Gabriel Cramer

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Gabriel Cramer
Gabriel Cramer.jpg
Gabriel Cramer (1704-1752). Portrait by Robert Gardelle, year unknown.
Born 31 July 1704
Geneva, Republic of Geneva
Died 4 January 1752 (age 47)
Bagnols-sur-Cèze, France
Residence Switzerland
Nationality Swiss
Fields Mathematics and physics
Institutions University of Geneva
Alma mater University of Geneva
Known for Cramer's rule
Cramer's paradox

Gabriel Cramer (French: [kʁamɛʁ]; 31 July 1704 – 4 January 1752) was a Swiss mathematician, born in Geneva. He was the son of physician Jean Cramer and Anne Mallet Cramer.


Cramer showed promise in mathematics from an early age. At 18 he received his doctorate and at 20 he was co-chair[1] of mathematics at the University of Geneva.

In 1728 he 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 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.

He 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.

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.

Selected works

See also


  1. 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 jfriend Jean-Louis Calandrini; the two alternated as chairs.

External links