]), met Newton on one of a number of visits to England,
corresponded with Leibnitz, but remained on good terms with both sides
+
corresponded with Leibniz, but remained on good terms with both sides
 
during the strife between their followers.   
 
during the strife between their followers.   
 
The summation of finite series is an element of Montmort's mathematical
 
The summation of finite series is an element of Montmort's mathematical
Line 68: Line 67:
 
the mathematical properties and is thus written for mathematicians
 
the mathematical properties and is thus written for mathematicians
 
rather than gamblers.  The Royal Society elected Montmort a Fellow in
 
rather than gamblers.  The Royal Society elected Montmort a Fellow in
1715 and the ''Acad&eacute;mie Royale des Sciences'' made him an
+
1715 and the ''Académie Royale des Sciences'' made him an
 
associate member (as he was not a resident of Paris) the following year.
 
associate member (as he was not a resident of Paris) the following year.
  
Line 87: Line 86:
 
September 9, 1713, Nicolaus proposed the following problems to Montmort:
 
September 9, 1713, Nicolaus proposed the following problems to Montmort:
 
<blockquote>
 
<blockquote>
it Quatri&egrave;me Probl&egrave;me: $A$ promises to give an it &eacute;cu
+
Quatrième Problème : $A$ promises to give an écu
to it B, if with an ordinary die he obtains a six with the first
+
to $B$, if with an ordinary die he obtains a six with the first
toss, two it &eacute;cus if he obtains a six with the second toss....
+
toss, two écus if he obtains a six with the second toss....
What is the expectation of $B$ ?
+
What is the expectation of $B$ ?
  
it Cinqui&egrave;me Probl&egrave;me: The same thing if  $A$  promises  
+
Cinquième Problème : The same thing if  $A$  promises  
$B$  it &eacute;cus in the progression 1, 2, 4, 8, 16,....
+
$B$  écus in the progression 1, 2, 4, 8, 16,....
 
</blockquote>
 
</blockquote>
  
Line 109: Line 108:
 
|valign="top"|{{Ref|1}}||valign="top"|    David, F. N. (1962). ''Games, Gods, and Gambling: The Origins and History of Probability and Statistical Ideas from the Earliest Times to the Newtonian Era.'' Griffin, London. Chap. 14.   
 
|valign="top"|{{Ref|1}}||valign="top"|    David, F. N. (1962). ''Games, Gods, and Gambling: The Origins and History of Probability and Statistical Ideas from the Earliest Times to the Newtonian Era.'' Griffin, London. Chap. 14.   
 
|-
 
|-
|valign="top"|{{Ref|2}}||valign="top"|  Fontenelle, B. (1721). &Eacute;loge de M. de Montmort. ''Histoire de l'Acad&eacute;mie Royale des Sciences pour l'Ann&eacute;e 1719'', pp. 83-93.  
+
|valign="top"|{{Ref|2}}||valign="top"|  Fontenelle, B. (1721). Éloge de M. de Montmort. ''Histoire de l'Académie Royale des Sciences pour l'Année 1719'', pp. 83-93.  
 
|-
 
|-
|valign="top"|{{Ref|3}}||valign="top"|    Hacking, I. (1974). Montmort, Pierre R&eacute;mond de. ''Dictionary of Scientific Biography'' (C. C. Gillispie, ed,), Scribner's, New York. '''9''', 499-500.   
+
|valign="top"|{{Ref|3}}||valign="top"|    Hacking, I. (1974). Montmort, Pierre Rémond de. ''Dictionary of Scientific Biography'' (C. C. Gillispie, ed,), Scribner's, New York. '''9''', 499-500.   
 
|-
 
|-
 
|valign="top"|{{Ref|4}}||valign="top"|  Hald, A. (1990). ''A History of Probability and Statistics and Their Applications Before 1750.'' Wiley, New York.  
 
|valign="top"|{{Ref|4}}||valign="top"|  Hald, A. (1990). ''A History of Probability and Statistics and Their Applications Before 1750.'' Wiley, New York.  

Latest revision as of 19:39, 8 March 2024

Copyright notice
This article Pierre Rémond de Montmort was adapted from an original article by E. Seneta, which appeared in StatProb: The Encyclopedia Sponsored by Statistics and Probability Societies. The original article ([http://statprob.com/encyclopedia/PierreRemondDeMONTMORT.html StatProb Source], Local Files: pdf | tex) is copyrighted by the author(s), the article has been donated to Encyclopedia of Mathematics, and its further issues are under Creative Commons Attribution Share-Alike License'. All pages from StatProb are contained in the Category StatProb.

Pierre Rémond de MONTMORT

b. 27 October 1678 - d. 7 October 1719

Summary. Montmort's fame rests on his Essay d analyse des jeux de hazard , which was virtually contemporaneous with Jacob Bernoulli's Ars Conjectandi and Abraham de Moivre's De Mensura Sortis; and on his collaboration with Nicolaus Bernoulli.

The second of three sons of François Reymond, Écuyer, Sieur de Breviande, and Marguerite Rémond, who were of the nobility, Pierre was born in Paris. He travelled widely in Europe in his youth after giving up the study of law. By 1699 he had returned to France, and came under the influence of Father Nicholas de Malebranche, with whom he studied religion, philosophy, and physics. Over a period of 3 years he and François Nicole taught themselves the new mathematics. He succeeded his elder brother as canon of Nôtre-Dame but resigned in 1706 to marry and settle down at the country estate of Montmort, which he had bought with the fortune his father had left him in 1699. His marriage was a happy one, and during this simple and retired life he set to work on the theory of probability. In 1708, the first edition of his Essay d'analyse sur les jeux de hazard appeared "...where with the courage of Columbus he revealed a new world to mathematicians..." according to Todhunter. At the time, Montmort was aware of, and partly motivated by, the work by the Bernoullis (which had been reviewed in 1705 and 1706) on the book that was to be published posthumously in 1713 as Jacob Bernoulli's "Ars Conjectandi, with a preface by Jacob's nephew Nicolaus Bernoulli (1687-1759). Nicolaus and Montmort had by then evolved an extensive and fruitful technical correspondence. Some of it is included [together with a single letter from Johann Bernoulli (1667-1748)] as the fifth part of the substantially expanded second edition of Montmort's Essay, also published, a few months later, in 1713, and prepared with the aid of Nicolaus during a 2-month stay at Montmort's estate. It is clear from the correspondence that the mathematical influence of the Bernoullis (not to mention their contributions) on the second edition, was substantial. Montmort was piqued by De Moivre's De Mensura Sortis (the latin precursor of the Doctrine of Chances), which appeared in 1711 and which he regarded as plagiaristic. It was, in fact, quite scathing in attacking his own first edition; Montmort retaliated with an Avertissement in his second edition. Contrary to popular opinion, the breach was never properly healed.

The value of Montmort's work is partly in his scholarship. He was well-versed in the work of chance of his predecessors (Pascal, Fermat, Huygens), met Newton on one of a number of visits to England, corresponded with Leibniz, but remained on good terms with both sides during the strife between their followers. The summation of finite series is an element of Montmort's mathematical interests which enters into his probability work and distinguishes it from the earlier purely combinatorial problems arising out of enumeration of equiprobable sample points. Although the Essay to a large extent deals with the analysis of popular gambling games, it focuses on the mathematical properties and is thus written for mathematicians rather than gamblers. The Royal Society elected Montmort a Fellow in 1715 and the Académie Royale des Sciences made him an associate member (as he was not a resident of Paris) the following year.

Montmort's best-known contribution to elementary probability is a result connected with the card games Rencontre, Treize, and Snap), in which $n$ distinct objects are assigned a specific order, while $n$

matching objects are assigned random order.  The probability  $u_n$ \

of at least one match is now well known to be $\Sigma_{j=1}^{n} (-1)^{j-1}/j!$. Montmort's general iterative procedure for calculating $u_n$ is from $nu_n = (n - 1) u_{n-1} + u_{n-2},$ a difference equation based on a conditional probability argument (given in a commentary by Nicolaus Bernoulli) according to the outcome at the first position.

Montmort also worked with Nicolaus on the problem of duration of play in the gambler's ruin problem, possibly prior to De Moivre, and at the time the most difficult problem solved in the subject. Finally, in a letter of September 9, 1713, Nicolaus proposed the following problems to Montmort:

Quatrième Problème : $A$ promises to give an écu to $B$, if with an ordinary die he obtains a six with the first toss, two écus if he obtains a six with the second toss.... What is the expectation of $B$ ?

Cinquième Problème : The same thing if $A$ promises $B$ écus in the progression 1, 2, 4, 8, 16,....

\indent It is clear that the St. Petersburg Paradox, as subsequently treated by Daniel Bernoulli in 1738 is but an insignificant step away. In his reply Montmort indicates the solution to Nicolaus' problems and describes them as being of no difficulty.

Montmort died of smallpox in Paris in 1719.


References

[1] David, F. N. (1962). Games, Gods, and Gambling: The Origins and History of Probability and Statistical Ideas from the Earliest Times to the Newtonian Era. Griffin, London. Chap. 14.
[2] Fontenelle, B. (1721). Éloge de M. de Montmort. Histoire de l'Académie Royale des Sciences pour l'Année 1719, pp. 83-93.
[3] Hacking, I. (1974). Montmort, Pierre Rémond de. Dictionary of Scientific Biography (C. C. Gillispie, ed,), Scribner's, New York. 9, 499-500.
[4] Hald, A. (1990). A History of Probability and Statistics and Their Applications Before 1750. Wiley, New York.
[5] Todhunter, I. (1865). A History of the Mathematical Theory of Probability. Macmillan, London. Chapter VIII. [Reprinted by Chelsea, New York, 1949 and 1965.]



Reprinted with permission from Christopher Charles Heyde and Eugene William Seneta (Editors), Statisticians of the Centuries, Springer-Verlag Inc., New York, USA.

How to Cite This Entry:
Montmort, Pierre Rémond de. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Montmort,_Pierre_R%C3%A9mond_de&oldid=39236