Nicolaus II Bernoulli
Encyclopedia
Nicolaus II Bernoulli, a.k.a. Niklaus Bernoulli, Nikolaus Bernoulli, (February 6, 1695, Basel
, Switzerland
– July 31, 1726, St. Petersburg
, Russia
) was a Swiss
mathematician
and was one of the many prominent mathematicians in the Bernoulli family.
Nicolaus worked mostly on curve
s, differential equation
s, and probability
. He was a contemporary of Leonhard Euler
. He also contributed to fluid dynamics
.
He was older brother of Daniel Bernoulli
, to whom he also taught mathematics. He discussed with him the St. Petersburg paradox
. Even in his youth he had learned several languages. From the age of 13, he studied mathematics and law at the University of Basel
. In 1711 he received his Master's of Philosophy; in 1715 he received a Doctorate in Law. In 1716-17 he was a private tutor in Venice
. From 1719 he had the Chair in Mathematics at the University of Padua
, as the successor of Giovanni Poleni
. He served as an assistant to his father, among other areas, in the correspondence over the priority dispute between Isaac Newton
and Leibniz, and also in the priority dispute between his father and the English mathematician Brook Taylor
. In 1720 he posed the problem of reciprocal orthogonal trajectories, which was intended as a challenge for the English Newtonians. From 1723 he was a law professor at the Berner Oberen Schule. In 1725 he together with his brother Daniel, with whom he was touring Italy and France at this time, was invited by Peter the Great to the newly founded St. Petersburg Academy. There he discussed with his brother Daniel the Saint Petersburg Paradox in the theory of probability, about which his brother later wrote several works. Eight months after his appointment he came down with a fever and died. His professorship was succeeded in 1727 by Leonhard Euler
, whom the Bernoulli brothers had recommended.
Basel
Basel or Basle In the national languages of Switzerland the city is also known as Bâle , Basilea and Basilea is Switzerland's third most populous city with about 166,000 inhabitants. Located where the Swiss, French and German borders meet, Basel also has suburbs in France and Germany...
, Switzerland
Switzerland
Switzerland name of one of the Swiss cantons. ; ; ; or ), in its full name the Swiss Confederation , is a federal republic consisting of 26 cantons, with Bern as the seat of the federal authorities. The country is situated in Western Europe,Or Central Europe depending on the definition....
– July 31, 1726, St. Petersburg
Saint Petersburg
Saint Petersburg is a city and a federal subject of Russia located on the Neva River at the head of the Gulf of Finland on the Baltic Sea...
, Russia
Russia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
) was a Swiss
Switzerland
Switzerland name of one of the Swiss cantons. ; ; ; or ), in its full name the Swiss Confederation , is a federal republic consisting of 26 cantons, with Bern as the seat of the federal authorities. The country is situated in Western Europe,Or Central Europe depending on the definition....
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and was one of the many prominent mathematicians in the Bernoulli family.
Nicolaus worked mostly on curve
Curve
In mathematics, a curve is, generally speaking, an object similar to a line but which is not required to be straight...
s, differential equation
Differential equation
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...
s, and probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
. He was a contemporary of Leonhard Euler
Leonhard Euler
Leonhard Euler was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion...
. He also contributed to fluid dynamics
Fluid dynamics
In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...
.
He was older brother of Daniel Bernoulli
Daniel Bernoulli
Daniel Bernoulli was a Dutch-Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics...
, to whom he also taught mathematics. He discussed with him the St. Petersburg paradox
St. Petersburg paradox
In economics, the St. Petersburg paradox is a paradox related to probability theory and decision theory. It is based on a particular lottery game that leads to a random variable with infinite expected value, i.e., infinite expected payoff, but would nevertheless be considered to be worth only a...
. Even in his youth he had learned several languages. From the age of 13, he studied mathematics and law at the University of Basel
University of Basel
The University of Basel is located in Basel, Switzerland, and is considered to be one of leading universities in the country...
. In 1711 he received his Master's of Philosophy; in 1715 he received a Doctorate in Law. In 1716-17 he was a private tutor in Venice
Venice
Venice is a city in northern Italy which is renowned for the beauty of its setting, its architecture and its artworks. It is the capital of the Veneto region...
. From 1719 he had the Chair in Mathematics at the University of Padua
University of Padua
The University of Padua is a premier Italian university located in the city of Padua, Italy. The University of Padua was founded in 1222 as a school of law and was one of the most prominent universities in early modern Europe. It is among the earliest universities of the world and the second...
, as the successor of Giovanni Poleni
Giovanni Poleni
Giovanni Poleni was a Marquess, physicist, and antiquarian; the son of Marquess Jacopo Poleni. He studied the classics, philosophy, theology, mathematics, and physics. He was appointed, at the age of twenty-five, professor of astronomy at Padua...
. He served as an assistant to his father, among other areas, in the correspondence over the priority dispute between Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...
and Leibniz, and also in the priority dispute between his father and the English mathematician Brook Taylor
Brook Taylor
Brook Taylor FRS was an English mathematician who is best known for Taylor's theorem and the Taylor series.- Life and work :...
. In 1720 he posed the problem of reciprocal orthogonal trajectories, which was intended as a challenge for the English Newtonians. From 1723 he was a law professor at the Berner Oberen Schule. In 1725 he together with his brother Daniel, with whom he was touring Italy and France at this time, was invited by Peter the Great to the newly founded St. Petersburg Academy. There he discussed with his brother Daniel the Saint Petersburg Paradox in the theory of probability, about which his brother later wrote several works. Eight months after his appointment he came down with a fever and died. His professorship was succeeded in 1727 by Leonhard Euler
Leonhard Euler
Leonhard Euler was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion...
, whom the Bernoulli brothers had recommended.