Joseph Diez Gergonne (19 June 1771 at Nancy,

France France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of Overseas France, overseas regions and territories in the Americas and the Atlantic Ocean, Atlantic, Pacific Ocean, Pac ...

– 4 May 1859 at

Montpellier Montpellier (, , ; oc, Montpelhièr ) is a city in southern France near the Mediterranean Sea. One of the largest urban centres in the region of Occitania, Montpellier is the prefecture of the department of Hérault. In 2018, 290,053 people ...

, France) was a French

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 ...

and

logician Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...

Life

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 The French Revolution ( ) was a period of radical political and societal change in France that began with the Estates General of 1789 and ended with the formation of the French Consulate in November 1799. Many of its ideas are consider ...

and restore

Louis XVI Louis XVI (''Louis-Auguste''; ; 23 August 175421 January 1793) was the last King of France before the fall of the monarchy during the French Revolution. He was referred to as ''Citizen Louis Capet'' during the four months just before he was e ...

to the throne of France. He saw action in the major

battle of Valmy The Battle of Valmy, also known as the Cannonade of Valmy, was the first major victory by the army of France during the Revolutionary Wars that followed the French Revolution. The battle took place on 20 September 1792 as Prussian troops com ...

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 Nîmes ( , ; oc, Nimes ; Latin: ''Nemausus'') is the prefecture of the Gard department in the Occitanie region of Southern France. Located between the Mediterranean Sea and Cévennes, the commune of Nîmes has an estimated population of 14 ...

. 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 Gaspard Monge, Comte de Péluse (9 May 1746 – 28 July 1818) was a French mathematician, commonly presented as the inventor of descriptive geometry, (the mathematical basis of) technical drawing, and the father of differential geometry. During ...

, the Director of the new

École polytechnique École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, Sav ...

Paris Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. S ...

. 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 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 ...

'' but generally referred to as the '' Annales de Gergonne''. The most common subject of articles in his journal was

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

, 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 The poncelet (symbol p) is an obsolete unit of power, once used in France and replaced by (ch, metric horsepower). The unit was named after Jean-Victor Poncelet.François Cardarelli, ''Encyclopaedia of Scientific Units, Weights and Measures: T ...

, 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.

Work

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 In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations. This means that, compared to elementary Euclidean geometry, projective geometry has a different setting, pr ...

, by noticing that every

theorem In mathematics, a theorem is a statement that has been proved, or can be proved. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of t ...

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 In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Analytic geometry is used in physics and engineerin ...

and in 1814, he devised an elegant coordinate solution to the classical

problem of Apollonius In Euclidean plane geometry, Apollonius's problem is to construct circles that are tangent to three given circles in a plane (Figure 1). Apollonius of Perga (c. 262 190 BC) posed and solved this famous problem in his work (', "Tangencies ...

: 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 Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (384 ...

'' and ''

synthesis Synthesis or synthesize may refer to: Science Chemistry and biochemistry *Chemical synthesis, the execution of chemical reactions to form a more complex molecule from chemical precursors **Organic synthesis, the chemical synthesis of organi ...

'', claiming they lacked clear meanings. Surprisingly for a geometer, he suggested that algebra is more important than geometry at a time when

algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary ...

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 In the design of experiments, optimal designs (or optimum 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 statist ...

experiments An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into cause-and-effect by demonstrating what outcome occurs when ...

for

polynomial regression 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 modelled as an ''n''th degree polynomial in ''x''. Polynomial regressio ...

. According to S. M. Stigler, Gergonne is the pioneer of

as well as

response surface methodology In statistics, response surface methodology (RSM) explores the relationships between several explanatory variables and one or more response variables. The method was introduced by George E. P. Box and K. B. Wilson in 1951. The main idea of RSM ...

. 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''.

Quote

*"It is not possible to feel satisfied at having said the last word about some theory as long as it cannot be explained in a few words to any passer-by encountered in the street."

Michel Chasles Michel Floréal Chasles (; 15 November 1793 – 18 December 1880) was a French mathematician. Biography He was born at Épernon in France and studied at the École Polytechnique in Paris under Siméon Denis Poisson. In the War of the Sixth Co ...

Aperçu historique
Volume 2. 1875.

Notes

References

* *

External links

*Biography in the MacTutor History of Mathematics archive

{{DEFAULTSORT:Gergonne, Joseph Diaz 1771 births 1859 deaths 18th-century French mathematicians 19th-century French mathematicians French logicians French geometers French military personnel of the French Revolutionary Wars Scientists from Nancy, France French philosophers French male non-fiction writers 19th-century French male writers 18th-century French male writers