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{{about|a mathematician|the publisher of the same name|Cramer brothers}}
{{about|a mathematician|the publisher of the same name|Cramer brothers}}
{{Infobox scientist
{{Infobox scientist
| name = Gabriel Cramer
| name = Gabriel Cramer
| image = Gabriel Cramer.jpg
| image = Gabriel Cramer.jpg
| image_size =
| image_size =
| caption = Cramer {{circa|1750}}
| caption = Gabriel Cramer (1704-1752). Portrait by [[Robert Gardelle]], year unknown.
| birth_date = 31 July 1704
| birth_date = 31 July 1704
| birth_place = [[Geneva]], [[Republic and Canton of Geneva|Republic of Geneva]]
| birth_place = [[Geneva]], [[Republic of Geneva]]
| death_date = 4 January 1752 (age 47)
| death_date = 4 January 1752 (age 47)
| death_place = [[Bagnols-sur-Cèze]], [[Kingdom of France|France]]
| death_place = [[Bagnols-sur-Cèze]], [[Kingdom of France|France]]
⚫
| field = [[Mathematics]] and [[physics]]
| residence = [[Geneva]]
| nationality = [[Republic and Canton of Geneva#History|Genevan]]
| work_institutions = Academy of Geneva
⚫
| alma_mater = [[University of Geneva|Academy of Geneva]]
⚫
| field = [[Mathematics]] and [[physics]]
⚫
| doctoral_advisor = <!--pls insert-->
| work_institutions = [[University of Geneva]]
⚫
| alma_mater = [[University of Geneva]]
⚫
| doctoral_advisor = <!--pls insert-->
| doctoral_students = <!--pls insert-->
| doctoral_students = <!--pls insert-->
| known_for = [[Cramer's rule]]<br>[[Cramer's theorem (algebraic curves)|Cramer's theorem for algebraic curves]]<br>[[Cramer's paradox]]
| known_for = [[Cramer's rule]]<br>[[Cramer's theorem (algebraic curves)|Cramer's theorem for algebraic curves]]<br>[[Cramer's paradox]]
| prizes =
| prizes =
| footnotes =
| footnotes =
}}
}}


'''Gabriel Cramer''' ({{IPA-fr|kʁamɛʁ|lang}}; 31 July 1704 – 4 January 1752) was a [[Geneva|Genevan]] [[mathematician]]. He was the son of physician Jean Cramer and Anne Mallet Cramer.
'''Gabriel Cramer''' ({{IPA|fr|kʁamɛʁ|lang}}; 31 July 1704 – 4 January 1752) was a Genevan [[mathematician]].


== Biography ==
== Biography ==
Cramer showed promise in [[mathematics]] from an early age. At 18 he received his doctorate and at 20 he was co-chair<ref>He did not get the chair of philosophy he had been a candidate for; but the [[University of Geneva]] was so impressed by him that it created a chair of mathematics for him and for his friend [[Jean-Louis Calandrini]]; the two alternated as chairs.</ref> of mathematics at the University of Geneva.
Cramer was born on 31 July 1704 in Geneva, [[Republic of Geneva]] to Jean-Isaac Cramer, a physician, and Anne Mallet.<ref name=HDS>{{HDS|25878|Cramer, Gabriel|author=Paul Chaix|date=17 August 2005}}</ref> The progenitor of the Cramer family in Geneva was Jean-Ulrich Cramer, Gabriel's great-grandfather, who immigrated from [[Strasbourg]] in 1634.<ref>{{HDS|25496|Cramer (GE)|author=Barbara Roth|date=16 March 2004}}</ref> Cramer's mother, a member of the [[Mallet family]], was of [[Huguenot]] origin.<ref>{{HDS|25530|Mallet|author=Jean de Senarclens|date=29 January 2008}}</ref> Cramer showed promise in mathematics from an early age. In 1722, aged 18, he received his doctorate from the [[University of Geneva|Academy of Geneva]], and at 20 he was made co-chair (along with [[Jean-Louis Calandrini]]){{efn|He did not get the chair of philosophy he had been a candidate for; but the Academy was so impressed by him that it created a chair of mathematics for him and for his friend Jean-Louis Calandrini; the two alternated as chairs}} of mathematics at the Academy.<ref name=HDS/>


He became the sole professor of mathematics in 1734 and was appointed professor of philosophy at the Academy in 1750.<ref name=HDS/> Cramer was also involved in the politics of the Republic of Geneva, entering first the [[Council of Two Hundred]] in 1734 then the Council of Sixty in 1750.<ref name=HDS/> He was a member of the science academies of [[Academy of Sciences of the Institute of Bologna|Bologna]], [[Academy of Lyon|Lyon]], and [[Montpellier]], as well as a foreign member of the [[Royal Society]] of London and the [[Prussian Academy of Sciences|Royal Academy of Sciences]] of Berlin.<ref name=HDS/> Cramer died on 4 January 1752 at [[Bagnols-sur-Cèze]] while traveling in southern France to restore his health.<ref name=HDS/>
⚫
In 1728 he proposed a solution to the [[St. Petersburg Paradox]] that came very close to the concept of [[expected utility hypothesis|expected utility theory]] given ten years later by [[Daniel Bernoulli]].


== Contributions to mathematics ==
⚫
He published his best-known work in his forties. This included his treatise on [[algebraic curve]]s (1750). It contains the earliest demonstration that a curve of the ''n''-th degree is determined by ''n''(''n'' + 3)/2 points on it, in [[general position]]. (See [[Cramer's theorem (algebraic curves)]].) This led to the misconception that is [[Cramer's paradox]], concerning the number of intersections of two curves compared to the number of points that determine a curve.


⚫
In 1728, Cramer proposed a solution to the [[St. Petersburg Paradox]] that came very close to the concept of [[expected utility hypothesis|expected utility theory]] given ten years later by [[Daniel Bernoulli]]. He did extensive travel throughout Europe in the late 1730s, which greatly influenced his works in mathematics.
⚫
He edited the works of the two elder [[Bernoulli family|Bernoulli]]s, and wrote on the physical cause of the spheroidal shape of the [[planet]]s and the motion of their [[apsides]] (1730), and on [[Isaac Newton|Newton]]'s treatment of [[cubic curve]]s (1746).


⚫
Cramer published his best-known work in his forties. This included his treatise on [[algebraic curve]]s (1750). It contains the earliest demonstration that a curve of the ''n''-th degree is determined by ''n''(''n'' + 3)/2 points on it, in [[general position]] (see [[Cramer's theorem (algebraic curves)]]). This led to the misconception that is [[Cramer's paradox]], concerning the number of intersections of two curves compared to the number of points that determine a curve.
⚫
In 1750 he published [[Cramer's rule]], giving a general formula for the solution for any unknown in a linear equation system having a unique solution, in terms of [[determinant (mathematics)|determinants]] implied by the system. This rule is still standard.


⚫
Cramer edited the works of the two elder [[Bernoulli family|Bernoulli]]s, and wrote on the physical cause of the spheroidal shape of the [[planet]]s and the motion of their [[apsides]] (1730), and on [[Isaac Newton|Newton]]'s treatment of [[cubic curve]]s (1746).
He did extensive travel throughout Europe in the late 1730s, which greatly influenced his works in mathematics. He died in 1752 at [[Bagnols-sur-Cèze]] while traveling in southern France to restore his health.

⚫
In 1750 he published [[Cramer's rule]], giving a general formula for the solution for any unknown in a linear equation system having a unique solution, in terms of [[determinant (mathematics)|determinants]] implied by the system. This rule is still standard.


== Selected works ==
== Selected works ==
Line 46: Line 46:
* [[Cramer–Castillon problem]]
* [[Cramer–Castillon problem]]
* [[Devil's curve]]
* [[Devil's curve]]

* [[Jean-Louis Calandrini]]
==Notes==
{{notes}}


== References ==
== References ==
⚫
{{reflist}}
* "Gabriel Cramer", in [http://www.ville-ge.ch/mhs/pdf/expo_2012_rousseau_livret.pdf ''Rousseau et les savants genevois''], p.&nbsp;29 {{in lang|fr}}
* "Gabriel Cramer", in [http://www.ville-ge.ch/mhs/pdf/expo_2012_rousseau_livret.pdf ''Rousseau et les savants genevois''], p.&nbsp;29 {{in lang|fr}}
* [[W. W. Rouse Ball]], ''A Short Account of the History of Mathematics'', (4th Edition, 1908)
* [[W. W. Rouse Ball]], ''A Short Account of the History of Mathematics'', (4th Edition, 1908)
* Isaac Benguigui, ''Gabriel Cramer : illustre mathématicien, 1704–1752'', Genève, Cramer & Cie, 1998 {{in lang|fr}}
* Isaac Benguigui, ''Gabriel Cramer : illustre mathématicien, 1704–1752'', Genève, Cramer & Cie, 1998 {{in lang|fr}}
* {{MacTutor|id=Cramer}}
* {{MacTutor|id=Cramer}}
⚫
{{reflist}}
* {{in lang|de}} Johann Christoph Strodtmann, « [http://www.e-rara.ch/zut/content/pageview/3863508 Geschichte des Herrn Gabriel Cramer] », in ''Das neue gelehrte Europa […]'', 4th part, Meissner, 1754 Also digitized by [[e-rara.ch]]
* {{in lang|de}} Johann Christoph Strodtmann, « [http://www.e-rara.ch/zut/content/pageview/3863508 Geschichte des Herrn Gabriel Cramer] », in ''Das neue gelehrte Europa […]'', 4th part, Meissner, 1754 Also digitized by [[e-rara.ch]]


==External links==
==External links==
*{{Commons category inline}}
*{{Commons category-inline}}
* {{MacTutor Biography|id=Cramer}}
* {{MacTutor Biography|id=Cramer}}


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[[Category:1704 births]]
[[Category:1704 births]]
[[Category:1752 deaths]]
[[Category:1752 deaths]]
[[Category:18th-century Genevan scientists]]
[[Category:18th-century mathematicians from the Republic of Geneva]]
[[Category:Fellows of the Royal Society]]
[[Category:18th-century politicians from the Republic of Geneva]]
[[Category:18th-century mathematicians]]
[[Category:University of Geneva alumni]]
⚫
[[Category:Academic staff of the University of Geneva]]
[[Category:Foreign members of the Royal Society]]
[[Category:Linear algebraists]]
[[Category:Linear algebraists]]
⚫
[[Category:Mathematicians from the Republic of Geneva]]

Latest revision as of 17:26, 3 October 2024

This article is about a mathematician. For the publisher of the same name, see Cramer brothers.
Gabriel Cramer
Cramer c. 1750
Born31 July 1704
Geneva, Republic of Geneva
Died4 January 1752 (age 47)
Bagnols-sur-Cèze, France
Alma materAcademy of Geneva
Known forCramer's rule
Cramer's theorem for algebraic curves
Cramer's paradox
Scientific career
FieldsMathematics and physics
InstitutionsAcademy of Geneva

Gabriel Cramer (French: [kʁamɛʁ]; 31 July 1704 – 4 January 1752) was a Genevan mathematician.

Biography

[edit]

Cramer was born on 31 July 1704 in Geneva, Republic of Geneva to Jean-Isaac Cramer, a physician, and Anne Mallet.[1] The progenitor of the Cramer family in Geneva was Jean-Ulrich Cramer, Gabriel's great-grandfather, who immigrated from Strasbourg in 1634.[2] Cramer's mother, a member of the Mallet family, was of Huguenot origin.[3] Cramer showed promise in mathematics from an early age. In 1722, aged 18, he received his doctorate from the Academy of Geneva, and at 20 he was made co-chair (along with Jean-Louis Calandrini)[a] of mathematics at the Academy.[1]

He became the sole professor of mathematics in 1734 and was appointed professor of philosophy at the Academy in 1750.[1] Cramer was also involved in the politics of the Republic of Geneva, entering first the Council of Two Hundred in 1734 then the Council of Sixty in 1750.[1] He was a member of the science academies of Bologna, Lyon, and Montpellier, as well as a foreign member of the Royal Society of London and the Royal Academy of Sciences of Berlin.[1] Cramer died on 4 January 1752 at Bagnols-sur-Cèze while traveling in southern France to restore his health.[1]

Contributions to mathematics

[edit]

In 1728, Cramer proposed a solution to the St. Petersburg Paradox that came very close to the concept of expected utility theory given ten years later by Daniel Bernoulli. He did extensive travel throughout Europe in the late 1730s, which greatly influenced his works in mathematics.

Cramer published his best-known work in his forties. This included his treatise on algebraic curves (1750). It contains the earliest demonstration that a curve of the n-th degree is determined by n(n + 3)/2 points on it, in general position (see Cramer's theorem (algebraic curves)). This led to the misconception that is Cramer's paradox, concerning the number of intersections of two curves compared to the number of points that determine a curve.

Cramer edited the works of the two elder Bernoullis, and wrote on the physical cause of the spheroidal shape of the planets and the motion of their apsides (1730), and on Newton's treatment of cubic curves (1746).

In 1750 he published Cramer's rule, giving a general formula for the solution for any unknown in a linear equation system having a unique solution, in terms of determinants implied by the system. This rule is still standard.

Selected works

[edit]
Introduction à l'analyse des lignes courbes algébriques, 1750

See also

[edit]

Notes

[edit]
  1. ^ He did not get the chair of philosophy he had been a candidate for; but the Academy was so impressed by him that it created a chair of mathematics for him and for his friend Jean-Louis Calandrini; the two alternated as chairs

References

[edit]
  1. ^ a b c d e f Paul Chaix: Cramer, Gabriel in German, French and Italian in the online Historical Dictionary of Switzerland, 17 August 2005.
  2. ^ Barbara Roth: Cramer (GE) in German, French and Italian in the online Historical Dictionary of Switzerland, 16 March 2004.
  3. ^ Jean de Senarclens: Mallet in German, French and Italian in the online Historical Dictionary of Switzerland, 29 January 2008.
  • "Gabriel Cramer", in Rousseau et les savants genevois, p. 29 (in French)
  • W. W. Rouse Ball, A Short Account of the History of Mathematics, (4th Edition, 1908)
  • Isaac Benguigui, Gabriel Cramer : illustre mathématicien, 1704–1752, Genève, Cramer & Cie, 1998 (in French)
  • O'Connor, John J.; Robertson, Edmund F., "Gabriel Cramer", MacTutor History of Mathematics Archive, University of St Andrews
  • (in German) Johann Christoph Strodtmann, « Geschichte des Herrn Gabriel Cramer », in Das neue gelehrte Europa […], 4th part, Meissner, 1754 Also digitized by e-rara.ch
[edit]
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