Jacob Bernoulli is one of the most famous mathematicians of the 17th century, who stood at the origins of the foundation of probability theory, as well as the field of mathematical analysis. This person has a fairly bright biography and has made many discoveries over the years. The main facts from life and research are present in this article.
The start of the journey
It often happens that great people find themselves on the path of life in a completely different direction than they study or work. This happened to Jacob Bernoulli, who was born in 1655 in the family of a pharmacist. Father Nikolai was engaged in raising his son, and at his behest, after school, the guy entered the University of Basel, where he studied theology. He did not want to devote his life to serving the Lord, because he was attracted to higher mathematics even at the stage of study. He began to actively study this science, in which he greatly succeeded. In parallel, the future scientist studied five languages, and in 1671 he earned a master's degree in philosophy with his work.
Travel and Explore
In the biography of Jacob Bernoulli, 1676 was marked by the beginning of a journey through Europe. Its main goal was to study the works of other great people of this time. That is why helooked into France, where for a long time he devoted himself to understanding the thoughts of Descartes. After that, his path lay in Italy, but it is not known exactly what he did in this country. The man returned to Switzerland only in 1680, where he got a job as a private teacher. Such work for a brilliant mind was unbearable, and therefore, after two years, he again goes to other countries. This time his goal was England and the Netherlands, where he managed to get acquainted with the most prominent scientists. Among them were Huygens, Boyle and other people who tried to prove themselves in the field of mathematics. After arriving a year later, Jakob immediately marries Judith Shtupanus. Subsequently, their family was replenished with a son, and then a daughter.
Work and first triumphs
Jacob Bernoulli, after returning from his second trip, got a job at the university where he had previously studied. Within four years, his knowledge was highly appreciated, and he was appointed professor of mathematics. It is worth noting that Bernoulli worked at the University of Basel until the end of his days. The decisive event in the life of this learned man was the acquaintance with Leibniz's memoirs on mathematical analysis, or rather, his first book. At that time, the founder of the Berlin Academy of Sciences was already noted for his work in the field of higher mathematics. Bernoulli got acquainted in detail with the found work, after which he sent a letter to the author, in which he asked to explain some details that he did not understand. For three years there was no answer, but in 1690 Leibniz nevertheless answered him when he was in Paris. At this time withwith the involvement of his brother Johann, Jakob masters such areas of mathematics as integral and differential calculus.
Working Together
Among interesting facts about Jacob Bernoulli is his work in 1690, when the man became part of the leading trio in the field of mathematics. Together with him was his brother Johann and Leibniz, between whom an active correspondence began. Sharing speculation was useful to all parties, and together scientists have achieved great success. In the same year, Bernoulli completely solves the difficult problem of calculating the shape of a curve. It is based on the fact that a heavy point moves along this line and descends in equal time intervals by the same vertical distance. Before him, Huygens and Leibniz were able to establish that this would be a semicubic parabola, but it was Jacob who provided the proof. Thanks to the new mathematical analysis, he was able to derive a differential equation and integrate it. It was then that such terminology first appeared in this field of science.
Other achievements
Peru Jacob Bernoulli owns many other studies in the field of mathematics. The man made a huge contribution to the development of analytic geometry, and it was he who stood at the origins of the calculus of variations. Lemniscate Bernoulli is named after Jacob, because it was he who deduced its existence and proved it in practice. In further research, he was interested in a catenary and a cycloid, and the man even bequeathed to draw a logarithmic spiral on his grave. As a result of this, an error occurred, because instead of it they depicted the spiral of Archimedes. It was this scientist who was able to investigate compound interest thanks to his own observations. As a result, he was able to substantiate the possibility of the existence in mathematics of a marginal benefit that would be greater than 2.5, but less than 3. In addition, Jacob Bernoulli always returned to research in the fields of physics, algebra and geometry, which can be seen when reading his works.
Number theory
In number theory, Bernoulli considers almost a pioneer, because it was this scientist who made fundamental research in this area. He wrote the first version of the law of large numbers. Work began with the study of Huygens' work en titled "On Calculations in Gambling". At that time, no one was talking about the theory of probability, but instead the term "favorable case" was used. Bernoulli supplemented this work with his research, and therefore even now the numbers that are named after him are being studied. The scientist outlined all the works on the emergence of the theory of probability in his monograph, where there was also the law of large numbers. Unfortunately, he never got around to publishing it on his own. In 1692 he was diagnosed with tuberculosis, from which he died in 1705. The monograph was published posthumously in 1713 by the labors of his brother.
