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!Copyright notice <!-- don't remove! -->  
 
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| This article ''Anton Meyer'' was adapted from an original article by Eugene William Seneta, which appeared in ''StatProb: The Encyclopedia Sponsored by Statistics and Probability Societies''. The original article ([<nowiki>http://statprob.com/encyclopedia/AntonMEYER.html</nowiki> StatProb Source], Local Files: [[Media:AntonMEYER.pdf|pdf]] | [[Media:AntonMEYER.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 ''Anton Meyer'' was adapted from an original article by M.F. Jozeau, which appeared in ''StatProb: The Encyclopedia Sponsored by Statistics and Probability Societies''. The original article ([<nowiki>http://statprob.com/encyclopedia/AntonMEYER.html</nowiki> StatProb Source], Local Files: [[Media:AntonMEYER.pdf|pdf]] | [[Media:AntonMEYER.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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Although from a family of modest means (his father was a shoemaker),
 
Although from a family of modest means (his father was a shoemaker),
 
he completed his secondary schooling in the humanities in 1818, and
 
he completed his secondary schooling in the humanities in 1818, and
then pursued his scientific studies with brilliance at Li&egrave;ge
+
then pursued his scientific studies with brilliance at Liège
 
University.  During this period, in order to earn a living, he
 
University.  During this period, in order to earn a living, he
 
taught and also catalogued the scientific books at the University's
 
taught and also catalogued the scientific books at the University's
Line 34: Line 34:
 
to listen to the eminent scientists of the day. On his return to
 
to listen to the eminent scientists of the day. On his return to
 
Belgium, he taught at the Echternach College and later at the
 
Belgium, he taught at the Echternach College and later at the
Military School of Br&eacute;da.  In 1827, he published a paper in
+
Military School of Bréda.  In 1827, he published a paper in
Quetelet's (q.v.) "La correspondance math&eacute;matique et physique'',
+
[[Quetelet, Adolphe|Quetelet]]'s "La correspondance mathématique et physique",
 
about an instrument he had invented for drawing in perspective.  In
 
about an instrument he had invented for drawing in perspective.  In
 
1831 he taught at the Louvain College, and later from 1832 to 1837
 
1831 he taught at the Louvain College, and later from 1832 to 1837
Line 44: Line 44:
 
Brussels Military School, which had just opened, but he resigned
 
Brussels Military School, which had just opened, but he resigned
 
from this position in 1836.  In 1838, he was appointed to the Chair
 
from this position in 1836.  In 1838, he was appointed to the Chair
of Mathematical Analysis at the Universit&eacute; Libre de Bruxelles,
+
of Mathematical Analysis at the Université Libre de Bruxelles,
 
and later he replaced Lemaire in the Chair of Differential and
 
and later he replaced Lemaire in the Chair of Differential and
 
Integral Calculus, Higher Analysis and Calculus of Probabilities at
 
Integral Calculus, Higher Analysis and Calculus of Probabilities at
Li&egrave;ge University from 1849 until his death. Under Meyer, two
+
Liège University from 1849 until his death. Under Meyer, two
 
distinct subjects were taught, analysis, and  
 
distinct subjects were taught, analysis, and  
 
probability theory and political arithmetic.
 
probability theory and political arithmetic.
Line 59: Line 59:
 
probability were  published only many years after his death, in 1874 by F.
 
probability were  published only many years after his death, in 1874 by F.
 
Folie, based on the author's manuscripts, as the ''Cours de
 
Folie, based on the author's manuscripts, as the ''Cours de
Calcul des Probabilit&eacute;s fait \`a l'Universit&eacute; de Li&egrave;ge de
+
Calcul des Probabilités fait à l'Université de Liège de
1849 \`a 1857'' (F. Hayez, Bruxelles). This work, given the relative dearth of
+
1849 à 1857'' (F. Hayez, Bruxelles). This work, given the relative dearth of
 
treatises on probability at the time, created something of a stir,
 
treatises on probability at the time, created something of a stir,
 
and was translated into German in 1879 by E. Czuber under the title
 
and was translated into German in 1879 by E. Czuber under the title
''Vorlesungen &uuml;ber Wahrscheinlichkeitsrechnung''.  It contains
+
''Vorlesungen über Wahrscheinlichkeitsrechnung''.  It contains
 
a thoroughly researched account of the theory of errors. In the
 
a thoroughly researched account of the theory of errors. In the
 
preface, F. Folie points out:  "This book by Meyer is a very
 
preface, F. Folie points out:  "This book by Meyer is a very
complete summary of the most important works of Bernoulli (q.v),  
+
complete summary of the most important works of [[Bernoulli, Daniel|Bernoulli]],  
de Moivre (q.v.), Laplace (q.v.), Poisson (q.v.), Gauss (q.v.),
+
[[Moivre, Abraham de|de Moivre]],
Encke, Bienaym&eacute; (q.v.)... on the calculus of
+
[[Laplace, Pierre-Simon Marquis de|Laplace]], [[Poisson, Simeon-Denis|Poisson]], [[Gauss, Carl Friedrich|Gauss]],
 +
Encke, [[Bienaymé, Irenée-Jules|Bienaymé]]... on the calculus of
 
probabilities.  One might well suggest that there does not exist a
 
probabilities.  One might well suggest that there does not exist a
broader treatise on the subject, except for Laplace's "Th&eacute;orie
+
broader treatise on the subject, except for Laplace's "Théorie
analytique des probabilit&eacute;s''...".
+
analytique des probabilités''...".
  
 
The treatise is very theoretical, even in his chapters concerned with
 
The treatise is very theoretical, even in his chapters concerned with
 
the theory of errors, concentrating essentially on his proofs. This
 
the theory of errors, concentrating essentially on his proofs. This
 
is in contrast to J.B.J. Liagre (1815-1891), who, in his ''Calcul des
 
is in contrast to J.B.J. Liagre (1815-1891), who, in his ''Calcul des
probabilit&eacute;s et th&eacute;orie des erreurs'' published in 1852, gave a
+
probabilités et théorie des erreurs'' published in 1852, gave a
 
large number of applications of the theory of errors, particularly
 
large number of applications of the theory of errors, particularly
 
in geodesy.
 
in geodesy.
Line 89: Line 90:
 
From the 1830's, he personally carried out triangulations, working
 
From the 1830's, he personally carried out triangulations, working
 
out the calculations which were involved in them.  Traces of his
 
out the calculations which were involved in them.  Traces of his
notes are to be found in the ''Le&ccedil;ons de trigonom&eacute;trie
+
notes are to be found in the ''Leçons de trigonométrie
rectiligne'' and the ''Le&ccedil;ons de trigonom&eacute;trie sph&eacute;rique''
+
rectiligne'' and the ''Leçons de trigonométrie sphérique''
published in 1844, as well as his ''Cours de g&eacute;od&eacute;sie'' dated
+
published in 1844, as well as his ''Cours de géodésie'' dated
 
1845, which faithfully followed the French mathematical tradition.
 
1845, which faithfully followed the French mathematical tradition.
 
It is well known that since
 
It is well known that since
Line 122: Line 123:
 
squares. It was rejected by the Academy and never published.  
 
squares. It was rejected by the Academy and never published.  
 
The bibliography of a thesis by L. Bouvier entitled "Dissertation  
 
The bibliography of a thesis by L. Bouvier entitled "Dissertation  
sur la th&eacute;orie
+
sur la théorie des moindres carré'' which appeared in 1848 is identical with that
des moindres carr&eacute;s'' which appeared in 1848 is identical with that
 
 
of Meyer's report.  Thus Meyer attempted to spread the information he had
 
of Meyer's report.  Thus Meyer attempted to spread the information he had
 
gathered in Germany on the method of least squares and its
 
gathered in Germany on the method of least squares and its
Line 147: Line 147:
 
latter part of his life, some of them appearing posthumously.  In
 
latter part of his life, some of them appearing posthumously.  In
 
particular, we note his "Essai sur une exposition nouvelle de
 
particular, we note his "Essai sur une exposition nouvelle de
la th&eacute;orie des probabilit&eacute;s a posteriori'', 1857.  This work was
+
la théorie des probabilités a posteriori'', 1857.  This work was
 
at the printer's when Meyer died. The author goes over the enunciations
 
at the printer's when Meyer died. The author goes over the enunciations
 
and proofs of Bayes' theorem in the continuous case, Laplace's
 
and proofs of Bayes' theorem in the continuous case, Laplace's
Line 156: Line 156:
 
Also in 1857, Meyer published his reaction ``Examen critique de la notice  
 
Also in 1857, Meyer published his reaction ``Examen critique de la notice  
 
de M. Liagre"
 
de M. Liagre"
to a memoir entitled ``Sur la probabilit&eacute; de
+
to a memoir entitled "Sur la probabilité de
l'existence d'une cause d'erreur r&eacute;guli&egrave;re", which Liagre had
+
l'existence d'une cause d'erreur régulière", which Liagre had
 
presented to the Royal Academy of Belgium in 1855.  The topic is
 
presented to the Royal Academy of Belgium in 1855.  The topic is
 
the use of the calculus of probabilities to detect systematic
 
the use of the calculus of probabilities to detect systematic
Line 170: Line 170:
 
December 1846. An account of this conflict, in which Meyer invoked the
 
December 1846. An account of this conflict, in which Meyer invoked the
 
support of the leading authority of the day on statistical matters,
 
support of the leading authority of the day on statistical matters,
I.J.Bienaym&eacute; (q.v.), is given by Breny, Jongmans and Seneta (1992).  
+
[[Bienaymé, Irenée-Jules|I.J. Bienaymé]], is given by Breny, Jongmans and Seneta (1992).  
Bienaym&eacute;,
+
Bienaymé,
 
himself no stranger to controversies, recalled it in a paper of 1875, which
 
himself no stranger to controversies, recalled it in a paper of 1875, which
 
linked his name with the turning-points test.
 
linked his name with the turning-points test.
  
Meyer was
+
Meyer was not a  creator of originality in probability and statistics; but rather an
not a  creator of originality in probability and statistics; but rather an
 
 
interpreter, able to clarify, simplify and make rigorous in an age not
 
interpreter, able to clarify, simplify and make rigorous in an age not
 
noted for mathematical lucidity. He is better known in Luxemburg as the  
 
noted for mathematical lucidity. He is better known in Luxemburg as the  
first poet of the
+
first poet of the Luxemburg language, and a man who fostered the development of
Luxemburg language, and a man who fostered the development of
 
 
national culture.
 
national culture.
 
  
 
====References====
 
====References====
Line 191: Line 188:
 
|valign="top"|{{Ref|2}}||valign="top"|  Blum, M. (1902-1908). ''Biographie Luxembourgeoise'', Vol. 2. (Chez l'auteur, Luxembourg)  
 
|valign="top"|{{Ref|2}}||valign="top"|  Blum, M. (1902-1908). ''Biographie Luxembourgeoise'', Vol. 2. (Chez l'auteur, Luxembourg)  
 
|-
 
|-
|valign="top"|{{Ref|3}}||valign="top"|  Breny, H., Jongmans, F. and Seneta, E. (1992). Annexe: A. Meyer et l'Acad&eacute;mie. In ''Regards sur 175 ans de science \`a l'Universit&eacute; de Li&egrave;ge, 1817-1992.'' Anne-Marie Bern&egrave;s (Ed.). Centre d'Histoire des Sciences et des Techniques, Universit&eacute; de Li&egrave;ge. pp. 13-22bis.  
+
|valign="top"|{{Ref|3}}||valign="top"|  Breny, H., Jongmans, F. and Seneta, E. (1992). Annexe: A. Meyer et l'Académie. In ''Regards sur 175 ans de science à l'Université de Liège, 1817-1992.'' Anne-Marie Bernès (Ed.). Centre d'Histoire des Sciences et des Techniques, Université de Liège. pp. 13-22bis.  
 
|-
 
|-
|valign="top"|{{Ref|4}}||valign="top"|  Gloden, A. (1949). La vie et l'oevre scientifique de neuf math&eacute;maticiens belges d'origine luxembourgeoise. In ''Themecht Zeischrift f&uuml;r Luxemburger Geschichte'', '''1''', 13-16.   
+
|valign="top"|{{Ref|4}}||valign="top"|  Gloden, A. (1949). La vie et l'oeuvre scientifique de neuf mathématiciens belges d'origine luxembourgeoise. In ''Themecht Zeischrift für Luxemburger Geschichte'', '''1''', 13-16.   
 
|-
 
|-
|valign="top"|{{Ref|5}}||valign="top"|  Godeaux, L. (1956). Notice sur Antoine Meyer, membre de l'Acad&eacute;mie. ''Annuaire pour 1956.'' Acad&eacute;mie Royale de Belgique, Brussels. [In "Notices biographiques", pp.2-15.]
+
|valign="top"|{{Ref|5}}||valign="top"|  Godeaux, L. (1956). Notice sur Antoine Meyer, membre de l'Académie. ''Annuaire pour 1956.'' Académie Royale de Belgique, Brussels. [In "Notices biographiques", pp.2-15.]
 
|-
 
|-
 
|}
 
|}
 
 
M.F. Jozeau
 
 
 
<!-- \end{document} -->
 
<!-- \end{document} -->
  
  
 
<references />
 
<references />
 +
 +
Reprinted with permission from
 +
Christopher Charles Heyde and Eugene William Seneta (Editors),
 +
Statisticians of the Centuries, Springer-Verlag Inc., New York, USA.
  
 
[[Category:Statprob]]
 
[[Category:Statprob]]
 
[[Category:Biographical]]
 
[[Category:Biographical]]

Latest revision as of 16:32, 4 March 2024

Copyright notice
This article Anton Meyer was adapted from an original article by M.F. Jozeau, which appeared in StatProb: The Encyclopedia Sponsored by Statistics and Probability Societies. The original article ([http://statprob.com/encyclopedia/AntonMEYER.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.

Anton MEYER

b. 31 May 1801 - 29 April 1857


Summary. Meyer, a Belgian professor of Luxemburg origin, was the author of one of the few treatises of probability theory in the 19th century. He propagated the methods of Gauss, Bessel and Baeyer among geodesists of the French tradition.

Anton Meyer was born in Luxemburg, but became a naturalised Belgian on 2 April 1839. Although from a family of modest means (his father was a shoemaker), he completed his secondary schooling in the humanities in 1818, and then pursued his scientific studies with brilliance at Liège University. During this period, in order to earn a living, he taught and also catalogued the scientific books at the University's academic library. He worked towards a doctor's degree in the Mathematical and Physical Sciences, completing his thesis on "Maxima and minima" on 29 November 1823, though his defence only took place on 16 June 1832. In 1824-25, Meyer travelled to Paris to listen to the eminent scientists of the day. On his return to Belgium, he taught at the Echternach College and later at the Military School of Bréda. In 1827, he published a paper in Quetelet's "La correspondance mathématique et physique", about an instrument he had invented for drawing in perspective. In 1831 he taught at the Louvain College, and later from 1832 to 1837 at the Institut Gaggia in Brussels, where he prepared students for the Military School.

In 1834, he also became Professor of Analysis and Mechanics at the Brussels Military School, which had just opened, but he resigned from this position in 1836. In 1838, he was appointed to the Chair of Mathematical Analysis at the Université Libre de Bruxelles, and later he replaced Lemaire in the Chair of Differential and Integral Calculus, Higher Analysis and Calculus of Probabilities at Liège University from 1849 until his death. Under Meyer, two distinct subjects were taught, analysis, and probability theory and political arithmetic.

Meyer was clearly a dedicated teacher: his lessons, according to the reports of his pupils, were very appealing. After 1838, having achieved a stable position, he wrote a dozen text books. These were original, and written in simple and precise language; furthermore, Meyer was quick and accurate in his calculations, which were carried out with great ability. His lectures on probability were published only many years after his death, in 1874 by F. Folie, based on the author's manuscripts, as the Cours de Calcul des Probabilités fait à l'Université de Liège de 1849 à 1857 (F. Hayez, Bruxelles). This work, given the relative dearth of treatises on probability at the time, created something of a stir, and was translated into German in 1879 by E. Czuber under the title Vorlesungen über Wahrscheinlichkeitsrechnung. It contains a thoroughly researched account of the theory of errors. In the preface, F. Folie points out: "This book by Meyer is a very complete summary of the most important works of Bernoulli, de Moivre, Laplace, Poisson, Gauss, Encke, Bienaymé... on the calculus of probabilities. One might well suggest that there does not exist a broader treatise on the subject, except for Laplace's "Théorie analytique des probabilités...".

The treatise is very theoretical, even in his chapters concerned with the theory of errors, concentrating essentially on his proofs. This is in contrast to J.B.J. Liagre (1815-1891), who, in his Calcul des probabilités et théorie des erreurs published in 1852, gave a large number of applications of the theory of errors, particularly in geodesy.

Meyer was nevertheless interested in applications of mathematics, most particularly to geodesy. In 1835, while he was at the Military School in Brussels, Meyer's colleagues were Quetelet, Professor of Geodesy and Astronomy and Nerenburger, Professor of Descriptive Geometry. He collaborated with cartographic officers, and with the astronomer Houzeau, Quetelet's assistant. From the 1830's, he personally carried out triangulations, working out the calculations which were involved in them. Traces of his notes are to be found in the Leçons de trigonométrie rectiligne and the Leçons de trigonométrie sphérique published in 1844, as well as his Cours de géodésie dated 1845, which faithfully followed the French mathematical tradition. It is well known that since the 17th Century, particularly with the measurement of the metre during the French Revolution, France had played a leading role in the area of geodesy. But, from around 1820-1830, leadership passed fairly rapidly to Germany with the works of Gauss, Bessel and Baeyer who made systematic and relevant use of the method of least squares. Belgian scholars like Quetelet, Liagre, Nerenburger and Meyer, trained by the French, but open to other traditions, fostered the spread of German methods in Europe. A direct consequence of Meyer's travel to Germany in 1846 was the modification of his lectures on geodesy, and then of lecture material by other geodesists formerly written in the French tradition. Among these modifications are a section concerning the theory of errors, some lines on the personal equation, the use of the theory of least squares to obtain most probable values, an iteration method for the observation of angles, the use of the method of least squares as it arises in the calculation of most probable directions, and in the compensation theory for a network of triangles. The notation used for the solution by the method of indeterminate coefficients was that introduced by Gauss, and the weight equations correspond to those of Baeyer, as does also the study of their influence on the initial direction.

On February 6, 1847, Meyer presented a report on the application of the calculus of probabilities in operations of topographic surveying, to the science Section ("Classe") of the Royal Academy of Belgium. In this, he discussed an example of the use of the method of least squares. It was rejected by the Academy and never published. The bibliography of a thesis by L. Bouvier entitled "Dissertation sur la théorie des moindres carré which appeared in 1848 is identical with that of Meyer's report. Thus Meyer attempted to spread the information he had gathered in Germany on the method of least squares and its application to geodesy by channels other than those of Academic recognition. Bouvier remarked that there existed no special text describing the method of least squares, and that he hoped to fill this gap by giving an exposition from a practical viewpoint. Liagre's later work in 1852 would accomplish this on a larger scale. Bouvier does not discuss the foundations of the method. He concentrates essentially on the "method of equations" which are to be satisified. The author describes Gauss' two methods: he gives as an example the content of Meyer's note rejected by the Academy, and compares the formulae used by Gauss and Laplace to estimate the precision of arithmetic means. Both the importance of Meyer's contribution to geodesy and the obstacles which he encountered, as well as the militant devices he had to use to put his views, are evident.

Meyer's scientific opus consists of 30 papers and 12 textbooks. His publications on the calculus of probabilities were written in the latter part of his life, some of them appearing posthumously. In particular, we note his "Essai sur une exposition nouvelle de la théorie des probabilités a posteriori, 1857. This work was at the printer's when Meyer died. The author goes over the enunciations and proofs of Bayes' theorem in the continuous case, Laplace's theorem and the inverse theorem to J. Bernoulli's; but one cannot honestly claim that he brings much that is new to probabilistic thinking.

Also in 1857, Meyer published his reaction ``Examen critique de la notice de M. Liagre" to a memoir entitled "Sur la probabilité de l'existence d'une cause d'erreur régulière", which Liagre had presented to the Royal Academy of Belgium in 1855. The topic is the use of the calculus of probabilities to detect systematic errors, and is the precursor of a statistical test for the random nature of observations (the turning-point test). Liagre's article, which discusses the combinatorial aspects of the topic, is certainly subject to criticism, but so also is Meyer's reponse. This note, as well as another in 1856, was published at the author's expense; and provides further evidence of Meyer's disagreements with the science Section of the Royal Academy of Belgium, to which he had been elected a corresponding member on 16 December 1846. An account of this conflict, in which Meyer invoked the support of the leading authority of the day on statistical matters, I.J. Bienaymé, is given by Breny, Jongmans and Seneta (1992). Bienaymé, himself no stranger to controversies, recalled it in a paper of 1875, which linked his name with the turning-points test.

Meyer was not a creator of originality in probability and statistics; but rather an interpreter, able to clarify, simplify and make rigorous in an age not noted for mathematical lucidity. He is better known in Luxemburg as the first poet of the Luxemburg language, and a man who fostered the development of national culture.

References

[1] Bergmans, C. (1897). Notice sur A. Meyer. In Biographie Nationale de Belgique, Vol. XIV, columns 765-773.
[2] Blum, M. (1902-1908). Biographie Luxembourgeoise, Vol. 2. (Chez l'auteur, Luxembourg)
[3] Breny, H., Jongmans, F. and Seneta, E. (1992). Annexe: A. Meyer et l'Académie. In Regards sur 175 ans de science à l'Université de Liège, 1817-1992. Anne-Marie Bernès (Ed.). Centre d'Histoire des Sciences et des Techniques, Université de Liège. pp. 13-22bis.
[4] Gloden, A. (1949). La vie et l'oeuvre scientifique de neuf mathématiciens belges d'origine luxembourgeoise. In Themecht Zeischrift für Luxemburger Geschichte, 1, 13-16.
[5] Godeaux, L. (1956). Notice sur Antoine Meyer, membre de l'Académie. Annuaire pour 1956. Académie Royale de Belgique, Brussels. [In "Notices biographiques", pp.2-15.]



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:
Meyer, Anton. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Meyer,_Anton&oldid=37958