Jacob Bernoulli is one of the most famous mathematicians of the XVII century, who stood at the origins of the foundation of probability theory, as well as the field of mathematical analysis. This person has a rather vivid biography and has made many discoveries over his years. The main facts from life and research are present in this article.
The beginning of the way
It often happens that great people find themselves on a life path in a completely different direction than they study or work. It happened with Jacob Bernoulli, who was born in 1655 in the family of a pharmacist. Father Nikolay was engaged in raising his son, and according to his command, 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 still attracted by higher mathematics at the stage of training. He began to actively study this science, in which he greatly excelled. In parallel, the future scientist studied five languages, and in 1671, with his works, he earned a master's degree in philosophy.
Travel and study
In the biography of Jacob Bernoulli, 1676 marked the beginning of a trip to Europe. His main goal was to study the works of other great people of this time. That is why he looked 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. A man returned to Switzerland only in 1680, where he got a job as a private teacher. Such work was unbearable for the ingenious mind, and therefore, after two years, he again sent to other countries. This time, his goal was England and the Netherlands, where he managed to get acquainted with the most prominent learned men. Among them were Huygens, Boyle and other people who tried to prove themselves in the field of mathematics. After arriving a year later, Jacob immediately marries Judit Shtupanus. Subsequently, their family was replenished with a son, and then a daughter.
Work and the first triumphs
Jacob Bernoulli, after returning from his second trip, got a job at the university, where he had previously studied. For 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 husband was an acquaintance with Leibniz's memoirs about 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 higher mathematics. Bernoulli examined in detail the work found, and then sent a letter to the author, in which he asked to explain some incomprehensible details to him. For three years there was no answer, but in 1690 Leibniz nevertheless answered him when he was in Paris. At this time, with the involvement of his brother Johann, Jacob mastered such areas of mathematics as integral and differential calculus.
Joint work
Among the interesting facts about Jacob Bernoulli, it is worth noting his work in 1690, when the man became part of the leading trio in the field of mathematics. Together with him was 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 the curve. It is based on the fact that a heavy point moves along this line and falls over equal lengths of time by the same vertical distance. Before him, Huygens and Leibniz were able to establish that it would be a semi-cubic parabola, but it was Jacob who provided the evidence. Thanks to a new mathematical analysis, he was able to derive a differential equation and integrate it. It was then that the first terminology appeared in this field of science.
Other merits
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 appearance of the calculus of variations. Lemniskata Bernoulli is named after Jacob, because it was he who brought her existence and proved it in practice. In further studies, he was interested in the chain line and 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 a complex percentage due to his own observations. As a result of this, he was able to substantiate the possibility of the existence of a marginal benefit in mathematics, which will be more than 2.5, but less than 3. In addition, Jacob Bernoulli always returned to research in the fields of physics, algebra, and geometry, as is evident from 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 a study of Huygens's work entitled "On Calculations in the Gamble." Then no one spoke about probability theory, and instead the term “favorable case” was used. Bernoulli supplemented this work with his research, and therefore even now are studying the numbers that are named in his honor. The scientist outlined all the works on the appearance of probability theory in his monograph, which also had the law of large numbers. Unfortunately, he did not try to publish 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 works of his brother.