Gabriel Cramer (; 31 July 1704 – 4 January 1752) was a
Genevan
, neighboring_municipalities= Carouge, Chêne-Bougeries, Cologny, Lancy, Grand-Saconnex, Pregny-Chambésy, Vernier, Veyrier
, website = https://www.geneve.ch/
Geneva ( ; french: Genève ) frp, Genèva ; german: link=no, Genf ; it, Ginevra ...
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
. He was the son of physician Jean Cramer and Anne Mallet Cramer.
Biography
Cramer showed promise in
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
from an early age. At 18 he received his doctorate and at 20 he was co-chair
[He did not get the chair of philosophy he had been a candidate for; but the ]University of Geneva
The University of Geneva (French: ''Université de Genève'') is a public research university located in Geneva, Switzerland. It was founded in 1559 by John Calvin as a theological seminary. It remained focused on theology until the 17th centur ...
was so impressed by him that it created a chair of mathematics for him and for his friend Jean-Louis Calandrini
Jean-Louis Calandrini (August 30, 1703 – December 29, 1758) was a Genevan scientist. He was a professor of mathematics and philosophy. He was the author of some studies on the aurora borealis, comets, and the effects of lightning, as well as ...
; the two alternated as chairs. 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 The expected utility hypothesis is a popular concept in economics that serves as a reference guide for decisions when the payoff is uncertain. The theory recommends which option rational individuals should choose in a complex situation, based on the ...
given ten years later by
Daniel Bernoulli
Daniel Bernoulli FRS (; – 27 March 1782) was a Swiss mathematician and physicist and was one of the many prominent mathematicians in the Bernoulli family from Basel. He is particularly remembered for his applications of mathematics to mecha ...
.
He published his best-known work in his forties. This included his treatise on
algebraic curve
In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three variables. An affine algebraic plane ...
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
In algebraic geometry and computational geometry, general position is a notion of genericity for a set of points, or other geometric objects. It means the ''general case'' situation, as opposed to some more special or coincidental cases that are ...
. (See
Cramer's theorem (algebraic curves).) This led to the misconception that is
Cramer's paradox
In mathematics, Cramer's paradox or the Cramer–Euler paradoxWeisstein, Eric W. "Cramér-Euler Paradox." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Cramer-EulerParadox.html is the statement that the number of points of i ...
, 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
Bernoulli Bernoulli can refer to:
People
*Bernoulli family of 17th and 18th century Swiss mathematicians:
** Daniel Bernoulli (1700–1782), developer of Bernoulli's principle
**Jacob Bernoulli (1654–1705), also known as Jacques, after whom Bernoulli numbe ...
s, and wrote on the physical cause of the spheroidal shape of the
planet
A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a you ...
s and the motion of their
apsides
An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. For example, the apsides of the Earth are called the aphelion and perihelion.
General description
There are two apsides in any ellip ...
(1730), and on
Newton's treatment of
cubic curve
In mathematics, a cubic plane curve is a plane algebraic curve defined by a cubic equation
:
applied to homogeneous coordinates for the projective plane; or the inhomogeneous version for the affine space determined by setting in such an eq ...
s (1746).
In 1750 he published
Cramer's rule
In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution. It expresses the solution in terms of the determinants o ...
, giving a general formula for the solution for any unknown in a linear equation system having a unique solution, in terms of
determinants
In mathematics, the determinant is a scalar value that is a function of the entries of a square matrix. It characterizes some properties of the matrix and the linear map represented by the matrix. In particular, the determinant is nonzero if and ...
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
Bagnols-sur-Cèze (, literally ''Bagnols on Cèze''; oc, Banhòus de Céser) is a commune in the Gard department in the Occitanie région in southern France.
History
A small regional center, Bagnols-sur-Cèze was quite certainly a Roman town ...
while traveling in southern France to restore his health.
Selected works
* ''Quelle est la cause de la figure elliptique des planètes et de la mobilité de leur aphélies?'', Geneva, 1730
* . Geneva: Frères Cramer & Cl. Philibert, 1750
See also
*
Cramer–Castillon problem
In geometry, the Cramer–Castillon problem is a problem stated by the Swiss mathematician Gabriel Cramer solved by the Italian mathematician, resident in Berlin, Jean de Castillon in 1776.
The problem consists of (see the image):
Given a circle ...
*
Devil's curve
In geometry, a Devil's curve, also known as the Devil on Two Sticks, is a curve defined in the Cartesian plane by an equation of the form
: y^2(y^2 - b^2) = x^2(x^2 - a^2).
The polar equation of this curve is of the form
:r = \sqrt = \sqrt.
D ...
*
Jean-Louis Calandrini
Jean-Louis Calandrini (August 30, 1703 – December 29, 1758) was a Genevan scientist. He was a professor of mathematics and philosophy. He was the author of some studies on the aurora borealis, comets, and the effects of lightning, as well as ...
References
* "Gabriel Cramer", i
''Rousseau et les savants genevois'' p. 29
*
W. W. Rouse Ball
Walter William Rouse Ball (14 August 1850 – 4 April 1925), known as W. W. Rouse Ball, was a British mathematician, lawyer, and fellow at Trinity College, Cambridge, from 1878 to 1905. He was also a keen amateur magician, and the founding ...
, ''A Short Account of the History of Mathematics'', (4th Edition, 1908)
* Isaac Benguigui, ''Gabriel Cramer : illustre mathématicien, 1704–1752'', Genève, Cramer & Cie, 1998
*
* Johann Christoph Strodtmann, �
Geschichte des Herrn Gabriel Cramer», in ''Das neue gelehrte Europa
��', 4th part, Meissner, 1754 Also digitized by
e-rara.ch
External links
*
*
{{DEFAULTSORT:Cramer, Gabriel
1704 births
1752 deaths
18th-century scientists from the Republic of Geneva
Fellows of the Royal Society
18th-century mathematicians
Linear algebraists
Mathematicians from the Republic of Geneva