Daniel Bernoulli (February 8, 1700 – March 17, 1782) was a Dutch-born
mathematician who spent much of his life in Basel,
Switzerland where he died. A member of a talented family of mathematicians, physicists and
philosophers, he is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and
statistics.
Early life
Born in Groningen, the son of Johann
Bernoulli, nephew of Jakob Bernoulli, younger brother of Nicolaus II Bernoulli, and older brother of Johann II, Daniel Bernoulli has been described as "by
far the ablest of the younger Bernoullis".[1] 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.[2]
When Daniel was five, his younger brother Johann II Bernoulli was born. Around schooling age, his father, Johann Bernoulli,
encouraged him to study business, there being poor rewards awating a mathematician. However, Daniel refused, because he wanted to
study mathematics. He later gave in to his father's wish and studied business. His father then asked him to study in
medicine, and Daniel agreed under the condition that his father would teach him mathematics
privately, which they continued for some time.[2]
He was a contemporary and intimate friend of Leonard Euler. He went to
St. Petersburg in 1724 as professor of mathematics, but
was unhappy there, and a temporary illness in 1733 gave him an excuse for leaving.[2] He returned to the University of Basel, where he successively held the chairs of medicine, metaphysics and natural
philosophy until his death.[3]
Mathematical work
His earliest mathematical work was the Exercitationes (Mathematical Exercises), published in 1724 (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
Joseph Louis Lagrange's Méchanique 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.[1]
Statistics
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),[4] in which the St. Petersburg paradox was the base of
the economic theory of risk aversion, risk premium
and utility.[5]
One of the earliest attempts to analyse a statistical problem involving censored
data was Bernoulli's 1766 analysis of smallpox morbidity
and mortality data to demonstrate the efficacy of vaccination.[6]
Physics
He is the earliest writer who attempted to formulate a kinetic theory of gases, and he
applied the idea to explain Boyle's law.[1]
He worked with Euler on elasticity and the development of the Euler-Bernoulli beam equation.[7] Bernoulli's principle is of critical use in
aerodynamics.[3]
References
- ^ a b c Rouse Ball (1908)
- ^ a b c O'Connor &
Robertson (1998)
- ^ a b
- ^ English translation in Econometrica 22 (1954)
pp23-36
- ^ Martin (2004)
- ^ reprinted in Blower (2004)
- ^ Timoshenko (1983)
Bibliography
Original entry based on the public domain Rouse History of Mathematics
- [Anon.] (1911) "Bernoulli,
Encyclopaedia Britannica
- [Anon.] (2001) "Daniel Bernoulli", Encyclopaedia Britannica
- Blower, S. (2004), D, Bernoulli's "An attempt at a
new analysis of the mortality caused by smallpox and of the advantages of inoculation to prevent itPDF", Reviews of Medical Virolology,
14: 275–288
- Cardwell, D.S.L. (1971). From Watt to Clausius: The Rise of Thermodynamics in
the Early Industrial Age. Heinemann: London. ISBN 0-435-54150-1.
- Martin, R. M. (2004). The St. Petersburg Paradox. Stanford Encyclopedia of
Philosophy. Stanford University. Retrieved on 2007-09-07.
- O'Connor, John J; Edmund F. Robertson "Daniel
Bernoulli". MacTutor History of Mathematics
archive.
(1998)
- Pacey, A.J. & Fisher, S.J. (1967) "Daniel Bernoulli and the vis viva of compressed air", British Journal for
the History of Science 3, 388-92
- Rouse Ball, W. W. [1908] (2003) "The
Bernoullis", in A Short Account of the History of Mathematics, 4th ed., Dover, ISBN 0486206300
- Timoshenko, S. P. [1953] (1983).
History of Strength of Materials. New York: Dover Publications. ISBN 0486611876.
External links
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