Joseph Diez Gergonne | |
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| Born | 19 June 1771 Nancy, France |
| Died | 4 May 1859 (aged 87) Montpellier, France |
| Scientific career | |
| Fields | Mathematics Logic |
Joseph Diez Gergonne (19 June 1771 at Nancy, France – 4 May 1859 at Montpellier, France) was a French mathematician and logician.
In 1791, Gergonne enlisted in the French army as a captain. That army was undergoing rapid expansion because the French government feared a foreign invasion intended to undo the French Revolution and restore Louis XVI to the throne of France. He saw action in the major battle of Valmy on 20 September 1792. He then returned to civilian life but soon was called up again and took part in the French invasion of Spain in 1794.
In 1795, Gergonne and his regiment were sent to Nîmes. At this point, he made a definitive transition to civilian life by taking up the chair of "transcendental mathematics" at the new École centrale. He came under the influence of Gaspard Monge, the Director of the new École polytechnique in Paris.
In 1810, in response to difficulties he encountered in trying to publish his work, Gergonne founded his own mathematics journal, officially named the Annales de mathématiques pures et appliquées but generally referred to as the Annales de Gergonne . The most common subject of articles in his journal was geometry, Gergonne's specialty. Over a period of 22 years, the Annales de Gergonne published about 200 articles by Gergonne himself, and other articles by many distinguished mathematicians, including Poncelet, Servois, Bobillier, Steiner, Plücker, Chasles, Brianchon, Dupin, Lamé, even Galois.
Gergonne was appointed to the chair of astronomy at the University of Montpellier in 1816. In 1830, he was appointed Rector of the University of Montpellier, at which time he ceased publishing his journal. He retired in 1844.
Gergonne was among the first mathematicians to employ the word polar. In a series of papers beginning in 1810, he contributed to elaborating the principle of duality in projective geometry, by noticing that every theorem in the plane connecting points and lines corresponds to another theorem in which points and lines are interchanged, provided that the theorem embodied no metrical notions. Gergonne was an early proponent of the techniques of analytical geometry and in 1814, he devised an elegant coordinate solution to the classical problem of Apollonius: to find a circle which touches three given circles, thus demonstrating the power of the new methods.
In 1813, Gergonne wrote the prize-winning essay for the Bordeaux Academy, Methods of synthesis and analysis in mathematics, unpublished to this day and known only via a summary. The essay is very revealing of Gergonne's philosophical ideas. He called for the abandonment of the words analysis and synthesis , claiming they lacked clear meanings. Surprisingly for a geometer, he suggested that algebra is more important than geometry at a time when algebra consisted almost entirely of the elementary algebra of the real field. He predicted that one day quasi-mechanical methods would be used to discover new results.
In 1815, Gergonne wrote the first paper on the optimal design of experiments for polynomial regression. According to S. M. Stigler, Gergonne is the pioneer of optimal design as well as response surface methodology.
He published his "Essai sur la théorie des définitions" (An essay on the theory of definition) in his Annales in 1818. This essay is generally credited for first recognizing and naming the construct of implicit definition. [1] [2]
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems. Classically, it studies zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects.
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science.
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 with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline.
Pappus of Alexandria was a Greek mathematician of Late Antiquity known for his Synagoge (Συναγωγή) or Collection, and for Pappus's hexagon theorem in projective geometry. Almost nothing is known about his life except for what can be found in his own writings, many of which are lost. Pappus apparently lived in Alexandria were he worked as a mathematics teacher to higher level students, such one named Hermodorus.
Jean-Robert Argand was a Genevan amateur mathematician. In 1806, while managing a bookstore in Paris, he published the idea of geometrical interpretation of complex numbers known as the Argand diagram and is known for the first rigorous proof of the Fundamental Theorem of Algebra.
Stephen Mack Stigler is the Ernest DeWitt Burton Distinguished Service Professor at the Department of Statistics of the University of Chicago. He has authored several books on the history of statistics; he is the son of the economist George Stigler.
In the design of experiments, optimal experimental designs are a class of experimental designs that are optimal with respect to some statistical criterion. The creation of this field of statistics has been credited to Danish statistician Kirstine Smith.
In mathematics, the mathematician Sophus Lie initiated lines of study involving integration of differential equations, transformation groups, and contact of spheres that have come to be called Lie theory. For instance, the latter subject is Lie sphere geometry. This article addresses his approach to transformation groups, which is one of the areas of mathematics, and was worked out by Wilhelm Killing and Élie Cartan.
In statistics, response surface methodology (RSM) explores the relationships between several explanatory variables and one or more response variables. RSM is an empirical model which employs the use of mathematical and statistical techniques to relate input variables, otherwise known as factors, to the response. RSM became very useful due to the fact that other methods available, such as the theoretical model, could be very cumbersome to use, time-consuming, inefficient, error-prone, and unreliable. The method was introduced by George E. P. Box and K. B. Wilson in 1951. The main idea of RSM is to use a sequence of designed experiments to obtain an optimal response. Box and Wilson suggest using a second-degree polynomial model to do this. They acknowledge that this model is only an approximation, but they use it because such a model is easy to estimate and apply, even when little is known about the process.
In statistical modeling, polynomial functions and rational functions are sometimes used as an empirical technique for curve fitting.
In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable y is modeled as an nth degree polynomial in x. Polynomial regression fits a nonlinear relationship between the value of x and the corresponding conditional mean of y, denoted E(y |x). Although polynomial regression fits a nonlinear model to the data, as a statistical estimation problem it is linear, in the sense that the regression function E(y | x) is linear in the unknown parameters that are estimated from the data. For this reason, polynomial regression is considered to be a special case of multiple linear regression.
Harold Mortimer Edwards, Jr. was an American mathematician working in number theory, algebra, and the history and philosophy of mathematics.
The mathematical manuscripts of Karl Marx are a manuscript collection of Karl Marx's mathematical notes where he attempted to derive the foundations of infinitesimal calculus from first principles.
François-Joseph Servois was a French priest, military officer and mathematician. His most notable contribution came in his publication of Essai sur un nouveau mode d’exposition des principes du calcul différentiel in 1814, where he first introduced the mathematical terms for commutative and distributive.
Jean Prestet (1648–1690) was a French Oratorian priest and mathematician who contributed to the fields of combinatorics and number theory.
Isabella Grigoryevna Bashmakova was a Russian historian of mathematics. In 2001, she was a recipient of the Alexander Koyré́ Medal of the International Academy of the History of Science.
Pierre Joseph Étienne Finck (1797–1870) was a French mathematician.
The Annales de Mathématiques Pures et Appliquées, commonly known as the Annales de Gergonne, was a mathematical journal published in Nimes, France from 1810 to 1831 by Joseph Diez Gergonne. The annals were largely devoted to geometry, with additional articles on history, philosophy, and mathematics education showing interdisciplinarity.
Morihiko Saitō is a Japanese mathematician, specializing in algebraic analysis and algebraic geometry.
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