Johann Bernoulli (also known as Jean or John; – 1 January 1748) was a
Swiss Swiss may refer to: * the adjectival form of Switzerland , french: Suisse(sse), it, svizzero/svizzera or , rm, Svizzer/Svizra , government_type = Federalism, Federal semi-direct democracy under an assembly-independent Directorial ...

mathematician and was one of the many prominent mathematicians in the
Bernoulli family The Bernoulli family () of Basel was a patrician family, notable for having produced eight mathematically gifted academics who, among them, contributed substantially to the development of mathematics and physics during the Early Modern Switzerlan ...
. He is known for his contributions to
infinitesimal calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimal In mathematics, infinitesimals or infinitesimal numbers are quantities that are closer to zero than any standard real number, but are not zero. They do not ex ...
and educating
Leonhard Euler Leonhard Euler ( ; ; 15 April 170718 September 1783) was a Swiss mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ) ...

Leonhard Euler
in the pupil's youth.


Early life

Johann was born in
Basel , french: link=no, Bâlois(e), it, Basilese , neighboring_municipalities= Allschwil , neighboring_municipalities= Baselland (BL), Binningen, Switzerland, Binningen, Buschwiller (FR-68), Hégenheim (FR-68), Neuwiller (FR-68), Oberwil, Basel- ...

, the son of Nicolaus Bernoulli, an
apothecary :''"Apothecary" may also refer to Pharmacy (shop) A pharmacy (also called "drugstore" in American English or "community pharmacy" or "chemist" in Commonwealth English, or rarely, apothecary) is a retail shop which provides pharmaceutical drugs ...

, and his wife, Margaretha Schonauer, and began studying medicine at
Basel University The University of Basel (Latin language, Latin: ''Universitas Basiliensis'', German language, German: ''Universität Basel'') is a university in Basel, Switzerland. Founded on 4 April 1460, it is Switzerland's oldest university and among the List ...
. His father desired that he study business so that he might take over the family spice trade, but Johann Bernoulli did not like business and convinced his father to allow him to study medicine instead. Johann Bernoulli began studying mathematics on the side with his older brother
Jacob Jacob (; ; ar, يَعْقُوب, Yaʿqūb; gr, Ἰακώβ, Iakṓb), later given the name Israel Israel (; he, יִשְׂרָאֵל, translit=Yīsrāʾēl; ar, إِسْرَائِيل, translit=ʾIsrāʾīl), officially the State ...
. Throughout Johann Bernoulli's education at
Basel University The University of Basel (Latin language, Latin: ''Universitas Basiliensis'', German language, German: ''Universität Basel'') is a university in Basel, Switzerland. Founded on 4 April 1460, it is Switzerland's oldest university and among the List ...
the Bernoulli brothers worked together spending much of their time studying the newly discovered infinitesimal calculus. They were among the first mathematicians to not only study and understand
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 generalizations ...

but to apply it to various problems. In 1690 he completed a degree dissertation in medicine, (here cited p. 133). reviewed by Leibniz, whose title was ''De Motu musculorum et de effervescentia et fermentatione''.

Adult life

After graduating from Basel University, Johann Bernoulli moved to teach differential equations. Later, in 1694, he married Dorothea Falkner, the daughter of an alderman of Basel, and soon after accepted a position as the professor of mathematics at the University of Groningen. At the request of his Parent-in-law, father-in-law, Bernoulli began the voyage back to his home town of Basel in 1705. Just after setting out on the journey he learned of his brother's death to tuberculosis. Bernoulli had planned on becoming the professor of Greek at Basel University upon returning but instead was able to take over as professor of mathematics, his older brother's former position. As a student of Gottfried Wilhelm Leibniz, Leibniz's calculus, Bernoulli sided with him in 1713 in the Leibniz–Newton calculus controversy, Leibniz–Newton debate over who deserved credit for the discovery of calculus. Bernoulli defended Leibniz by showing that he had solved certain problems with his methods that Isaac Newton, Newton had failed to solve. Bernoulli also promoted Descartes' Mechanical explanations of gravitation#Vortex, vortex theory over Newton's law of universal gravitation, Newton's theory of gravitation. This ultimately delayed acceptance of Newton's theory in continental Europe. In 1724, Johann Bernoulli entered a competition sponsored by the French Académie Royale des Sciences, which posed the question: :What are the laws according to which a perfectly hard body, put into motion, moves another body of the same nature either at rest or in motion, and which it encounters either in a vacuum or in a Plenum chamber, plenum? In defending a view previously espoused by Leibniz, he found himself postulating an infinite external force required to make the body elastic by overcoming the infinite internal force making the body hard. In consequence, he was disqualified for the prize, which was won by Colin Maclaurin, Maclaurin. However, Bernoulli's paper was subsequently accepted in 1726 when the Académie considered papers regarding elastic bodies, for which the prize was awarded to Pierre Mazière. Bernoulli received an honourable mention in both competitions.

Disputes and controversy

Although Johann and his brother Jacob Bernoulli worked together before Johann graduated from Basel University, shortly after this, the two developed a jealous and competitive relationship. Johann was jealous of Jacob's position and the two often attempted to outdo each other. After Jacob's death Johann's jealousy shifted toward his own talented son, Daniel Bernoulli, Daniel. In 1738 the father–son duo nearly simultaneously published separate works on hydrodynamics. Johann attempted to take precedence over his son by purposely and falsely predating his work two years prior to his son's. The Bernoulli brothers often worked on the same problems, but not without friction. Their most bitter dispute concerned the brachistochrone curve problem, or the equation for the path followed by a particle from one point to another in the shortest amount of time, if the particle is acted upon by gravity alone. Johann presented the problem in 1696, offering a reward for its solution. Entering the challenge, Johann proposed the cycloid, the path of a point on a moving wheel, also pointing out the relation this curve bears to the path taken by a ray of light passing through layers of varied density. Jacob proposed the same solution, but Johann's derivation of the solution was incorrect, and he presented his brother Jacob's derivation as his own. Bernoulli was hired by Guillaume de l'Hôpital for tutoring in mathematics. Bernoulli and l'Hôpital signed a contract which gave l'Hôpital the right to use Bernoulli's discoveries as he pleased. L'Hôpital authored the first textbook on infinitesimal calculus, ''Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes'' in 1696, which mainly consisted of the work of Bernoulli, including what is now known as l'Hôpital's rule. Subsequently, in letters to Leibniz, Varignon and others, Bernoulli complained that he had not received enough credit for his contributions, in spite of the preface of his book:


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See also

*Sophomore's dream – a pair of analytical identities by Bernoulli *Partial fraction decomposition



External links

* * * * Golba, Paul, "
Bernoulli, Johan
''" * "
Johann Bernoulli
'" * * discusses the strange agreement between Bernoulli and de l'Hôpital on pages 59–62. {{DEFAULTSORT:Bernoulli, Johann 1667 births 1748 deaths People from Basel-Stadt University of Groningen faculty 17th-century Swiss mathematicians 18th-century Swiss mathematicians Swiss Calvinist and Reformed Christians 17th-century Swiss people 18th-century Swiss people History of calculus Fluid dynamicists Fellows of the Royal Society Bernoulli family, Johann Swiss expatriates in the Dutch Republic