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Jakob Bernoulli
 
 
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For other family members named Jacob, see Bernoulli family.


Jacob Bernoulli (also known as James or Jacques) (Basel
Basel

Basel is Switzerland's third most populous city . With 731,000 inhabitants in the tri-national metropolitan area , Basel is Switzerland's third-largest urban area....
, 27 December 1654 – 16 August 1705) was one of the many prominent mathematicians in the Bernoulli family.

Following his father's wish, Jacob studied theology and entered the ministry. But contrary to the desires of his parents, he also studied mathematics and astronomy.






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For other family members named Jacob, see Bernoulli family.


Jacob Bernoulli (also known as James or Jacques) (Basel
Basel

Basel is Switzerland's third most populous city . With 731,000 inhabitants in the tri-national metropolitan area , Basel is Switzerland's third-largest urban area....
, 27 December 1654 – 16 August 1705) was one of the many prominent mathematicians in the Bernoulli family.

Following his father's wish, Jacob studied theology and entered the ministry. But contrary to the desires of his parents, he also studied mathematics and astronomy. He traveled throughout Europe from 1676 to 1682, learning about the latest discoveries in mathematics and the sciences. This included the work of Robert Boyle
Robert Boyle

Robert Boyle was an Irish People theologian, natural philosopher, chemist, physicist, inventor, and early gentleman scientist, noted for his work in physics and chemistry....
 and Robert Hooke
Robert Hooke

Robert Hooke, Fellow of the Royal Society was an England natural philosopher and polymath who played an important role in the scientific revolution, through both experimental and theoretical work....
.

He became familiar with calculus
Calculus

Calculus is a branch of mathematics that includes the study of limit , derivatives, integrals, and infinite series, and constitutes a major part of modern university education....
 through a correspondence with Gottfried Leibniz
Gottfried Leibniz

Gottfried Wilhelm Leibniz was a Germany polymath who wrote primarily in Latin and French language.He occupies an equally grand place in both the history of philosophy and the history of mathematics....
, then collaborated with his brother Johann
Johann Bernoulli

Johann Bernoulli was a Switzerland mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is known for his contributions to calculus and educated the great mathematician Leonhard Euler in his youth....
 on various applications, notably publishing papers on transcendental curve
Transcendental curve

In mathematics, a transcendental curve is a curve that is not an algebraic curve. Here for a curve C what matters is the point set underlying C, not a given parametrisation....
s (1696) and isoperimetry
Isoperimetry

The isoperimetric inequality is a geometry inequality involving the square of the circumference of a closed curve in the plane and the area of a plane region it encloses, as well as its various generalizations....
 (1700, 1701). In 1690, Jacob became the first person to develop the technique for solving separable differential equation
Separable differential equation

In mathematics, a separable differential equation may refer to one of two related things, both of which are differential equations that can be attacked by a method of separation of variables....
s.

Upon returning to Basel
Basel

Basel is Switzerland's third most populous city . With 731,000 inhabitants in the tri-national metropolitan area , Basel is Switzerland's third-largest urban area....
 in 1682, he founded a school for mathematics
Mathematics

Mathematics is the study of quantity, structure, space, change, and related topics of pattern and form. Mathematicians seek out patterns whether found in numbers, space, natural science, computers, imaginary abstractions, or elsewhere....
 and the sciences. He was appointed professor of mathematics at the University of Basel
University of Basel

The University of Basel is located at Basel, Switzerland....
 in 1687, remaining in this position for the rest of his life.

Jacob is best known for the work Ars Conjectandi
Ars Conjectandi

Ars Conjectandi is a mathematics paper written by Jakob Bernoulli and published eight years after his death by his nephew, Nicolaus II Bernoulli, in 1713....
 (The Art of Conjecture), published eight years after his death in 1713 by his nephew Nicholas. In this work, he described the known results in probability theory and in enumeration, often providing alternative proofs of known results. This work also includes the application of probability theory to games of chance and his introduction of the theorem known as the law of large numbers
Law of large numbers

The law of large numbers is a theorem in probability that describes the long-term stability of the arithmetic mean of a random variable. Given a random variable with a finite expected value, if its values are repeatedly sampled, as the number of these observations increases, their mean will tend to approach and stay close to the expected va...
. The terms Bernoulli trial
Bernoulli trial

IntroductionIn the theory of probability and statistics, a Bernoulli trial is an experiment whose outcome is random and can be either of two possible outcomes, "success" and "failure"....
 and Bernoulli numbers result from this work. The lunar crater Bernoulli
Bernoulli (crater)

Bernoulli is a moon impact crater that is located in the northeast part of the Moon. It lies to the south of the crater Messala , and east of Geminus ....
 is also named after him jointly with his brother Johann.

Bernoulli chose a figure of a logarithmic spiral
Logarithmic spiral

A logarithmic spiral, equiangular spiral or growth spiral is a special kind of spiral curve which often appears in nature. The logarithmic spiral was first described by Ren? Descartes and later extensively investigated by Jakob Bernoulli, who called it Spira mirabilis, "the marvelous spiral"....
 and the motto Eadem mutata resurgo
Eadem mutata resurgo

Eadem mutata resurgo is a Latin language phrase that literally translates to "Although changed, I shall arise the same." The phrase was first known to be used by Jakob Bernoulli , a member of the famous Swiss mathematical family, and appears on his tombstone in Basel....
 ("Changed and yet the same, I rise again") for his gravestone; the spiral executed by the stonemasons was, however, an Archimedean spiral
Archimedean spiral

The Archimedean spiral is a spiral named after the 3rd century BC Ancient Greece mathematician Archimedes. It is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line which rotates with constant angular velocity....
. “[Jacques Bernoulli] wrote that the logarithmic spiral ‘may be used as a symbol, either of fortitude and constancy in adversity, or of the human body, which after all its changes, even after death, will be restored to its exact and perfect self’.” (Livio 2002: 116). Jacob had five daughters and three sons.

Further reading

  • Schneider, I., 2005, "Ars conjectandi" in Grattan-Guiness, I.
    Ivor Grattan-Guinness

    Ivor Grattan-Guinness is a historian of mathematics and logic.He gained his Bachelor degree as a Mathematics Scholar at Wadham College, Oxford, got an M.Sc in Mathematical Logic and the Philosophy of Science at the London School of Economics in 1966....
    , ed., Landmark Writings in Western Mathematics. Elsevier: 88-104.
  • Livio, Mario, 2002, The golden ratio: the story of Phi, the extraordinary number of nature, art, and beauty. London.
he has five daughters and two sons

External links

  • Jakob Bernoulli: (pdf)