Daniel Bernoulli was born in Groningen, in the Netherlands, into a family of distinguished mathematicians.[6] The Bernoulli family came originally from Antwerp, at that time in the Spanish Netherlands, but emigrated to escape the Spanish persecution of the Protestants. After a brief period in Frankfurt the family moved to Basel, in Switzerland.
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.[citation needed] Daniel's attempts at reconciliation with his father were unsuccessful.[8]
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.[8] Daniel studied medicine at Basel, Heidelberg, and Strasbourg, and earned a PhD in anatomy and botany in 1721.[9]
His earliest mathematical work was the Exercitationes (Mathematical Exercises), published in 1724 with the help of Goldbach. Two years later he pointed out for the first time the frequent desirability of resolving a compound motion into motions of translation and motion of rotation. His chief work is Hydrodynamica, published in 1738. It resembles Joseph Louis Lagrange's Mécanique Analytique in being arranged so that all the results are consequences of a single principle, namely, 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 Philosophiae Naturalis Principia Mathematica and the investigations of Pierre-Simon 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 Jean le Rond d'Alembert.[7]
A 1738 copy of Bernoulli's Hydrodynamica
First page of the first section of a 1738 copy of Hydrodynamica
Economics and statistics
In his 1738 book Specimen theoriae novae de mensura sortis (Exposition of a New Theory on the Measurement of Risk),[15] Bernoulli offered a solution to the St. Petersburg paradox as the basis of the economic theory of risk aversion, risk premium, and utility.[16] Bernoulli often noticed that when making decisions that involved some uncertainty, people did not always try to maximize their possible monetary gain, but rather tried to maximize "utility", an economic term encompassing their personal satisfaction and benefit. Bernoulli realized that for humans, there is a direct relationship between money gained and utility, but that it diminishes as the money gained increases. For example, to a person whose income is $10,000 per year, an additional $100 in income will provide more utility than it would to a person whose income is $50,000 per year.[17]
According to Léon Brillouin, the principle of superposition was first stated by Daniel Bernoulli in 1753: "The general motion of a vibrating system is given by a superposition of its proper vibrations."[20]
Works
Pieces qui ont remporté le Prix double de l'Academie royale des sciences en 1737
^Anderson, John David (1997). A History of Aerodynamics and its Impact on Flying Machines. New York, NY: Cambridge University Press. ISBN0-521-45435-2.
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