Johann Bernoulli
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Johann Bernoulli (also known as Jean or John; – 1 January 1748) was a Swiss mathematician and was one of the many prominent mathematicians in the
Bernoulli family The Bernoulli family () of Basel was a patrician family, notable for having produced eight mathematically gifted academics who, among them, contributed substantially to the development of mathematics and physics during the early modern period. ...
. He is known for his contributions to infinitesimal calculus and educating
Leonhard Euler Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in ma ...
in the pupil's youth.


Biography


Early life

Johann was born in
Basel , french: link=no, Bâlois(e), it, Basilese , neighboring_municipalities= Allschwil (BL), Hégenheim (FR-68), Binningen (BL), Birsfelden (BL), Bottmingen (BL), Huningue (FR-68), Münchenstein (BL), Muttenz (BL), Reinach (BL), Riehen (BS ...
, the son of Nicolaus Bernoulli, an
apothecary ''Apothecary'' () is a mostly archaic term for a medical professional who formulates and dispenses '' materia medica'' (medicine) to physicians, surgeons, and patients. The modern chemist (British English) or pharmacist (British and North Amer ...
, and his wife, Margarethe Schongauer, and began studying medicine at
University of Basel The University of Basel (Latin: ''Universitas Basiliensis'', German: ''Universität Basel'') is a university in Basel, Switzerland. Founded on 4 April 1460, it is Switzerland's oldest university and among the world's oldest surviving universit ...
. His father desired that he study business so that he might take over the family spice trade, but Johann Bernoulli did not like business and convinced his father to allow him to study medicine instead. Johann Bernoulli began studying mathematics on the side with his older brother
Jacob Bernoulli Jacob Bernoulli (also known as James or Jacques; – 16 August 1705) was one of the many prominent mathematicians in the Bernoulli family. He was an early proponent of Leibnizian calculus and sided with Gottfried Wilhelm Leibniz during the Le ...
. Throughout Johann Bernoulli's education at
Basel University The University of Basel ( Latin: ''Universitas Basiliensis'', German: ''Universität Basel'') is a university in Basel, Switzerland. Founded on 4 April 1460, it is Switzerland's oldest university and among the world's oldest surviving universi ...
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 Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithm ...
but to apply it to various problems. In 1690, he completed a degree dissertation in medicine, (here cited p. 133). reviewed by
Leibniz Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of ma ...
, whose title was ''De Motu musculorum et de effervescent et fermentation''.


Adult life

After graduating from Basel University, Johann Bernoulli moved to teach differential equations. Later, in 1694, he married Dorothea Falkner, the daughter of an
alderman An alderman is a member of a municipal assembly or council in many jurisdictions founded upon English law. The term may be titular, denoting a high-ranking member of a borough or county council, a council member chosen by the elected members t ...
of Basel, and soon after accepted a position as the professor of mathematics at the
University of Groningen The University of Groningen (abbreviated as UG; nl, Rijksuniversiteit Groningen, abbreviated as RUG) is a public research university of more than 30,000 students in the city of Groningen in the Netherlands. Founded in 1614, the university is th ...
. At the request of his
father-in-law A parent-in-law is a person who has a legal affinity (law), affinity with another by being the parent of the other's spouse. Many cultures and legal systems impose duties and responsibilities on persons connected by this relationship. A person i ...
, 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 Tuberculosis (TB) is an infectious disease usually caused by '' Mycobacterium tuberculosis'' (MTB) bacteria. Tuberculosis generally affects the lungs, but it can also affect other parts of the body. Most infections show no symptoms, i ...
. 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 Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of ma ...
's calculus, Bernoulli sided with him in 1713 in the Leibniz–Newton debate over who deserved credit for the discovery of calculus. Bernoulli defended Leibniz by showing that he had solved certain problems with his methods that Newton had failed to solve. Bernoulli also promoted Descartes' vortex theory over
Newton's theory of gravitation Newton's law of universal gravitation is usually stated as that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distan ...
. This ultimately delayed acceptance of Newton's theory in continental Europe. In 1724, Johann Bernoulli entered a competition sponsored by the French
Académie Royale des Sciences The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at the ...
, 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
vacuum A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or " void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often di ...
or in a
plenum Plenum may refer to: * Plenum chamber, a chamber intended to contain air, gas, or liquid at positive pressure * Plenism, or ''Horror vacui'' (physics) the concept that "nature abhors a vacuum" * Plenum (meeting), a meeting of a deliberative asse ...
? 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 Maclaurin or MacLaurin is a surname. Notable people with the surname include: * Colin Maclaurin (1698–1746), Scottish mathematician * Normand MacLaurin (1835–1914), Australian politician and university administrator * Henry Normand 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 Pierre Mazière. Bernoulli received an honourable mention in both competitions.


Disputes and controversy

Although Johann and his brother Jacob Bernoulli worked together before Johann graduated from Basel University, shortly after this, the two developed a jealous and competitive relationship. Johann was jealous of Jacob's position and the two often attempted to outdo each other. After Jacob'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 attempted to take precedence over his son by purposely and falsely predating his work two years prior to his son's. The Bernoulli brothers often worked on the same problems, but not without friction. Their most bitter dispute concerned the
brachistochrone curve In physics and mathematics, a brachistochrone curve (), or curve of fastest descent, is the one lying on the plane between a point ''A'' and a lower point ''B'', where ''B'' is not directly below ''A'', on which a bead slides frictionlessly un ...
problem, or the equation for the path followed by a particle from one point to another in the shortest amount of time, if the particle is acted upon by gravity alone. Johann presented the problem in 1696, offering a reward for its solution. Entering the challenge, Johann proposed the cycloid, the path of a point on a moving wheel, also pointing out the relation this curve bears to the path taken by a ray of light passing through layers of varied density. Jacob proposed the same solution, but Johann's derivation of the solution was incorrect, and he presented his brother Jacob's derivation as his own. Bernoulli was hired by
Guillaume de l'Hôpital Guillaume François Antoine, Marquis de l'Hôpital (; sometimes spelled L'Hospital; 1661 – 2 February 1704), also known as Guillaume-François-Antoine Marquis de l'Hôpital, Marquis de Sainte-Mesme, Comte d'Entremont, and Seigneur d'Ouques-la- ...
for tutoring 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 ''Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes'' (literal translation: ''Analysis of the infinitely small to understand curves''), 1696, is the first textbook published on the infinitesimal calculus of Leibniz. It was writ ...
'' in 1696, which mainly consisted of the work of Bernoulli, including what is now known as
l'Hôpital's rule In calculus, l'Hôpital's rule or l'Hospital's rule (, , ), also known as Bernoulli's rule, is a theorem which provides a technique to evaluate limits of indeterminate forms. Application (or repeated application) of the rule often converts an i ...
. Subsequently, in letters to Leibniz, Varignon and others, Bernoulli complained that he had not received enough credit for his contributions, in spite of the preface of his book:


Works

* * * ** ** ** * * File:Johannis Bernoulli Opera Omnia.jpg, alt=, Volumes I-IV of Bernoulli's 1742 ''Opera Omnia'' File:Bernoulli-1.jpg, alt=, Portrait of Bernoulli in volume I of his 1742 ''Opera omnia'' File:Bernoulli-2.jpg, alt=, The front page of volume I of ''Opera omnia''


See also

*
Sophomore's dream In mathematics, the sophomore's dream is the pair of identities (especially the first) :\begin \int_0^1 x^\,dx &= \sum_^\infty n^ \\ \end :\begin \int_0^1 x^x \,dx &= \sum_^\infty (-1)^n^ = - \sum_^\infty (-n)^ \end discovered in 1697 by Jo ...
– a pair of analytical identities by Bernoulli *
Partial fraction decomposition In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as ...


Notes


References


External links

* * * * Golba, Paul, "
Bernoulli, Johan
''" * "
Johann Bernoulli
'" * * discusses the strange agreement between Bernoulli and de l'Hôpital on pages 59–62. {{DEFAULTSORT:Bernoulli, Johann 1667 births 1748 deaths Scientists from Basel-Stadt University of Groningen faculty 17th-century Swiss mathematicians 18th-century Swiss mathematicians Swiss Calvinist and Reformed Christians History of calculus Fluid dynamicists Fellows of the Royal Society
Johann Johann, typically a male given name, is the German form of ''Iohannes'', which is the Latin form of the Greek name ''Iōánnēs'' (), itself derived from Hebrew name ''Yochanan'' () in turn from its extended form (), meaning "Yahweh is Gracious" ...
Swiss expatriates in the Dutch Republic