Johann Bernoulli
Encyclopedia
Johann Bernoulli was a Swiss
mathematician
and was one of the many prominent mathematicians in the Bernoulli family. He is known for his contributions to infinitesimal calculus
and educated Leonhard Euler
in his youth.
, the son of Nikolaus Bernoulli, an apothecary, and his wife, Margaretha Schonauer and began studying medicine at Basel University
. His father desired that he study business so that he might take over the family spice trade, but Johann Bernoulli disliked business and convinced his father to allow him to study medicine instead. However, Johann Bernoulli did not enjoy medicine either and began studying mathematics on the side with his older brother Jacob. Throughout Johann Bernoulli’s education at Basel University the Bernoulli brothers worked together spending much of their time studying the newly discovered infinitesimal calculus
. They were among the first mathematicians to not only study and understand calculus but to apply it to various problems.
. At the request of Johann Bernoulli’s father-in-law, Johann Bernoulli began the voyage back to his home town of Basel
in 1705. Just after setting out on the journey he learned of his brother’s death to tuberculosis
. Johann Bernoulli had planned on becoming the professor of Greek at Basel University upon returning but instead was able to take over as professor of mathematics, his older brother’s former position. As a student of Leibniz’s calculus, Johann Bernoulli sided with him in 1713 in the Newton–Leibniz debate
over who deserved credit for the discovery of calculus. Johann Bernoulli defended Leibniz by showing that he had solved certain problems with his methods that Newton had failed to solve. However, due to his opposition to Newton
and the study that he had done under the followers of Descartes, Johann Bernoulli also promoted Descartes’ vortex theory over Newton’s theory of gravitation
which ultimately delayed acceptance of Newton’s theory in continental Europe
.
In 1724 he entered a competition sponsored by the French Académie Royale des Sciences, which posed the question:
In defending a view previously espoused by Leibniz he found himself postulating an infinite external force required to make the body elastic by overcoming the infinite internal force making the body hard. In consequence he was disqualified for the prize, which was won by Maclaurin
. However, Bernoulli's paper was subsequently accepted in 1726 when the Académie considered papers regarding elastic bodies, for which the prize was awarded to Mazière. Bernoulli received an honourable mention in both competitions.
Johann married Dorothea Falkner, daughter of an Alderman of Basel. He was the father of Nicolaus II Bernoulli
, Daniel Bernoulli
and Johann II Bernoulli
and uncle of Nicolaus I Bernoulli
.
presented by Jakob. In 1696 Johann Bernoulli proposed the problem of the brachistochrone, despite already having solved the problem himself. Within two years he received five answers, one of which was from his older brother, Jacob. Bernoulli also proposed a fluid
energy
perpetual motion
machine. Gabriel Cramer
published his collected works under the title Johannis Bernoulli Operi Omnia.
to tutor him in mathematics. Bernoulli and L'Hôpital signed a contract which gave L'Hôpital the right to use Bernoulli’s discoveries as he pleased. L'Hôpital authored the first textbook on infinitesimal calculus
, "Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes", which mainly consisted of the work of Bernoulli, including what is now known as L'Hôpital's rule
.
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 known for his contributions to infinitesimal calculus
Infinitesimal calculus
Infinitesimal calculus is the part of mathematics concerned with finding slope of curves, areas under curves, minima and maxima, and other geometric and analytic problems. It was independently developed by Gottfried Leibniz and Isaac Newton starting in the 1660s...
and educated 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...
in his youth.
Early life and education
Johann was born in BaselBasel
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...
, the son of Nikolaus Bernoulli, an apothecary, and his wife, Margaretha Schonauer and began studying medicine at Basel University
University of Basel
The University of Basel is located in Basel, Switzerland, and is considered to be one of leading universities in the country...
. His father desired that he study business so that he might take over the family spice trade, but Johann Bernoulli disliked business and convinced his father to allow him to study medicine instead. However, Johann Bernoulli did not enjoy medicine either and began studying mathematics on the side with his older brother Jacob. Throughout Johann Bernoulli’s education at Basel University the Bernoulli brothers worked together spending much of their time studying the newly discovered infinitesimal calculus
Infinitesimal calculus
Infinitesimal calculus is the part of mathematics concerned with finding slope of curves, areas under curves, minima and maxima, and other geometric and analytic problems. It was independently developed by Gottfried Leibniz and Isaac Newton starting in the 1660s...
. They were among the first mathematicians to not only study and understand calculus but to apply it to various problems.
Adult life
After graduating from Basel University Johann Bernoulli moved to teach differential equations. Later, in 1694, Johann Bernoulli married Dorothea Falkner and soon after accepted a position as the professor of mathematics at the University of GroningenUniversity of Groningen
The University of Groningen , located in the city of Groningen, was founded in 1614. It is one of the oldest universities in the Netherlands as well as one of its largest. Since its inception more than 100,000 students have graduated...
. At the request of Johann Bernoulli’s father-in-law, Johann Bernoulli began the voyage back to his home town of Basel
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...
in 1705. Just after setting out on the journey he learned of his brother’s death to tuberculosis
Tuberculosis
Tuberculosis, MTB, or TB is a common, and in many cases lethal, infectious disease caused by various strains of mycobacteria, usually Mycobacterium tuberculosis. Tuberculosis usually attacks the lungs but can also affect other parts of the body...
. Johann Bernoulli had planned on becoming the professor of Greek at Basel University upon returning but instead was able to take over as professor of mathematics, his older brother’s former position. As a student of Leibniz’s calculus, Johann Bernoulli sided with him in 1713 in the Newton–Leibniz debate
Newton v. Leibniz calculus controversy
The calculus controversy was an argument between 17th-century mathematicians Isaac Newton and Gottfried Leibniz over who had first invented calculus...
over who deserved credit for the discovery of calculus. Johann Bernoulli defended Leibniz by showing that he had solved certain problems with his methods that Newton had failed to solve. However, due to his opposition to 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 the study that he had done under the followers of Descartes, Johann Bernoulli also promoted Descartes’ vortex theory over Newton’s theory of gravitation
Newton's law of universal gravitation
Newton's law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them...
which ultimately delayed acceptance of Newton’s theory in continental Europe
Continental Europe
Continental Europe, also referred to as mainland Europe or simply the Continent, is the continent of Europe, explicitly excluding European islands....
.
In 1724 he entered a competition sponsored by the French Académie Royale des Sciences, which posed the question:
- What are the laws according to which a perfectly hard body, put into motion, moves another body of the same nature either at rest or in motion, and which it encounters either in a vacuumVacuumIn everyday usage, vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty". A perfect vacuum would be one with no particles in it at all, which is impossible to achieve in...
or in a plenumPlenum chamberA plenum chamber is a pressurised housing containing a gas or fluid at positive pressure . One function of the plenum can be to equalise pressure for more even distribution, because of irregular supply or demand...
?
In defending a view previously espoused by Leibniz he found himself postulating an infinite external force required to make the body elastic by overcoming the infinite internal force making the body hard. In consequence he was disqualified for the prize, which was won by 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....
. However, Bernoulli's paper was subsequently accepted in 1726 when the Académie considered papers regarding elastic bodies, for which the prize was awarded to Mazière. Bernoulli received an honourable mention in both competitions.
Private Life
Although Jakob and Johann worked together before Johann graduated from Basel University, shortly after this the two developed a jealous and competitive relationship. Johann was jealous of Jakob's position and the two often attempted to outdo each other. After Jakob's death Johann's jealousy shifted toward his own talented son, Daniel. In 1738 the father–son duo nearly simultaneously published separate works on hydrodynamics. Johann Bernoulli attempted to take precedence over his son by purposely predating his work two years prior to his son’s.Johann married Dorothea Falkner, daughter of an Alderman of Basel. He was the father of Nicolaus II Bernoulli
Nicolaus II Bernoulli
Nicolaus II Bernoulli, a.k.a. Niklaus Bernoulli, Nikolaus Bernoulli, was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family....
, 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...
and 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...
and uncle of Nicolaus I Bernoulli
Nicolaus I Bernoulli
Nicolaus Bernoulli , was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family....
.
Contributions to mathematics
In 1691 Johann Bernoulli again fueled the tensions between himself and his brother when he solved the problem of the catenaryCatenary
In physics and geometry, the catenary is the curve that an idealised hanging chain or cable assumes when supported at its ends and acted on only by its own weight. The curve is the graph of the hyperbolic cosine function, and has a U-like shape, superficially similar in appearance to a parabola...
presented by Jakob. In 1696 Johann Bernoulli proposed the problem of the brachistochrone, despite already having solved the problem himself. Within two years he received five answers, one of which was from his older brother, Jacob. Bernoulli also proposed a fluid
Fluid
In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....
energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
perpetual motion
Perpetual motion
Perpetual motion describes hypothetical machines that operate or produce useful work indefinitely and, more generally, hypothetical machines that produce more work or energy than they consume, whether they might operate indefinitely or not....
machine. Gabriel Cramer
Gabriel Cramer
Gabriel Cramer was a Swiss mathematician, born in Geneva. He showed promise in mathematics from an early age. At 18 he received his doctorate and at 20 he was co-chair of mathematics.In 1728 he proposed a solution to the St...
published his collected works under the title Johannis Bernoulli Operi Omnia.
L'Hôpital controversy
Bernoulli was hired by Guillaume François Antoine de L'HôpitalGuillaume de l'Hôpital
Guillaume François Antoine, Marquis de l'Hôpital was a French mathematician. His name is firmly associated with l'Hôpital's rule for calculating limits involving indeterminate forms 0/0 and ∞/∞...
to tutor him in mathematics. Bernoulli and L'Hôpital signed a contract which gave L'Hôpital the right to use Bernoulli’s discoveries as he pleased. L'Hôpital authored the first textbook on infinitesimal calculus
Infinitesimal calculus
Infinitesimal calculus is the part of mathematics concerned with finding slope of curves, areas under curves, minima and maxima, and other geometric and analytic problems. It was independently developed by Gottfried Leibniz and Isaac Newton starting in the 1660s...
, "Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes", which mainly consisted of the work of Bernoulli, including what is now known as L'Hôpital's rule
L'Hôpital's rule
In calculus, l'Hôpital's rule uses derivatives to help evaluate limits involving indeterminate forms. Application of the rule often converts an indeterminate form to a determinate form, allowing easy evaluation of the limit...
.
External links
- Golba, Paul, "Bernoulli, Johan"
- "Johann Bernoulli"
- C. Truesdell The New Bernoulli Edition Isis, Vol. 49, No. 1. (Mar., 1958), pp. 54–62, discusses the strange agreement between Bernoulli and de l'Hôpital on pages 59–62.