IntroductionSome texts start the tale of probability and statistics by mentioning the isolated efforts of Cardano (Liber de Ludo Aleae (1565), first published in 1663) and Galilei (Sopra le Scoperte dei Dadi (around 1620), first published in 1718), but there is a consensus that it all began with some questions on gambling posed by Antoine Gombaud, Chevalier de Méré and Damien Mitton to Pascal in 1654.
As there are no journals in those days, other means are needed to obtain and divulge the latest scientific developments. Writing letters was one way of dealing with this obstacle. It is Marin Mersenne who plays a central part as a communication link between scientists and philosophers all over Europe by writing and receiving letters and passing them to others. Among his acquaintances are Descartes, Pascal, Fermat, Galilei and Huygens.
|1654||Between July and October of that year seven letters are written by
and Pierre de Fermat which
form the genesis of the probability theory.
One of the topics of these letters, the forementioned question of de Méré, is known as the problème des partis (problem of points): two players P1 and P2 agree to play a series of fair games until one of them has won a specified number of games N. The play is suddenly interrupted. P1 has won N1 games and P2 N2 games. How should the stakes be divided?
Pascal had plans to write a tract about the problème des partis called Aleae Geometria as he explained in November that year to the Académie Parisienne:
Novissima autem ac penitùs intentatæ materiæ tractatio, scilicet de compositione aleæ in ludis ipsi subjectis, quod gallico nostro idiomate dicitur (faire les partis des jeux): ubi anceps fortuna æquitate rationis ita reprimitur ut utrique lusorum quod jure competit exactè semper assignetur Quod quidem eo fortiùs ratiocinando quærendum, quo minùs tentando investigari possit: ambigui enim sortis eventus fortuitæ contingentiæ potiùs quam naturali necessitati meritò tribuuntur. Ideò res hactenus erravit incerta; nunc autem quæ experimento rebellis fuerat, rationis dominium effugere non potuit: eam quippe tantâ securitate in artem per geometriam reduximus, ut certitudinis ejus particeps facta, jam audacter prodeat; et sic matheseos demonstrationes cum aleæ incertitudine jungendo, et quæ contraria videntur conciliando, ab utrâque nominationem suam accipiens stupendum hunc titulum jure sibi arrogat: aleæ geometria.but he never wrote it, although he may have included some of the intended material in his Traité du Triangle Arithmétique that was published in 1665.
Early that year Christiaan
Huygens writes a draft version of Van Rekeningh in Spelen van Geluck and sends it to Frans van Schooten, professor of mathematics at the Leyden University.
Huygens was one of his former students. Van Schooten is interested and wants to add it to the last part of a book on mathematics he is preparing.
Van Rekeningh in Spelen van Geluck is a short treatise of about 15 pages, that Huygens probably based on what he heard, during his stay in Paris the previous year, about the correspondence of Pascal and Fermat.
In its final form it contains fourteen problems (Voorstellen) with their solution/proof and five problems to be solved by the reader. These last five problems are in part by Fermat and Pascal.
The second and fourth problems of these last five problems are concerned with picking black and white chips while blindfolded (a precursor of the urn model). The last of the five problems becomes known as the Gambler's Ruin and stems from the correspondence of Pascal and Fermat that was resumed in 1656. It was from Pierre Carcavy that Huygens heard of these Pascal-Fermat problems
The last five problems become a touchstone for later mathematicians (e.g. Jacob and Nicholas Bernoulli, de Moivre and Montmort) to emulate or improve on the solutions that Huygens will publish.
|1657||De Ratiociniis in Ludo Aleae, a
Latin translation of Van Rekeningh in Spelen van Geluck by Frans
van Schooten, together with an introductory
letter from Huygens, is the first publication on probability (i.e.
gambling). It is the very last part of Van Schootens Exercitationum Mathematicarum
libri quinque (Five books with Mathematical Exercizes).
More on the latin text can be found via my Christiaan Huygens 'under construction' page
The original Dutch text of Van Rekeningh in Spelen van Geluck,
together with an introductory letter from Huygens is published
in Mathematische Oeffeningen, begrepen in vijf boecken (the
Dutch translation of the 1657 publication) by Van Schooten.
More on the dutch text can be found via my Christiaan Huygens 'under construction' page
starts publishing his Observations on the Bills of Mortality. These weekly bills,
first published in 1604,
are used to detect the beginning of a plague epidemic, but had never been analyzed properly. He is the
first to condense data into tables and to do some descriptive statistical
analysis on these tables.
He discusses the reliability of the data. He is the first to demonstrate 'statistically' that the number of males and females is nearly equal and that the sex ratio at birth is stable. He is one of the first to construct a life table, which forms the corner stone of life insurance mathematics.
|1666||In Le Journal des Sçavans xxxi, august 2, 1666 (359-370(=364)) appears a review of the third edition (1665) of John Graunt's Observations on the Bills of Mortality. This review gives a summary of 'plusieurs reflexions curieuses', of which the second are Graunt's data on life expectancy. This review is used by Nicolaus Bernoulli in his De Usu Artis Conjectandi in Jure (1709).|
|1669||Christiaan Huygens and his brother Lodewijk discuss between August and December that year Graunts mortality table (Graunt 1662, p.62) in letters #1755, 1756, 1771+1772, 1775, 1776+1777+1778 (OC VI).|
|1670||Juan Caramuel Lobkowitz
publishes Mathesis Biceps, a mathematical encyclopedia, in which he
reprints Huygens' tract De Ratiociniis in Ludo Aleae. He incorrectly
attributes the tract to a Danish astronomer C.S. Longomontanus
(04/oct/1562-1647), an assistant of Tycho Brahe.
More on later editions can be found via my Christiaan Huygens 'under construction' page
|1671||Johan de Witt's Waerdije van Lijfrenten Naer Proportie van Losrenten is published. It was quite rare as can be learned from Todhunter (1865) and Van der Waerden (1975). Letters written between Jacob Bernoulli and Leibnitz in 1703-1705 show that Jacob knew the book and tried to obtain it from Leibnitz, who had owned a copy, but seemed to have lost it.|
|1684||In the next five years Jacob Bernoulli develops his idea's on probability as described in his Meditationes. These are the foundation of his Ars Conjectandi (1713)|
translation of Huygens' De Ratiociniis in Ludo Aleae becomes the first publication on probability in the English language.
It is titled Of the Laws of Chance, or, a method of Calculation of the Hazards of Game, Plainly demonstrated, And applied to Games as present most in Use.
The preface contains the following observations:
|1693||Edmond Halley's work on life tables is published in An estimate of the Degrees of Mortality of Mankind, drawn from curious Tables of the Births and Funerals at the City of Breslaw; with an Attempt to ascertain the Price of Annuities upon Lives. and Some further Considerations on the Breslaw Bills of Mortality, By the same Hand, &c.|