Antoine Arbogast
Encyclopedia
Louis François Antoine Arbogast (October 4, 1759 – April 8, or April 18, 1803) was a French mathematician
. He was born at Mutzig
in Alsace and died at Strasbourg
, where he was professor. He wrote on series
and the derivatives
known by his name: he was the first writer to separate the symbols of operation from those of quantity. In 1800, he published a calculus
treatise
where the first known statement of what is currently known as Faà di Bruno's formula
appears, 55 years before the first published paper of Francesco Faà di Bruno
on that topic.
and entered a mathematical competition which was run by the St Petersburg Academy. His entry was to bring him fame and an important place in the history of the development of the calculus. Arbogast submitted an essay to the St Petersburg Academy in which he came down firmly on the side of Euler. In fact he went much further than Euler in the type of arbitrary functions introduced by integrating partial differential equation
s, claiming that the functions could be discontinuous not only in the limited sense claimed by Euler, but discontinuous in a more general sense that he defined that allowed the function to consist of portions of different curves. Arbogast won the prize with his essay and his notion of discontinuous function became important in Cauchy's more rigorous approach to analysis.
In 1789 he submitted in Strasbourg a major report on the differential and integral calculus to the Académie des Sciences in Paris which was never published. In the Preface of a later work he described the ideas that prompted him to write the major report of 1789. Essentially he realised that there was no rigorous methods to deal with the convergence of series, and Arbogast's career reached new heights. In addition to his mathematics post, he was appointed as professor of physics at the Collège Royal in Strasbourg and from April 1791 he served as its rector until October 1791 when he was appointed rector of the University of Strasbourg; in 1794 he was appointed Professor of Calculus at the École centrale (soon to become the École polytechnique
) but he taught at the École préparatoire.
His contributions to mathematics show him as a philosophical thinker that has to face his era. As well as introducing discontinuous functions, as we discussed above, he conceived the calculus as operational symbols. The formal algebraic manipulation of series investigated by Lagrange
and Laplace in the 1770s has been put in the form of operator equalities by Arbogast in 1800. We owe him the general concept of factorial
as a product of a finite number of terms in arithmetic progression
.
The original version of this article was taken from the public domain resource the Rouse History of Mathematics.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. He was born at Mutzig
Mutzig
Mutzig is a commune located at the entrance of the Bruche River Valley, in the Bas-Rhin department in Alsace, in north-eastern France. the commune of Mutzig is on the Route des Vins d'Alsace.-History:...
in Alsace and died at Strasbourg
Strasbourg
Strasbourg is the capital and principal city of the Alsace region in eastern France and is the official seat of the European Parliament. Located close to the border with Germany, it is the capital of the Bas-Rhin département. The city and the region of Alsace are historically German-speaking,...
, where he was professor. He wrote on series
Series (mathematics)
A series is the sum of the terms of a sequence. Finite sequences and series have defined first and last terms, whereas infinite sequences and series continue indefinitely....
and the derivatives
Calculus
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...
known by his name: he was the first writer to separate the symbols of operation from those of quantity. In 1800, he published a calculus
Calculus
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...
treatise
Treatise
A treatise is a formal and systematic written discourse on some subject, generally longer and treating it in greater depth than an essay, and more concerned with investigating or exposing the principles of the subject.-Noteworthy treatises:...
where the first known statement of what is currently known as Faà di Bruno's formula
Faà di Bruno's formula
Faà di Bruno's formula is an identity in mathematics generalizing the chain rule to higher derivatives, named after , though he was not the first to state or prove the formula...
appears, 55 years before the first published paper of Francesco Faà di Bruno
Francesco Faà di Bruno
Francesco Faà di Bruno was an Italian mathematician and priest, born at Alessandria. He was of noble birth, and held, at one time, the rank of captain-of-staff in the Sardinian Army. He is the eponym of Faà di Bruno's formula...
on that topic.
Biography
He was professor of mathematics at the Collège de ColmarColmar
Colmar is a commune in the Haut-Rhin department in Alsace in north-eastern France.It is the capital of the department. Colmar is also the seat of the highest jurisdiction in Alsace, the appellate court....
and entered a mathematical competition which was run by the St Petersburg Academy. His entry was to bring him fame and an important place in the history of the development of the calculus. Arbogast submitted an essay to the St Petersburg Academy in which he came down firmly on the side of Euler. In fact he went much further than Euler in the type of arbitrary functions introduced by integrating partial differential equation
Partial differential equation
In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...
s, claiming that the functions could be discontinuous not only in the limited sense claimed by Euler, but discontinuous in a more general sense that he defined that allowed the function to consist of portions of different curves. Arbogast won the prize with his essay and his notion of discontinuous function became important in Cauchy's more rigorous approach to analysis.
In 1789 he submitted in Strasbourg a major report on the differential and integral calculus to the Académie des Sciences in Paris which was never published. In the Preface of a later work he described the ideas that prompted him to write the major report of 1789. Essentially he realised that there was no rigorous methods to deal with the convergence of series, and Arbogast's career reached new heights. In addition to his mathematics post, he was appointed as professor of physics at the Collège Royal in Strasbourg and from April 1791 he served as its rector until October 1791 when he was appointed rector of the University of Strasbourg; in 1794 he was appointed Professor of Calculus at the École centrale (soon to become the École polytechnique
École Polytechnique
The École Polytechnique is a state-run institution of higher education and research in Palaiseau, Essonne, France, near Paris. Polytechnique is renowned for its four year undergraduate/graduate Master's program...
) but he taught at the École préparatoire.
His contributions to mathematics show him as a philosophical thinker that has to face his era. As well as introducing discontinuous functions, as we discussed above, he conceived the calculus as operational symbols. The formal algebraic manipulation of series investigated by Lagrange
Joseph Louis Lagrange
Joseph-Louis Lagrange , born Giuseppe Lodovico Lagrangia, was a mathematician and astronomer, who was born in Turin, Piedmont, lived part of his life in Prussia and part in France, making significant contributions to all fields of analysis, to number theory, and to classical and celestial mechanics...
and Laplace in the 1770s has been put in the form of operator equalities by Arbogast in 1800. We owe him the general concept of factorial
Factorial
In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n...
as a product of a finite number of terms in arithmetic progression
Arithmetic progression
In mathematics, an arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant...
.
The original version of this article was taken from the public domain resource the Rouse History of Mathematics.