Louis François Antoine Arbogast
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Louis François Antoine Arbogast (4 October 1759 – 8 April 1803) 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, mathematical structure, structure, space, Mathematica ...
. He was born at
Mutzig Mutzig ( or ; german: Mützig) is a commune in the Bas-Rhin department in Grand Est, in north-eastern France. The commune of Mutzig is located at the entrance of the Bruche river valley, on the Route des Vins d'Alsace. History Evidences of ...
in Alsace and died at
Strasbourg Strasbourg (, , ; german: Straßburg ; gsw, label=Bas Rhin Bas-Rhin (; Alsatian: ''Unterelsàss'', ' or '; traditional german: links=no, Niederrhein; en, Lower Rhine) is a department in Alsace which is a part of the Grand Est super-re ...
, where he was professor. He wrote on series and the
derivatives The derivative of a function is the rate of change of the function's output relative to its input value. Derivative may also refer to: In mathematics and economics *Brzozowski derivative in the theory of formal languages *Formal derivative, an ...
known by his name: he was the first writer to separate the symbols of operation from those of quantity, introducing systematically the operator notation ''DF'' for the derivative of the function ''F''. In 1800, he published a
calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizati ...
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.


Biography

He was professor of mathematics at the Collège de
Colmar Colmar (, ; Alsatian: ' ; German during 1871–1918 and 1940–1945: ') is a city and commune in the Haut-Rhin department and Grand Est region of north-eastern France. The third-largest commune in Alsace (after Strasbourg and Mulhouse), ...
and entered a mathematical competition run by the
St Petersburg Saint Petersburg ( rus, links=no, Санкт-Петербург, a=Ru-Sankt Peterburg Leningrad Petrograd Piter.ogg, r=Sankt-Peterburg, p=ˈsankt pʲɪtʲɪrˈburk), formerly known as Petrograd (1914–1924) and later Leningrad (1924–1991), i ...
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 equations,See : according to this source, he submitted his memoir in 1792. 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 des travaux publics et militarisée (soon to become École Polytechnique) but he taught at the École préparatoire. His contributions to mathematics show him as a philosophical thinker. 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 (born Giuseppe Luigi LagrangiaLaplace 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.''


See also

* Discontinuous function * Operational calculus


Notes


References


General references

* Available fro
Persee
* *. *. Available fro
Persee
*. Maybe the earliest biography of Arbogast, printed only few years after his death. Entirely freely available from
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. * (Review of the first edition), available from
Project Gutenberg Project Gutenberg (PG) is a volunteer effort to digitize and archive cultural works, as well as to "encourage the creation and distribution of eBooks." It was founded in 1971 by American writer Michael S. Hart and is the oldest digital li ...
. * Available fro
Persee
*.


Scientific references

*, Entirely freely available from
Google books Google Books (previously known as Google Book Search, Google Print, and by its code-name Project Ocean) is a service from Google Inc. that searches the full text of books and magazines that Google has scanned, converted to text using optical ...
. *. *. A well-known paper where Francesco Faà di Bruno presents the two versions of the formula that now bears his name, published in the journal founded by Barnaba Tortolini.


Further reading

*


External links

* {{DEFAULTSORT:Arbogast, Antoine 1759 births 1803 deaths 18th-century French mathematicians 19th-century French mathematicians