english version | version française | česká verze |

He was professor of mathematics at the Collège de Colmar 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, 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 Ecole Centrale (soon to become the Ecole Polytechnique) but he taught at the Ecole 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 algebric 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 finished number of terms in arithmetic progression.

Back to main page

Abraham de Moivre is a french mathematician born in Vitry (France) on May 26th 1667 and died in London (England) on November 27th 1754.

A French Protestant, de Moivre emigrated to England in 1685 following the revocation of the Edict of Nantes and the expulsion of the Huguenots; and In 1697, he was elected a fellow member of the Royal Society.

De Moivre pioneered the development of analytic geometry and the theory of probability. He published

Back to main page

Leonhard Euler is a swiss mathematician, physicist, engineer and philosopher, born in Basel (Switzerland) on April 15th 1707 and died in St Petersburg (Russia) on September 18th 1783.

Euler went there to the university and took lessons by Jean Bernoulli and passed his master's degree at sixteen. In 1727, invited by Catherine 1st, Empress of Russia, he becomes a member of the faculty of the Science Academy in Saint-Petersburg. He's appointed professor of physics in 1730 and professor of mathematics in 1733. In 1741, at the request of king of Prussia Frederic le Grand, he becomes professor of mathematics to the Science Academy of Berlin. He comes back to St Petersburg in 1766 and remains there until his death. Although handicapped before the thirty years age by a partial sight's loss and later by a quasi total blindness, Euler completed many significant mathematical works and hundreds of mathematical and scientific books.

In his

Euler had also a big interest in philosophy, fought againgst Wolff and Leinbniz's theories, was devoted to syllogistic of Aristote, and tried to formalize them with circles, precursors of Venn diagrams. In Chess, he studied the walk of the knight.

Back to main page

Christian Kramp's father was has teacher at grammar school in Strasbourg. Kramp studied medicine and, after graduating, practised medicine in the area around where patients lived in a fairly wide area. However his interests certainly ranged outside medicine for, in addition to a number of medical publications, he published a work on crystallography in 1793. In 1795 France annexed the Rhineland area in which medical Kramp was carrying out his work and after this he became has teacher at Cologne (this city was a french one from 1794 to 1815), teaching mathematics, chemistry and physics.

Kramp was appointed professor of mathematics at Strasbourg, the town of his birth, in 1809. He was elected to the geometry section of the Academy of Science in 1817. As Bessel, Legendre and Gauss did, Kramp worked on the generalised factorial function which applied to non-integers. His work on factorials is independent of that of Stirling and Vandermonde. He was the first to uses the notation n! (

Parts of

Back to main page

His talent was found by Newton. In 1717 Stirling taught in Venezia and published his first work in Roma

In London in 1730, significant Stirling published his most significant work

Back to main page

The year 1714 also marks the year Taylor was elected Secretary to the Royal Society. It was a position Taylor held from January 14th of that year until October 21st 1718, when he resigned, partly for health reasons, partly due to his lack of interest. The period during which Taylor was Secretary of the Royal Society marks his mathematically most productive period. Two books which appeared in 1715,

Taylor made several visits in France. These were made partly for health let us reasons and partly to visit the friends. He meets Pierre Rémond de Montmort and corresponds with him over various mathematical topics after his return. In particular they discussed infinite series and probability. Taylor also corresponded with De Moivre over probability and there was a three-way discussion going one between these mathematicians.

Taylor added to mathematics a new branch now called the

James Gregory, Newton, Leibniz, Johann Bernoulli and De Moivre had all discovered variable of Taylor's theorem. All these mathematicians made their discoveries independently and Taylor's work was also independent of the others' work. The importance of Taylor's theorem remained unrecognised until 1772 when Lagrange proclaimed it the

Back to main page

In this page