There are so many Mr. Bernoulliās that Iām not sure which achievements are which Bernoulliās. Even if you look at their faces, they are all wearing the example wigs.
- [Daniel Bernoulli, February 8, 1700 - March 17, 1782
- [Johann Bernoulli (July 27, 1667 - January 1, 1748) was a Swiss mathematician. He is also known as Jean Bernoulli (French pronunciation: Jean Bernoulli). He is the discoverer of the mean value theorem for derivatives, known as L'HĆ“pital's theorem.
- His father was Nicholas Bernoulli (1623 - 1708) of French descent, a leader of the city of Basel. Jacob Bernoulli (1654 - 1705), a mathematician whose name survives in the Lemniscate, was Nicholas' eldest son; Johann Bernoulli was his tenth child. The Bernoulli family produced at least eight mathematicians during the 17th and 18th centuries. Three of Johann's children, Nicholas II (English version), Daniel, and Johann II, as well as Nicholas, the son of the painter Nicholas, brother of Jacob and of Johann, are also mathematicians.
- Together with his brother, he contributed to the development of Leibniz's calculus. He also made many other contributions in various areas of applied mathematics, such as problems concerning the motion of particles in a gravitational field. He also discovered the equation of the catenary curve in 1690 and established the calculus of exponential functions in 1691.
- [[Nicholas Bernoulli, son of Nicholas]]
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Nicolaus Bernoulli (born 21 October 1687 in Basel, died 29 November 1759 in Basel; also spelled Nicolas or Nikolas), was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family.
- He was the son of Nicolaus Bernoulli, painter and Alderman of Basel. In 1704 he graduated from the University of Basel under Jakob Bernoulli and obtained his PhD five years later (in 1709) with a work on probability theory in law. His thesis was titled Dissertatio Inauguralis Mathematico-Juridica de Usu Artis Conjectandi in Jure.1
- In 1716 he obtained the Galileo-chair at the University of Padua, where he worked on differential equations and geometry. In 1722 he returned to Switzerland and obtained a chair in Logics at the University of Basel.
- He was elected a Fellow of the Royal Society of London in March, 1714.2
- His most important contributions can be found in his letters, in particular to Pierre RĆ©mond de Montmort. In these letters, he introduced in particular the St. Petersburg Paradox. He also communicated with Gottfried Wilhelm Leibniz and Leonhard Euler.
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In 1713, Nicholas Bernoulli pointed out the inconsistency of the expected value theory by means of a decision-making problem called the āSt. Petersburg paradox. In a paper published in 1738, Daniel Bernoulli showed that a rational solution to this paradox problem is possible in risk-averse decision making by using the expected value of the utility obtained as a logarithmic function of the amount of profit or loss, rather than the expected value of the amount itself.
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In 1944, John von Neumann and Oskar Morgenstern co-authored āGame Theory and Economic Behavior. In their formulation of game theory, they developed D. Bernoulliās theory of utility functions and defined the theory of expected utility.
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Jacob Bernoulli (December 27, 1654 - August 16, 1705), also known as Jacob, Jacques, or James Bernoulli, was a Swiss mathematician and scientist. He was one of the most outstanding mathematicians of the Bernoulli family and brother of Johann Bernoulli.
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He interacted with and learned calculus from Gottfried Leibniz, and collaborated with his brother Johann. His early work on transcendental curves (1696) and isoperimetry (1700, 1701) were the result of this collaboration. He showed that the extending open and contracting closed lines of a logarithmic spiral coincide with themselves.
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Ars Conjectandi, Opus Posthumum (Methods of Guessing, 1713), is his great contribution to probability theory. Bernoulli trials and Bernoulli numbers are named from this work to commemorate his achievements.
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