Daniel Bernoulli

Lore & Background

Daniel Bernoulli was born in Groningen, in the Netherlands, into a family of distinguished mathematicians. The Bernoulli family came originally from Antwerp, at that time in the Spanish Netherlands, but emigrated to escape the Spanish persecution of the Protestants. Daniel was the son of Johann Bernoulli (one of the early developers of calculus) and a nephew of Jacob Bernoulli (an early researcher in probability theory and the discoverer of the mathematical constant e). He had two brothers, Niklaus and Johann II. Daniel Bernoulli was described by W. W. Rouse Ball as "by far the ablest of the younger Bernoullis". He is said to have had a bad relationship with his father. Both of them entered and tied for first place in a scientific contest at the University of Paris. Johann banned Daniel from his house, allegedly being unable to bear the "shame" of Daniel being considered his equal. Johann allegedly plagiarized key ideas from Daniel's book Hydrodynamica in his book Hydraulica and backdated them to before Hydrodynamica. When he was in school, Johann encouraged Daniel to study business citing poor financial compensation for mathematicians. Daniel initially refused but later relented and studied both business and medicine at his father's behest under the condition that his father would teach him mathematics privately. Daniel studied medicine at Basel, Heidelberg, and Strasbourg, and earned a PhD in anatomy and botany in 1721. He was a contemporary and close friend of Leonhard Euler. He went to St. Petersburg in 1724 as professor of mathematics, but was very unhappy there. A temporary illness together with the censorship by the Russian Orthodox Church and disagreements over his salary gave him an excuse for leaving St. Petersburg in 1733. He returned to the University of Basel, where he successively held the chairs of medicine, metaphysics, and natural philosophy until his death. In May 1750 he was elected a Fellow of the Royal Society.

Reader's Guide

Daniel Bernoulli's significance spans fluid mechanics, probability, statistics, and physics. In fluid mechanics, Bernoulli's principle describes the conservation of energy and underlies the carburetor and the aeroplane wing. His chief work, Hydrodynamica (1738), laid the basis for the kinetic theory of gases and applied the idea to explain Boyle's law. He worked with Euler on elasticity and the development of the Euler–Bernoulli beam equation. In probability and statistics, his 1738 book Specimen theoriae novae de mensura sortis offered a solution to the St. Petersburg paradox as the basis of the economic theory of risk aversion, risk premium, and utility. He also conducted one of the earliest statistical analyses involving censored data: his 1766 analysis of smallpox morbidity and mortality data to demonstrate the efficacy of inoculation. In 1753 he first stated the principle of superposition for vibrating systems. His legacy includes induction into the International Air & Space Hall of Fame in 2002.

Did You Know?

• Daniel Bernoulli earned a PhD in anatomy and botany in 1721.
• He and his father Johann Bernoulli tied for first place in a scientific contest at the University of Paris, after which Johann banned Daniel from his house.
• Bernoulli's 1766 analysis of smallpox data was one of the earliest attempts to analyze a statistical problem involving censored data.
• He was a contemporary and close friend of Leonhard Euler.
• In May 1750 he was elected a Fellow of the Royal Society.