# Bernoulli History

A Bonus point project for MA265.

The History of Daniel Bernoulli

Daniel Bernoulli was born on February 8, 1700 in the town of Basel, Switzerland. He was the son of Johann Bernoulli and also had an uncle named Jacob Bernoulli. They were all leading mathematicians at the time, so it was no surprise he was born in a mathematically oriented family. However, his family was immensely envious, and there was often intense rivalry between the different members of the family. When Daniel was five years old living in the town of Basel, his father was a chairman on the board of mathematics at the university.

His father Johann was so adamant on his son being a businessman that he often pushed him towards that profession. When Daniel was only 13, his father already sent him to the local university to study Philosophy and Logic. He got his degree in 1715, followed by his master’s degree a year later in 1716. However, Daniels interests were so passionate that he wanted to study mathematics like his father. Because of his keen interest, his father taught him the methods of Calculus while he was in college studying Philosophy. His older brother Nicholas Bernoulli taught him mathematical concepts as well. When young Bernoulli got out of college, his father had plans for him to be a traveling merchant. His father was able to relate to his plight because his father had wanted him to be in business, but he choose mathematics as his profession. Johann insisted to Daniel that there was no money to be made in a profession of mathematics, so he sent Daniel back to college to study medicine. He finally completed his doctorate of medicine in 1720 at the University of Basel.

By the time he finished his medical degree, Johann saw fit to teach Daniel more mathematics and also his Kinetic Theory that he had been working on. When his father taught him the conversation of energy theory, he applied it in his doctoral dissertation and related it to the human breathing patterns. He just like his father applied mathematical concepts to a medical application to earn his degree.

Daniel finally decided that he wanted to follow his father’s footsteps and become involved in academia. He applied for two positions at Basel University. He applied to a chair in anatomy and botany, but due to a random drawing, was not picked for the job. He also applied to a position in logic department, but again he was unlucky and didn’t win the random drawing. Due to the fact that he could not earn any academic post, he packed up his stuff and went to practice medicine in Venice. While he was in Venice, he got very ill and was unable to continue his studies in medicine. However, he opted to work in mathematics and had his first publication in 1724. His first work was called Mathematical Exercises. It consisted of four different topics that had attracted his interest while in Venice. The first topic included information about the game of Faro, but was merely used as a means to express his interest in probability. The second part incorrectly tried to discuss Newtonian mechanics and apply it to fluids. He was trying to solve the theory of pressure, but was unable to correctly solve it until later parts in his life. Due to his medical work with blood flow and fluid flow, he developed a strong interest in fluid dynamics. The final part of his work was on an unrelated geometrical question.

One of his less famous achievements was the creation of an hour glass that trickled sand at a constant rate so that even while a ship was in heavy tide, it was still even. He sent his work to the Paris academy in 1725, and was surprised to learn that he had won the prize of the academy. Because of his earlier works and fame, he was instantly asked to take a position as a chairman of mathematics at St. Petersburg University. His brother Nicholas took a job as chairman of mathematics at the same university, so the two brothers worked together. Unfortunately, 8 months later, Nicholas died of fever. Daniel was devastated by the loss of his brother, and also he did not enjoy the climate of conditions of where he lived. After sending an angry letter to his father about coming back to Basel, Johann decided to send one of his best graduate students to work with him. The student was Leonardo Euler and he worked with him from 1727 to 1733, which was regarded by most as his most productive time. Bernoulli and Euler both studied vibrating systems and published many papers about the topic. While working in St. Petersburg, he made a famous discovery where he “defined the simple nodes and the frequencies of oscillation of a system. He showed that the movements of strings of musical instruments are composed of and infinite number of harmonic vibrations all superimposed on the string.” (O'Connor)

One of the second most important works that Bernoulli worked on was that of probability and political economy. He agreed upon that the “moral value of the increase in a person's wealth is inversely proportional to the amount of that wealth.” (John J) However, his most important work that he worked on in his life was involved with fluid mechanics. He wrote a book called Hydrodynamica which was published in 1738, and he wrote most of the content while at University. The monumental work included correct analysis of how water flows from a hole in a container. He applied the principle of the conservation of energy which his father had taught him years earlier. He also discussed about other means to draw water from the ground. In his book, he also dabbled in gas laws, and was able to predict the Van der Walls equation before it officially existed and was proven. However, Bernoulli was never truly happy while working in St. Petersburg. He kept applying for teaching posts in Basel, but every time he would be turned down because of other limitations.

In 1734, he submitted an essay to the Paris academy on his work in astronomy. This was awkward because his father had also submitted a work to the Paris academy, and they were both declared joint winners. Because of this, Daniel was upset and was envious and a rivalry was born. His father took it personally because he had seen himself not as equal, but superior to his son. When Daniel returned to Basel, he was not allowed to see his father and was banished from his house. Because of this episode, it lessened his interest in mathematics and was never as productive as he was while in St. Petersburg. Even though he left St. Petersburg, Daniel still worked with his student Euler and they continued to develop new ideas and works. During the 1737 Grand Prize at the Paris Academy, it was again jointly won by Daniel Bernoulli and another person named Poleni. It was for the best shape of a ship anchor. His father made a disgusting attempt to earn fame off his sons name by publishing a book called Hydraulica which was basically Daniels ideas that he wrote in Hydrodynamica. However, Johann made his book look like it was written first and that it was published in 1732 rather than 1739. This was a bad attempt to gain credit for work that was not his and just made relations between the two even worse than before. Daniel tried many times to fix the relationship between his father and him, but his father was always very envious of his son’s success. Daniel was never jealous of anyone in his family and often produced joint work with his siblings.

In 1750, he finally earned a position on the teaching faculty at Basil University, and started to teach physiology. However, a few months later, he was appointed to the Physics department where he became known for his legendary lectures and experiments that he performed. He taught Physics for 26 years until 1776. During that time, he confirmed many Physical theories that were not officially proved or observed. One observance that he saw was Coulombs Law before it was officially proved. Some things that made Bernoulli’s work so monumental was that he accepted Calculus for what it was and mended it together with Newton’s Mechanical theories which at the time were considered unproven and not very reliable. As he aged, he continued to produce small works, but his monumental work that he did while at St. Petersburg was unparalleled. Finally, he passed away of old age in 1782. In Basil, there is a honorary statue of him placed in the city streets.

Works Cited:

O'Connor, John J; Edmund F. Robertson "Daniel Bernoulli". MacTutor History of Mathematics archive.

Mathematik.ch Biography: http://www.mathematik.ch/mathematiker/daniel_bernoulli.php

http://en.wikipedia.org/wiki/Daniel_Bernoulli

http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Bernoulli_Daniel.html