Daniel Bernoulli

Encyclopedia

**Daniel Bernoulli**was a Dutch

Netherlands

The Netherlands is a constituent country of the Kingdom of the Netherlands, located mainly in North-West Europe and with several islands in the Caribbean. Mainland Netherlands borders the North Sea to the north and west, Belgium to the south, and Germany to the east, and shares maritime borders...

-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. He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics

Fluid mechanics

Fluid mechanics is the study of fluids and the forces on them. Fluid mechanics can be divided into fluid statics, the study of fluids at rest; fluid kinematics, the study of fluids in motion; and fluid dynamics, the study of the effect of forces on fluid motion...

, and for his pioneering work in 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...

and statistics

Statistics

Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

. Bernoulli's work is still studied at length by many schools of science throughout the world.

## Early life

Bernoulli was born in Groningen, in the NetherlandsNetherlands

The Netherlands is a constituent country of the Kingdom of the Netherlands, located mainly in North-West Europe and with several islands in the Caribbean. Mainland Netherlands borders the North Sea to the north and west, Belgium to the south, and Germany to the east, and shares maritime borders...

into a family of distinguished mathematicians. The son of Johann Bernoulli

Johann Bernoulli

Johann Bernoulli was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family...

(one of the "early developers" of calculus

Calculus

Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...

), nephew of Jakob Bernoulli (who "was the first to discover the theory of probability

Probability theory

Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...

"), and older brother of Johann II

Johann II Bernoulli

Johann II Bernoulli , the youngest of the three sons of Johann Bernoulli. He studied law and mathematics, and, after travelling in France, was for five years professor of eloquence in the university of his native city...

, Daniel Bernoulli has been described as "by far the ablest of the younger Harpers". 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

University of Paris

The University of Paris was a university located in Paris, France and one of the earliest to be established in Europe. It was founded in the mid 12th century, and officially recognized as a university probably between 1160 and 1250...

, Johann, unable to bear the "shame" of being compared as Daniel's equal, banned Daniel from his house. Johann Bernoulli also plagiarized some key ideas from Daniel's book

*Hydrodynamica*in his own book

*Hydraulica*which he backdated to before

*Hydrodynamica*. Despite Daniel's attempts at reconciliation, his father carried the grudge until his death.

When Daniel was seven, his younger brother Johann II Bernoulli

Johann II Bernoulli

Johann II Bernoulli , the youngest of the three sons of Johann Bernoulli. He studied law and mathematics, and, after travelling in France, was for five years professor of eloquence in the university of his native city...

was born. Around schooling age, his father, Johann Bernoulli, encouraged him to study business, there being poor rewards awaiting 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

Medicine

Medicine is the science and art of healing. It encompasses a variety of health care practices evolved to maintain and restore health by the prevention and treatment of illness....

, and Daniel agreed under the condition that his father would teach him mathematics privately, which they continued for some time.

He was a contemporary and close friend 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 went to 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...

in 1724 as professor of mathematics, but was unhappy there, and a temporary illness in 1733 gave him an excuse for leaving. He returned to 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...

, where he successively held the chairs of medicine

Medicine

Medicine is the science and art of healing. It encompasses a variety of health care practices evolved to maintain and restore health by the prevention and treatment of illness....

, metaphysics

Metaphysics

Metaphysics is a branch of philosophy concerned with explaining the fundamental nature of being and the world, although the term is not easily defined. Traditionally, metaphysics attempts to answer two basic questions in the broadest possible terms:...

and natural philosophy

Natural philosophy

Natural philosophy or the philosophy of nature , is a term applied to the study of nature and the physical universe that was dominant before the development of modern science...

until his death.

In May, 1750 he was elected a Fellow of the Royal Society.

## Mathematical work

His earliest mathematical work was the*Exercitationes*(

*Mathematical Exercises*), published in 1724 with the help of Goldbach

Christian Goldbach

Christian Goldbach was a German mathematician who also studied law. He is remembered today for Goldbach's conjecture.-Biography:...

. 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

Joseph Louis Lagrange

Joseph-Louis Lagrange , born Giuseppe Lodovico Lagrangia, was a mathematician and astronomer, who was born in Turin, Piedmont, lived part of his life in Prussia and part in France, making significant contributions to all fields of analysis, to number theory, and to classical and celestial mechanics...

's

*Mécanique Analytique*in being arranged so that all the results are consequences of a single principle, namely, conservation of energy

Conservation of energy

The nineteenth century law of conservation of energy is a law of physics. It states that the total amount of energy in an isolated system remains constant over time. The total energy is said to be conserved over time...

. This was followed by a memoir on the theory of the tides, to which, conjointly with the memoirs by Euler and Colin Maclaurin

Colin Maclaurin

Colin Maclaurin was a Scottish mathematician who made important contributions to geometry and algebra. The Maclaurin series, a special case of the Taylor series, are named after him....

, 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

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."...

's

*Philosophiae Naturalis Principia Mathematica*

and the investigations of Pierre-Simon Laplace

Philosophiae Naturalis Principia Mathematica

Philosophiæ Naturalis Principia Mathematica, Latin for "Mathematical Principles of Natural Philosophy", often referred to as simply the Principia, is a work in three books by Sir Isaac Newton, first published 5 July 1687. Newton also published two further editions, in 1713 and 1726...

Pierre-Simon Laplace

Pierre-Simon, marquis de Laplace was a French mathematician and astronomer whose work was pivotal to the development of mathematical astronomy and statistics. He summarized and extended the work of his predecessors in his five volume Mécanique Céleste...

. Bernoulli also wrote a large number of papers on various mechanical questions, especially on problems connected with vibrating string

Vibrating string

A vibration in a string is a wave. Usually a vibrating string produces a sound whose frequency in most cases is constant. Therefore, since frequency characterizes the pitch, the sound produced is a constant note....

s, and the solutions given by 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 :...

and by Jean le Rond d'Alembert

Jean le Rond d'Alembert

Jean-Baptiste le Rond d'Alembert was a French mathematician, mechanician, physicist, philosopher, and music theorist. He was also co-editor with Denis Diderot of the Encyclopédie...

.

## 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)*, in which 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...

was the base of the economic theory of risk aversion

Risk aversion

Risk aversion is a concept in psychology, economics, and finance, based on the behavior of humans while exposed to uncertainty....

, risk premium

Risk premium

A risk premium is the minimum amount of money by which the expected return on a risky asset must exceed the known return on a risk-free asset, in order to induce an individual to hold the risky asset rather than the risk-free asset...

and utility

Utility

In economics, utility is a measure of customer satisfaction, referring to the total satisfaction received by a consumer from consuming a good or service....

.

One of the earliest attempts to analyze a statistical problem involving censored data

Censoring (statistics)

In statistics, engineering, and medical research, censoring occurs when the value of a measurement or observation is only partially known.For example, suppose a study is conducted to measure the impact of a drug on mortality. In such a study, it may be known that an individual's age at death is at...

was Bernoulli's 1766 analysis of smallpox

Smallpox

Smallpox was an infectious disease unique to humans, caused by either of two virus variants, Variola major and Variola minor. The disease is also known by the Latin names Variola or Variola vera, which is a derivative of the Latin varius, meaning "spotted", or varus, meaning "pimple"...

morbidity and mortality

Mortality rate

Mortality rate is a measure of the number of deaths in a population, scaled to the size of that population, per unit time...

data to demonstrate the efficacy of vaccination

Vaccination

Vaccination is the administration of antigenic material to stimulate the immune system of an individual to develop adaptive immunity to a disease. Vaccines can prevent or ameliorate the effects of infection by many pathogens...

.

## Physics

He is the earliest writer who attempted to formulate a kinetic theory of gases, and he applied the idea to explain Boyle's lawBoyle's law

Boyle's law is one of many gas laws and a special case of the ideal gas law. Boyle's law describes the inversely proportional relationship between the absolute pressure and volume of a gas, if the temperature is kept constant within a closed system...

.

He worked with Euler on elasticity

Elasticity (physics)

In physics, elasticity is the physical property of a material that returns to its original shape after the stress that made it deform or distort is removed. The relative amount of deformation is called the strain....

and the development of the Euler-Bernoulli beam equation

Euler-Bernoulli beam equation

Euler–Bernoulli beam theory is a simplification of the linear theory of elasticity which provides a means of calculating the load-carrying and deflection characteristics of beams. It covers the case for small deflections of a beam which is subjected to lateral loads only...

. Bernoulli's principle

Bernoulli's principle

In fluid dynamics, Bernoulli's principle states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy...

is of critical use in aerodynamics

Aerodynamics

Aerodynamics is a branch of dynamics concerned with studying the motion of air, particularly when it interacts with a moving object. Aerodynamics is a subfield of fluid dynamics and gas dynamics, with much theory shared between them. Aerodynamics is often used synonymously with gas dynamics, with...

.

## External links

- Rothbard, MurrayMurray RothbardMurray Newton Rothbard was an American author and economist of the Austrian School who helped define capitalist libertarianism and popularized a form of free-market anarchism he termed "anarcho-capitalism." Rothbard wrote over twenty books and is considered a centrally important figure in the...

. Daniel Bernoulli and the Founding of Mathematical Economics,*Mises Institute*(excerpted from*An Austrian Perspective on the History of Economic Thought*)An Austrian Perspective on the History of Economic ThoughtAn Austrian Perspective on the History of Economic Thought is a work of economic history written by Murray N. Rothbard. Rothbard notes in the introduction that the book was originally conceived as a "standard Adam Smith-to-the-present moderately sized book"; however, in the process of writing it,...

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