b. 6 August 1667 Basel, Switzerland
d. 1 January 1748, Basel.
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Johann (Jean) was a younger brother of Jacob I Bernoulli who studied mathematics privately under him at the University of Basel. Johann earned a master of arts in 1685, and completed his doctoral dissertation in 1694. Through the aid of Huygens he was offered the mathematic's chair at Groningen, Netherlands in 1695. Upon Jacob's death in 1705, Johann replaced him at Basel.
Johann published in the Acta Eruditorum and the Journal des Sçavans. He was a member of academy of sciences at Paris and Berlin, the Royal Society, the academy of St. Petersburg and the Institute of Bologna. He corresponded with Huygens, Varignon and Leibniz.
Jacob and Johann both made important contributions to the development of Leibniz's calculus. Sometime during or after the fall of 1691, Johann was engaged by l'Hôpital to instruct him in the calculus first at Paris and then at Oucques. These lessons continued by correspondence and ultimately became the foundation of the first textbook on the calculus, the Analyse des infiniment petits pour l'intelligence des lignes courbes of l'Hôpital published at Paris in 1696. It is suspected that this deal precipitated the intense rivalry between the brothers. As Johann was the pupil of Jacob, Jacob may have feared that Johann would take Jacob's work as his own and, in particular, sell the results to l'Hôpital. But Johann had a quarrelsome nature. In any event, by 1697, the letters of Johann to Leibniz repeatedly complain of the situation. The bitterness continued past the death of Jacob in relationships with his heirs.
Johann made but little contribution to the theory of probability. In his Opera Johannis Bernoullii (1742) we have a short work of unknown date, De Alea, sive ars conjectandi, which is a collection of 7 problems. It would appear that this was unknown until the release of the volume containing it. Maple output of the solutions to Problems 5 and 6 are presented here. The only other item of notice is a letter to Montmort, dated 17 May 1710, printed in the second edition of the Essay d'Analyse sur les Jeux de Hazard and containing observations on the 1708 edition of it. Paired with this letter is the response of Montmort to Johann Bernoulli.
The collected works will be published as Die Werke von Johann I und Nicolaus II Bernoulli by Birkhäuser Verlag in 10 volumes. These are
Mathematik I - Algebra; Analysis: Series, Integrals, Differential Equations; Probability
Mathematik II - Geometry (In preparation)
Mathematick III - Calculus: Lectures to L'Hôpital
Mathematik IV - Trajectories
Mathematik IV - Priority Dispute
Mechanik I - General Mechanics, Elasticity (In preparation)
Mechanik II - Friction Problems, Hydrodynamics
Physik I - Technology, Natural Philosophy
Physik II - General Physics, Medicine and Physiology, Varia
Weitere Schriften - Biographical and Academical Items, School Reform, Reading Notes
In addition there is Die Streitschriften von Jacob und Johann Bernoulli, Variationsrechnung, 1991. This is the Conflict between Jacob and Johann Bernoulli
Der Briefwechsel von Johann I Bernoulli in four volumes.