Daniel Bernoulli

Daniel Bernoulli (1700–1782) was a Swiss mathematician and physicist, one of many prominent mathematicians from the Bernoulli family of Basel. He is best known for applying mathematics to mechanics, especially fluid mechanics, and for pioneering work in probability and statistics. His name lives on in Bernoulli's principle, an example of energy conservation that explains the math behind two key 20th-century technologies: the carburetor and the airplane wing.

Born in Groningen, Netherlands, Daniel came from a family of distinguished mathematicians. The Bernoullis originally fled Antwerp (then in the Spanish Netherlands) to escape persecution of Protestants, moving first to Frankfurt and then to Basel, Switzerland. He was the son of Johann Bernoulli, an early calculus developer, and nephew of Jacob Bernoulli, an early probability researcher who discovered the constant *e*. Daniel had two brothers, Niklaus and Johann II. W. W. Rouse Ball called him "by far the ablest of the younger Bernoullis."

Daniel reportedly had a bad relationship with his father. Both entered a scientific contest at the University of Paris and tied for first place. Johann banned Daniel from his house, allegedly unable to bear the "shame" of being considered his equal. Johann also allegedly plagiarized key ideas from Daniel's book *Hydrodynamica* in his own *Hydraulica*, backdating them. Daniel's attempts at reconciliation failed.

In school, Johann encouraged Daniel to study business, citing poor pay for mathematicians. Daniel initially refused but later studied both business and medicine on the condition his father would teach him mathematics privately. He studied medicine at Basel, Heidelberg, and Strasbourg, earning a PhD in anatomy and botany in 1721.

A close friend of Leonhard Euler, Daniel went to St. Petersburg in 1724 as a mathematics professor but was unhappy there. A temporary illness, censorship by the Russian Orthodox Church, and salary disputes gave him an excuse to leave in 1733. He returned to the University of Basel, holding chairs in medicine, metaphysics, and natural philosophy until his death. He was elected a Fellow of the Royal Society in May 1750.

His earliest mathematical work, *Exercitationes* (Mathematical Exercises), was published in 1724 with Goldbach's help. In 1726, he first pointed out the desirability of resolving compound motion into translation and rotation. In 1729, he published a polynomial root-finding algorithm now called Bernoulli's method. His chief work, *Hydrodynamica* (1738), is arranged so all results follow from a single principle: conservation of *vis viva*, an early version of energy conservation. He also wrote a prize-winning memoir on tides, alongside Euler and Colin Maclaurin, which covered everything on the topic between Newton's *Principia* and Laplace's work. He published many papers on mechanical questions, especially vibrating strings and solutions by Brook Taylor and Jean le Rond d'Alembert.

In economics and statistics, his 1738 book *Specimen theoriae novae de mensura sortis* offered a solution to the St. Petersburg paradox, forming the basis of risk aversion, risk premium, and utility theory. He noted that people making uncertain decisions try to maximize "utility" (personal satisfaction) rather than monetary gain, and that utility from money diminishes as income rises. In 1766, he analyzed smallpox morbidity and mortality data to demonstrate inoculation's efficacy, an early use of censored data.

In physics, *Hydrodynamica* laid the basis for the kinetic theory of gases, applying it to explain Boyle's law. He worked with Euler on elasticity and the Euler–Bernoulli beam equation. His principle is critical in hydrodynamics. According to Léon Brillouin, Daniel Bernoulli first stated the principle of superposition in 1753: "The general motion of a vibrating system is given by a superposition of its proper vibrations."

His works include *Pieces qui ont remporté le Prix double de l'Academie royale des sciences en 1737* (1737). In 2002, he was inducted into the International Air & Space Hall of Fame at the San Diego Air & Space Museum.