John Bernoulli

Born July 27, 1667 in Basel, Switzerland

Died 1 January 1748 in Basel, Switzerland

John Bernoulli

Johann Bernoulli was a Swiss mathematician who studied the reflection and refraction of light, the orthogonal trajectories of the curve family, the orthogonal and fast time lines of the series area.

John Bernoulli was the tenth child of Nicholas and Margaretsa Bernoulli. He was the younger brother of Jacob Bernoulli, but John was twelve years younger than his younger brother Jacob, which meant jacob was already a young man and John was still a child. The two brothers will have had an important impact on each other's mathematical development, especially in John's early years, when he saw Jacob despite his parents' objections and enter a career in mathematics, which must have had a great influence on him. Regarding his education as a child, John wrote in his autobiography that his parents:-

... No effort was spared to provide me with proper moral and religious education.

This religion was a Calvinist belief that forced his grandparents to flee Antwerp to avoid religious persecution.

Nicolaus and Margaretha Bernoulli tried to put John on the path of a business career, but despite his father's push, John seemed completely unfit for future business. John's father had intended for him to take over the family's spice business, and in 1682, when he was 15 years old, John worked in the spice trade for a year, but he didn't do well because he didn't like the job. John's father reluctantly agreed to Enter the University of Basel in 1683. Johann Bernoulli studied medicine at university, and although many members of the Bernoulli family loved mathematics and mathematical physics, they eventually chose medicine.

At the University of Basel, John took medical courses, but he and his brother Jacob studied mathematics. When John entered the university, Jacob was lecturing on experimental physics at the University of Basel and soon discovered that much of John's time was spent working on Leibniz's papers on calculus with his brother Jacob. After two years of study together, John was on par with his brother in mathematical skills.

John published his first article on the fermentation process in 1690, which was certainly not a mathematical subject, but in 1691 John went to Geneva, where he taught calculus. John came to Paris from Geneva, where he met mathematicians in the circle of Mare-Berant, where the French mathematical emphasis was at the time. There John met de l'Hôpital, and they had an in-depth mathematical conversation. Contrary to what is now commonly said, de Hopital was a brilliant mathematician, perhaps the best mathematician in Paris at the time, although he was not at the same level as Johann Bernoulli.

De l'Hôpital was pleased to find that Johann Bernoulli understood that the new calculus methods proposed by Leibniz had just been published, and he asked John to teach him these methods. John agreed to do so, and the course was taught in Paris and in the country house of de l'Hôpital in Oucques. Bernoulli was handsomely paid for these courses from de l'Hôpital, and in fact, these courses are invaluable to few people who are able to offer them. After Bernoulli returned to Basel, he continued his calculus courses through correspondence, which was not cheap for hospitals that paid Bernoulli half of his professor's salary. However, since he published the first calculus book, it did ensure the place of de l'Hôpital in the history of mathematics analysis des infiniment petits pour l'intelligence des lignes courbes (T) (1696) Which was based on the course given to him by Johann Bernoulli.

As one might expect, Johann Bernoulli was unhappy because the work did not acknowledge the fact that it was based on his lectures. The preamble to this book contains only the following declarations:-

Then I would like to thank Mr. Bernoulli for the many brilliant ideas he has put forward; in particular, the young Mr. Bernoulli, who is now a professor in Groningen.

The well-known de l'Hôpital rule is included in this calculus book, so it is the result of Johann Bernoulli. In fact, it was not until 1922, when his nephew Nicolaus (I) Bernoulli discovered a copy of Johann Bernoulli's course in Basel, that evidence of the work attributed to Bernoulli was obtained. Bernoulli's curriculum is almost identical to de l'Hôpital's book, but it is worth pointing out that de l'Hôpital corrects many mistakes, such as Bernoulli mistakenly believing that 1/x1/x is limited. After the death of the De L'General Hospital in 1704 Bernoulli strongly protested, his author de L'Hopital's calculus book. It seems that the huge sum paid by the hospital to Bernoulli was conditional on which he could not speak out sooner. However, before the evidence was discovered in 1922, few people believed John Bernoulli.

Let's go back to Bernoulli's time in Paris. In 1692, while in Paris, he met Varignon, which led to a deep friendship, and also Varignon during the years of their correspondence, from John Bernoulli learned a lot about the application of calculus. John Bernoulli also began to correspond with Leibniz, which proved to be very productive. In fact, it was the most important communication Leibniz had ever made. For John Bernoulli, it was a period of great mathematical achievement. Although he is pursuing a medical doctoral dissertation, he has published numerous papers on mathematical topics and has published many important results that are also included in his correspondence.

John Bernoulli had already solved the problem of catenarys raised by his brother in 1691. He solved the problem the same year that his brother proposed it, the first important mathematical result he came up with independently of his brother, although it used the ideas given by Jacob when he posed the problem. At this stage, John and Jacob learned a great deal from each other in a fairly friendly competition that, after a few years, would fall into open hostility. For example, they worked together on caustic curves during the period 1692-93, although they did not co-publish this work. Even at this stage, the competition was too fierce to allow joint publications, and although they worked on similar topics, they would never publish joint works at any time.

We mentioned above that John's doctoral dissertation was on the subject of medicine, but it was actually about the application of mathematics in medicine, about muscle movement, and it was submitted in 1694. However, John did not want to pursue a career in medicine, but since Jacob took up the position, the president of the Basel Mathematics Department has had little prospect.

Johann Bernoulli continued to emerge with a series of mathematical ideas. In 1694, he considered the function y = x^{x} is = XX and he also studied the series using the method of partial integrals. Bernoulli's integral is simply seen as the inverse of differentiation, and he was a great success with integrating differential equations. He summarized the series and discovered their additive laws using differential equations satisfies trigonometric and hyperbolic functions. This outstanding contribution to mathematics received two invitations to the chair in 1695. He received professorships at Halle University and professorships in mathematics at the University of Groningen. At Huygens's suggestion, the latter's chair was offered to John Bernoulli, and it was this position that John was very happy to accept, especially since he now held the same status as his brother Jacob, who soon became very jealous of John's progress. However, the fault was not all on Jacob's side, and John was also responsible for the deterioration of relations. Interestingly, John was appointed head of the mathematics department, but his letter of appointment mentioned his medical skills and provided him with the opportunity to practice medicine during his time in Groningen.

Johann Bernoulli married Drothea Falkner, and their first child was only seven months old when the family went to Holland on 1 September 1695. The first child was Nicholas (II) Bernoulli, who later became a mathematician. Perhaps it was a good time to note that two other children of John later became mathematicians, Daniel Bernoulli, who was born, while the family was Groningen, and John (II) Benuri.

Both Bernoulli's wife and his father-in-law were delighted to move to Groningen, especially since the journey was so difficult with a young child. After departing on September 1, they had to cross an area where the armies were fighting, then sail along the Rhine by boat, and finally reach their destination in a carriage and another boat. They arrived in October on the 22nd to begin a difficult decade in Groningen. John was embroiled in some religious disputes, his second child, a daughter, was born in 1697 and lived only six weeks, and he was so ill that he reportedly died.

In one dispute, he was accused of denying the resurrection of the corpse, an allegation based on medical opinion he held. In a second controversy in 1702, Bernoulli was accused by Petrus Vinhesen, a student at the University of Groningen, who published a pamphlet that essentially accused Bernoulli of following Cartesian' philosophy. The pamphlet also accuses him of opposing calvinist beliefs and depriving believers of comfort in the passion of Christ. Bernoulli wrote a 12-page reply to the university president that still exists[16] :-

...... If [Vin hessen] wasn't one of the worst students, a man of utter ignorance, not known, respected, or believed by any learned person, I wouldn't mind so much, and he certainly wouldn't have been blackened by the name of an honest man, let alone a professor who is widely known in academia

...... I have confessed my Reformed Christian faith all my life, and I still do... Pagans; Indeed, he has very evilly attempted to make me an abomination of the world and to expose me to the retribution of the authorities and ordinary people...

This was not the only controversy during John's time in Groningen. He introduced physics experiments into his teaching, but Sierksma wrote in [16]:-

...... It was disgusting to the Scientists of the Cartesians and Calvinists. The Cartesians naturally emphasized "reason" and argued that ... The world of sensory perception is secondary; Calvinists try to understand God's underlying plan by carefully analyzing natural phenomena. Explanations of these natural phenomena alone are incompatible with either.

When John Bernoulli was president in Groningen, he engaged in an interesting mathematical struggle with his brother, but unfortunately a painful personal struggle. Johann raised the slowness problem in June 1696 and challenged others to solve it. Leibniz persuaded him to give him a longer time so that foreign mathematicians would also have a chance to solve the problem. Five solutions were obtained, and in addition to John Bernoulli, Jacob Bernoulli and Leibniz all solved the problem. Galileo, who had given the wrong solution earlier, did not find a solution to the cycloid. Not to be outdone, his younger brother Jacob then proposed the equal week problem to minimize the area surrounded by the curve.

John's solution to this problem was not as satisfactory as Jacob's, but when John returned to the problem after reading Taylor's work in 1718, he proposed an elegant solution that laid the foundation for the variational calculus.

In 1705 the Bernoulli family received a letter in Groningen saying that John's father was thinking of his daughter and grandson in law and did not live long. They decided to return to Basel with Nicholas (I) Bernoulli, his nephew, who had been studying mathematics with his uncle in Groningen. They left Groningen two days after Jacob's death, but of course they didn't know he died of tuberculosis, they only learned of his death during the trip. Therefore, John returned to Basel not expecting to take the mathematical presidency, but returned to fill the position of Greek presidency. Of course, his brother's death would lead to a change in plans.

Before arriving in Basel, however, Johann was attracted by a chair at Utrecht University. The rector of Utrecht University very much wanted Bernoulli to come here, and he set off after Bernoulli had caught up with them in Frankfurt. He tried to persuade John to go to Utrecht, but Bernoulli was ready to return to Basel.

Upon his return to Basel, John worked hard to ensure that he would take over his brother's presidency and was soon appointed Jacob's chairman of mathematics. It is worth mentioning that Bernoulli's father-in-law lived in Basel for three years and enjoyed returning to Basel with his daughter and grandson. John rejected other offers, such as a second offer from Leiden, Utrecht, and a generous offer to return him to Groningen in 1717.

In 1713 John became involved in the Newton-Leibniz controversy. He strongly supported Leibniz and added weight to the argument by demonstrating the power of his calculus in solving some of the problems Newton encountered. His method failed to solve it. Although Bernoulli was largely correct in supporting Leibniz's superior calculus method, he also supported Descartes' vortex theory rather than Newton's theory of gravitation, which he is certainly incorrect here. In fact, his support delayed Newton's acceptance of physics on the continent.

It is not surprising that Bernoulli also made important contributions to mechanics through his work on kinetic energy, another topic of debate among mathematicians for many years. His work Hydrolica (T) is another sign of his jealous nature. The date of this work is 1732, but this is incorrect, and it is John's attempt to gain priority over his own son Daniel. Daniel Bernoulli completed his most important work Hydrodynamica (T), published in 1734 and 1738, about the same time as John's publication of Hydraulics. It wasn't an isolated incident where he was competing with his brother and now he was competing with his own son. Since the historical record of the study has justified John's claim that the author de L'Hopital's calculus book, therefore it has been shown that his son wrote Hydrodynamica before he claimed to have published Hydrodynamica were all false.

Johann Bernoulli rose to prominence during his lifetime. He was elected a fellow of the academies of Paris, Berlin, London, St Petersburg and Bologna. He was known as the "Archimedes of his time", which is indeed inscribed on his tombstone.