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High School Physics: Help and Review22 chapters | 267 lessons

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Johann Bernoulli was a Swiss mathematician who lived from 1667-1748. In this lesson, you will learn more about Bernoulli and his contributions to the field of mathematics and take a quiz covering the highlights of his career.

Johann Bernoulli was born in Basel, Switzerland in 1667. His father was an **apothecary**, dispensing medicines and performing medical procedures. Bernoulli's grandfather was in the spice trade, and Johann's father pushed him to study business so he could take over for his grandfather. He was not interested in business, but he did desire to study medicine. This was acceptable to his father, and Johann headed to the University of Basel where his older brother, Jacob, was a mathematics professor.

After beginning his medical studies, he decided that medicine was not where his passion was, and he began spending more and more time with his brother studying the newly created area of calculus. He went on to get his doctorate in medicine but decided to make a career out of the study of mathematics. This did not make his father happy, but Johann continued to meet with his brother uncovering the mysteries of calculus. For a time, the Bernoulli brothers were in a select group of people who alone understood the theories and ideas in the field of calculus being published by Newton and Leibniz.

Johann married and had three sons. One of his sons, Daniel, also became famous with his work in the field of mathematics. Johann Bernoulli died in 1748.

Calculus is the mathematical study of change. Its earliest roots can be found in the works of Descartes, Pascal, Fermat and others who, in the early 17th century, discussed the idea of the derivative. In the late 1600s, both Isaac Newton and Gottfried Leibniz, working independently of each other, developed the theory of **infinitesimal calculus**, which is what Bernoulli and his brother were studying at the university. Infinitesimal calculus is the study of finding tangent lines to curves, areas under curves, minima and maxima, and other geometric and analytic problems.

Johann and his brother Jacob spent most of their time studying Leibniz's papers on calculus until they became experts in his theories and ideas. This new field of infinitesimal calculus stumped many mathematicians of the time, but Bernoulli studied the principles until he had them mastered.

This caught the attention of Guillaume François Antoine Marquis de L'Hôpital, who asked Johann to teach him the principles of calculus. He spent time in Paris and at L'Hôpital's home teaching him these principals. After a time, Bernoulli returned to Switzerland, but the lessons continued by correspondence. L'Hopital paid Bernoulli handsomely for his time and talents and then went on to publish the first book on calculus based on the lectures of Bernoulli.

Bernoulli was extremely upset about this publication. He felt that he did not get the credit he deserved for the work. The only mention of Bernoulli in the book is in the preface, which says

'And then I am obliged to the gentlemen Bernoulli for their many bright ideas; particularly to the younger Mr Bernoulli who is now a professor in Groningen.'

After L'Hopital's death, Bernoulli attempted to convince others that, in fact, he was the author of the book, but his protests were not well received. It was not until 1922, when papers were found proving that the work presented in L'Hopital's book were actually Bernoulli's, that he finally got the credit he deserved.

While Bernoulli was in France, he published many papers on the study of calculus, including solutions to problems that stumped both his brother and other prominent mathematicians of the time. He also did much study and wrote prolifically on the application of mathematical principals to the field of medicine and muscular movement.

He had great success in integrating differential equations and summed series. He also discovered addition theorems for trigonometric and hyperbolic functions.

One of Bernoulli's greatest contributions came with the solution to the **brachistochrone curve**. A brachistochrone curve, or curve of fastest descent, is the distance between two points that can be covered in the fastest time. To derive the brachistochrone curve, Bernoulli used Fermat's principal that the actual path between two points taken by a beam of light is the one that is traversed in the least time.

In June of 1696, Johann published the problem of the brachistochrone curve in *Acta Eruditorum*, a German scientific journal. In May of the following year, he published his solution. Five scientists (Isaac Newton, Jacob Bernoulli, Gottfried Leibniz, Ehrenfried Walther von Tschirnhaus and Guillaume de l'Hôpital) replied with their solutions. Four of these solutions were published in the same edition of *Acta Eruditorum*.

By staying true to his love for mathematics, Johann Bernoulli attained great fame in his lifetime. He spent a large amount of time working out and understanding the principles of calculus. He was also able to teach these principles to other men like L'Hopital, who became famous mathematicians in their own right. He was also able to solve many calculus problems, including the brachistochrone curve. Because of his work, he was known as the 'Archimedes of his age,' a moniker which was inscribed on his tombstone.

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