Shulou(Shulou.com)11/24 Report--

People who have studied physics usually do not forget Bernoulli's Law, even if the content has not been remembered clearly, but the nickname "Bai Li" is always remembered in mind. Bernoulli's law is related to the velocity and pressure of fluid, from the safety line in front of subway and train, to the "spinning ball" of table tennis, football and baseball, from the sprayer to the fuel nozzle of gasoline engine, from the wall effect of high-speed fluid to the bending trend of ocean current, from the lift of aircraft to the speed tube on the wing, all of which are related to Bernoulli's law.

In addition to Bernoulli's law, there are many other Bernoulli names in mathematics, such as Bernoulli numbers, Bernoulli polynomials, Bernoulli equations, Bernoulli bicycloids, Bernoulli distributions, Bernoulli processes, Bernoulli paradoxes, Bernoulli velocity tubes, etc. A closer look at the data will reveal that there is more than one Bernoulli, and many Bernoulli come from a large family!

In the history of science, father and son scientists and brother scientists are not rare, such as J. J. Thomson and his son who discovered electrons and created atomic models, Bohr and his son who founded atomic theory, Wright brothers, inventors of airplanes, Alvarez and his son, etc. However, it is extremely rare for a family to be scientists for several generations in succession. In addition to Becquerel's four generations of ancestors and grandchildren, they are famous physicists. What is more peculiar is Switzerland's Bernoulli family. The whole family is fond of mathematics and proficient in mathematics. For nearly a century, regardless of social upheavals and family changes, the family has been immersed in mathematics, which is a miracle in the history of science.

The Bernoulli family produced eight famous mathematicians in three generations. These eight mathematicians were also astrophysicists, physicists or geographers. Among them, there were at least three outstanding people who had an important impact on the world: Jacob Bernoulli (1654-1705), Johann Bernoulli (1667-1748) and Daniel Bernoulli (1700-1782).

From left to right: Jacob Bernoulli, Johann Bernoulli and Daniel Bernoulli At least 120 other descendants of this family are renowned in mathematics, natural sciences, engineering, and even law, management, literature, and the arts.

The Bernoulli family in Switzerland originated from an aristocratic family in Antwerp, the Netherlands. Leon Bernoulli was a famous doctor in Antwerp. The Netherlands was under Spanish colonial rule at that time. After Leon died in 1561, in order to escape Spanish persecution, his son Jacob Bernoulli led his family to Frankfurt in Germany in 1570. In 1620 Jacob's grandson, also known as Jacob, became a small successful spice merchant. In order to develop his business, he led his family to Basel, Switzerland, which was the commercial and trading center of Europe at that time. After acquiring Swiss citizenship, the Bernoulli family settled in Switzerland. Three years later, in 1623, Nicholas Bernoulli was born, and he later gave birth to three sons, thus starting the Bernoulli family mathematical dynasty. Beginning with this old Nicolai, the Bernoulli family genealogy is as follows:

Nicholas Sr.'s eldest son Jacob I. Bernoulli (1654-1705)(Figure 1) was a mathematician who created Bernoulli numbers, the founder of early classical probability theory, and the author of textbooks on classical probability theory.

Johann Bernoulli (1667-1748), the youngest son of Nicholas the Elder, was a mathematician and founder of early calculus. John I's three sons were all mathematicians, the eldest son Nicholas III Bernoulli Daniel Bernoulli (1700 - 1782) was a mathematician and physicist, author of Bernoulli's law, and the first to propose the concept of expected utility in probability theory in order to solve Bernoulli's paradox; his youngest son, John II Bernoulli (1710-1790), was also a mathematician and physicist. Nicholas II Bernoulli (1687-1759) was a mathematician who first proposed St. Petersburg's paradox, Bernoulli's paradox. Daniel I's eldest son Johann III Bernoulli (1746-1807) was a mathematician, astronomer and geographer, and Daniel II's youngest son Jacob Bernoulli (1759-1789) was a mathematician and physicist.

This family has a natural affinity with mathematics. It seems that there is an invisible hand that always pulls them back to the mathematical life track.

Nicholas Bernoulli Sr. had intended his eldest son Jacob I. Bernoulli (1654-1705) to study philosophy or theology, which were venerable noble pursuits of the period. Jacob got his master's degree in philosophy, albeit reluctantly. However, an inexplicable inner drive made him fascinated by mathematics and astronomy. While studying philosophy, he secretly taught himself mathematics. Finally, he became the first person in the Bernoulli family to make outstanding contributions to the development of mathematics and was also the founder of the Bernoulli family of mathematics.

In desperation, Nicholas turned his eyes to his youngest son, Johann Bernoulli, hoping that Johann would follow him into the spice business. Unfortunately, John was so incompetent in business that he had to go to Bell University to study medicine. Medicine, like theology and philosophy, was recognized as a respectable and secure discipline. However, as if driven by an invisible hand, John asked his brother Jacob, who had become a professor of mathematics, to teach him mathematics during his medical studies. At first, Jacob was not optimistic about his brother, who was not a good businessman. To his surprise, John's brother gradually showed his mathematical talent and interest. Jacob invited his brother to study mathematics with him.

The Bernoulli family were not only obsessed with mathematics, they were also hot-blooded and eager to win. Some people say that their "blood is always boiling." John soon surpassed his brother, not only solving some calculus problems Newton had not solved, but also further verifying the law of gravity from a mathematical point of view. In 1695, his brother Jacob took over the chair of mathematics at Bell University. In a fit of anger, his brother John ran to the University of Holland, where he became the head of the chair of mathematics. He did not return to Bell University until his brother Jacob died.

Daniel I was the most talented of the Bernoulli family, the second son of John I. Daniel was born on 8 February 1700 in Groningen, Netherlands, where his father was professor of mathematics. His father, brother and uncle were math professors, and Daniel grew up in a family of math geniuses. When Daniel was five years old, his family moved back to Basel, Switzerland, where his grandfather Nicholas Sr. started his business. His brother Johann II Bernoulli was born, and all three of Daniel's brothers grew up to be mathematicians, but this was not what their father Johann wanted.

Daniel Bernoulli, who had been asked by his father to do business, had been refused, and strangely enough, when it was his turn to be a father, insisted on Daniel doing business. When Daniel was 13, he was sent to the University of Basel to study philosophy and logic. Daniel received a bachelor's degree in 1715 and a master's degree in 1716. Like his father, he was very fond of mathematics. At the same time as he studied philosophy, he also began to study mathematics. Although John discovered his son's mathematical genius, John and his wife repeatedly explained to Daniel that there was no money to study mathematics and that the family spice business needed someone to inherit it, and arranged for him to be an apprentice to learn business from a successful businessman, but Daniel strongly resisted.

After a heated argument, his father backed off and allowed him to return to university to study medicine. Daniel studied medicine in Heidelberg (1718) and Strasbourg (1719), but he also studied mathematics and physics.

On his return to Basel in 1720, Daniel received his medical doctorate. But this did not bury his mathematical talent. He applied mathematics to medicine and wrote papers on mathematical research on respiratory mechanisms. In the process, Daniel collaborated with mathematician Euler to study the relationship between the oscillation frequency, pitch and timbre of musical instruments. The two became friends, and gradually Daniel became famous in mathematics and physics.

In 1724, with the help of the German mathematician Goldbach, Daniel completed his first work, Mathematical Exercises, in which he collected a large number of mathematical problems and solved them one by one; two years later Daniel used mathematics to solve the first motion transformation of a compound rotation; from 1738 onwards, he began to enter the main subject, namely the mathematical study of fluid dynamics. He absorbed Lagrange's mechanical analysis results, and through the relationship of energy conservation, induced a simple principle expression from fluid mechanics phenomena, proposed the famous Bernoulli principle, and used this principle to explain the complex motion of vortex and other fluids. This paper on fluid mechanics was published in 1738 and won the prize for academic achievement from the French Academy of Sciences.

Daniel applied mathematics to many aspects of physical problems, resulting in numerous papers, in addition to fluid mechanics problems, on the vibration of sound, the vibration of strings, the relationship between blood flow and blood pressure, and experimental tests of water and air tubes. More than 270 years later, the pitot tubes installed on the wings of modern aircraft to measure the speed of aircraft flight are known as Bernoulli tubes.

In 1738, Daniel collaborated with Euler to publish the Euler-Bernoulli beam equation; the two then collaborated to use mathematical methods to analyze elastic bodies; and in 1753, he published the first principle of superposition of vibrations.

In 1757, Daniel was awarded a professorship at the University of Basel because of these rich results. As professor of Basel, he also gave numerous lectures, such as the mathematical explanation of Newton's tidal motion in 1776, lectures on electromagnetism in 1743-1746, and lectures on the effects of ship-to-ship interaction in 1753. For his achievements in mathematics and physics, Daniel has won 10 scientific awards from the French Academy of Sciences. During Daniel's illustrious life, he was elected a member of the academies of science in St. Petersburg, Berlin, Paris, London, Bonn, Turin, Zurich and Mannheim, where he became a leading scientific figure.

In 1734 Daniel became a member of the French Academy of Sciences at the same time as his father John and won the French Prize of Science at the same time as his father. This was something to be happy about, but John thought it was an insult to him to be on the same level as his son, and in a fit of anger he expelled Daniel from the house.

The famous Bernoulli mathematical family can be called a mathematical dynasty that gallops around the world. There is help and cooperation among geniuses, but it is also full of contradictions and frictions while pursuing independent spirit. In any case, the Bernoulli scientific family's love for mathematics, mathematical talent and contribution to the development of mathematics and physics are unique in the history of science.

Source: 365 Days in the History of Science, slightly deleted Author: Wei Fengwen Wu Yi Editor: Zhang Runxin This article comes from Weixin Official Accounts: Origin Reading (ID: tupyread), Author: Wei Fengwen, Wu Yi, Editor: Zhang Runxin

Welcome to subscribe "Shulou Technology Information " to get latest news, interesting things and hot topics in the IT industry, and controls the hottest and latest Internet news, technology news and IT industry trends.