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BERNOULLI



Johann Bernoulli (1667 – 1748) was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is known for his contributions to infinitesimal calculus and educated Leonhard Euler in his youth.
Johann was born in Basel, the son of Nikolaus Bernoulli, an apothecary, and his wife, Margaretha Schonauer and began studying medicine at Basel University. His father desired that he study business so that he might take over the family spice trade, but Johann Bernoulli disliked business and convinced his father to allow him to study medicine instead. However, Johann Bernoulli did not enjoy medicine either and began studying mathematics on the side with his older brother Jacob. Throughout Johann Bernoulli’s education at Basel 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 understand calculus but to apply it to various problems.
After graduating from Basel University Johann Bernoulli moved to teach differential equations. Later, in 1694, Johann Bernoulli married Dorothea Falkner and soon after accepted a position as the professor of mathematics at the University of Groningen. At the request of Johann Bernoulli’s father-in-law, Johann 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. Johann 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 Leibniz’s calculus, Johann Bernoulli sided with him in 1713 in the Newton–Leibniz debate over who deserved credit for the discovery of calculus. Johann Bernoulli defended Leibniz by showing that he had solved certain problems with his methods that Newton had failed to solve. However, due to his opposition to Newton and the study that vortex theory over Newton’s theory of gravitation which ultimately delayed acceptance of Newton’s theory in continental Europe.
In 1724 he entered a competition sponsored by the French Academie 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?
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 Maclaurin. However, Bernoulli's paper was subsequently accepted in 1726 when the Academie considered papers regarding elastic bodies, for which the prize was awarded to Maziere. Bernoulli received an honorable mention in both competitions.
Although Jakob and Johann worked together before Johann graduated from Basel University, shortly after this the two developed a jealous and competitive relationship. Johann was jealous of Jakob's position and the two often attempted to outdo each other. After Jakob's death Johann's jealousy shifted toward his own talented son, Daniel. In 1738 the father–son duo nearly simultaneously published separate works on hydrodynamics. Johann Bernoulli attempted to take precedence over his son by purposely 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 finding the equation for the path followed by a particle from one point to another in the shortest time, if the particle is acted upon by gravity alone, a problem originally discussed by Galileo. In 1697 Jakob offered a reward for its solution. Accepting the challenge, Johann proposed the cycloid, the path of a point on a moving wheel, pointing out at the same time the relation this curve bears to the path described by a ray of light passing through strata of variable density. A protracted, bitter dispute then arose when Jakob challenged the solution and proposed his own. The dispute marked the origin of a new discipline, the calculus of variations.
Bernoulli was hired by Guillaume de l'Hospital to tutor him in mathematics. Bernoulli and L'Hospital signed a contract which gave l'Hospital the right to use Bernoulli’s discoveries as he pleased. L'Hospital 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'Hopital'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 fact that l'Hospital acknowledged fully his debt in the preface of his book: "I recognize I owe much to MM. Bernoulli's insights, above all to the young (John) actually Teacher in Groningue. I did use casually (sans facon) 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 let me."


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Last updated: August 4, 2012