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Daniel Bernoulli

Daniel Bernoulli (Groningen, February 8, 1700 – Basel, March 17, 1782) was a Dutch-born mathematician who spent much of his life in Basel, Switzerland. He worked with Leonhard Euler on the equations bearing their names. Bernoulli's principle is of critical use in aerodynamics. It is applicable to steady, inviscid, incompressible flow, along a streamline.

Born as the son of Johann Bernoulli, nephew of Jakob Bernoulli, younger brother of Nicolaus II Bernoulli, and older brother of Johann II, Daniel Bernoulli was by far the ablest of the younger Bernoullis. He is said to have had a bad relationship with his father. Upon both of them entering and tying for first place in a scientific contest at the University of Paris, Johann, unable to bear the "shame" of being compared to his offspring, banned Daniel from his house. Johann Bernoulli also tried to steal Daniel's book Hydrodynamica and rename it Hydraulica. Despite Daniel's attempts at reconciliation, his father carried the grudge until his death.

When Daniel was five, his younger brother Johann Bernoulli II was born.

Around schooling age, His father, Johann Bernoulli, wished for him to study business, but Daniel refused, because he wanted to study mathematics. His father then asked him to go to school in medicine, and Daniel agreed under the condition that his father would teach him mathematics on the side, which they continued for some time.

He was a contemporary and intimate friend of Euler. He went to St. Petersburg in 1724 as professor of mathematics, but did not like it there, and a temporary illness in 1733 gave him an excuse for leaving. He returned to the University of Basel, where he successively held the chairs of medicine, metaphysics and natural philosophy until his death. His father wanted him to do this because he believed that there was no money in mathematics.

His earliest mathematical work was the Exercitationes (Mathematical Exercises), published in 1724, which contains a solution of the differential equation proposed by Jacopo Riccati (the Riccati equation). Two years later he pointed out for the first time the frequent desirability of resolving a compound motion into motions of translation and motions of rotation. His chief work is his Hydrodynamique (Hydrodynamica), published in 1738; it resembles Lagrange's Méchanique Analytique in being arranged so that all the results are consequences of a single principle, namely, in this case, the conservation of energy. This was followed by a memoir on the theory of the tides, to which, conjointly with the memoirs by Euler and Colin Maclaurin, a prize was awarded by the French Academy: these three memoirs contain all that was done on this subject between the publication of Isaac Newton's Principia and the investigations of Laplace. Bernoulli also wrote a large number of papers on various mechanical questions, especially on problems connected with vibrating strings, and the solutions given by Brook Taylor and by d'Alembert.

To understand the significance of Bernoulli's work on kinetic theory in the context of the development of thermodynamics, see timeline Edit

He is the earliest writer who attempted to formulate a kinetic theory of gases, and he applied the idea to explain the law associated with the names of Robert Boyle and Edme Mariotte.

Daniel Bernoulli was also the author in 1738 of Specimen theoriae novae de mensura sortis (Exposition of a New Theory on the Measurement of Risk), (English translation in Econometrica vol 22 (1954), pp23-36; Stanford Encyclopaedia of Philosophy) in which the St. Petersburg paradox was the base of the economic theory of risk aversion, risk premium and utility.

• Euler-Bernoulli beam equation
• History of the molecule
• St. Petersburg paradox

• O'Connor, John J., and Edmund F. Robertson. "Daniel Bernoulli". MacTutor History of Mathematics archive.
• Mathematik.ch Biography: http://www.mathematik.ch/mathematiker/daniel_bernoulli.php
• Eric W. Weisstein, Bernoulli, Daniel (1700-1782) at ScienceWorld.

Original entry based on the public domain Rouse History of Mathematics