Antoine Arbogast
| Louis François Antoine Arbogast | |
|---|---|
| Born |
4 October 1759 Mutzig |
| Died | 18 April 1803 (aged 43) Strasbourg |
| Nationality | French |
| Fields | Mathematical analysis |
| Institutions | Collège de Colmar, École d'Artillerie de Strasbourg, Université de Strasbourg |
| Influences | François Joseph Français |
| Notable awards | 1789 Prize of the Saint Petersburg Academy of Sciences |
Louis François Antoine Arbogast (4 October 1759 – 8 April 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.
He was professor of mathematics at the Collège de Colmar and entered a mathematical competition 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 equations, 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.
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