Dissertatio de effervescentia et fermentatione; Dissertatio Inauguralis Physico-Anatomica de Motu Musculorum (On the Mechanics of Effervescence and Fermentation and on the Mechanics of the Movement of the Muscles)(1694 (1690)[2])
Johann Bernoulli[a] (also known asJean in French orJohn in English; 6 August [O.S. 27 July] 1667 – 1 January 1748) was aSwiss mathematician and was one of the many prominent mathematicians in theBernoulli family. He is known for his contributions toinfinitesimal calculus and educatingLeonhard Euler in the pupil's youth.
Johann was born inBasel, the son of Nicolaus Bernoulli, anapothecary, and his wife, Margarethe Schongauer, and began studying medicine atUniversity of Basel. 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 brotherJacob Bernoulli.[5] Throughout Johann Bernoulli's education atBasel University, 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 understandcalculus but to apply it to various problems.[6] In 1690,[7] he completed a degree dissertation in medicine,[8] reviewed byGottfried Leibniz,[7] whose title wasDe Motu musculorum et de effervescent et fermentation.[9]
After graduating from Basel University, Johann Bernoulli moved to teachdifferential equations. Later, in 1694, he married Dorothea Falkner, the daughter of analderman of Basel, and soon after accepted a position as the professor of mathematics at theUniversity of Groningen. At the request of hisfather-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 totuberculosis. 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 ofLeibniz's calculus, Bernoulli sided with him in 1713 in theLeibniz–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 thatNewton had failed to solve. Bernoulli also promotedDescartes'vortex theory overNewton's theory of gravitation. This ultimately delayed acceptance of Newton's theory incontinental Europe.[10]
Commercium philosophicum et mathematicum (1745), a collection of letters betweenLeibnitz and Bernoulli
In 1724, Johann Bernoulli entered a competition sponsored by the FrenchAcadémie 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 avacuum or in aplenum?
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 byMaclaurin. 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.
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. In 1738 the father–son duo nearly simultaneously published separate works onhydrodynamics (Daniel'sHydrodynamica in 1738 and Johann'sHydraulica in 1743). Johann attempted to take precedence over his son by purposely and falsely predating his work six years prior to his son's.[11][12]
The Bernoulli brothers often worked on the same problems, but not without friction. Their most bitter dispute concerned thebrachistochrone 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.[13]
Bernoulli was hired byGuillaume 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 asl'Hôpital's rule.[14][15][16] Subsequently, in letters to Leibniz,Pierre Varignon and others, Bernoulli complained that he had not received enough credit for his contributions, in spite of the preface of his book:
I recognize I owe much to the insights of the Messrs. Bernoulli, especially to those of the younger (John), currently a professor in Groningen. I did unceremoniously use their discoveries, as well as those of Mr. Leibniz. For this reason I consent that they claim as much credit as they please, and will content myself with what they will agree to leave me.
Illustration fromDe motu corporum gravium published inActa Eruditorum, 1713
Truesdell, C. (March 1958). "The New Bernoulli Edition".Isis.49 (1):54–62.doi:10.1086/348639.JSTOR226604.S2CID143648596. discusses the strange agreement between Bernoulli and de l'Hôpital on pages 59–62.
