The Bernoulli family ( ; ; ) of

Basel Basel ( ; ), also known as Basle ( ), ; ; ; . is a city in northwestern Switzerland on the river Rhine (at the transition from the High Rhine, High to the Upper Rhine). Basel is Switzerland's List of cities in Switzerland, third-most-populo ...

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 The early modern period is a Periodization, historical period that is defined either as part of or as immediately preceding the modern period, with divisions based primarily on the history of Europe and the broader concept of modernity. There i ...

History

Originally from

Antwerp Antwerp (; ; ) is a City status in Belgium, city and a Municipalities of Belgium, municipality in the Flemish Region of Belgium. It is the capital and largest city of Antwerp Province, and the third-largest city in Belgium by area at , after ...

, a branch of the family relocated to Basel in 1620. While their origin in Antwerp is certain, proposed earlier connections with the Dutch family of Italian ancestry called ''Bornouilla'' (''Bernoullie''), or with the Castilian family ''de Bernuy'' (''Bernoille'', ''Bernouille''), are uncertain. The first known member of the family was Leon Bernoulli (d. 1561), a doctor in

, at that time part of the

Spanish Netherlands The Spanish Netherlands (; ; ; ) (historically in Spanish: , the name "Flanders" was used as a '' pars pro toto'') was the Habsburg Netherlands ruled by the Spanish branch of the Habsburgs from 1556 to 1714. They were a collection of States of t ...

. His son, Jacob, emigrated to

Frankfurt am Main Frankfurt am Main () is the most populous city in the States of Germany, German state of Hesse. Its 773,068 inhabitants as of 2022 make it the List of cities in Germany by population, fifth-most populous city in Germany. Located in the forela ...

in 1570 to escape from the Spanish persecution of the

Protestant Protestantism is a branch of Christianity that emphasizes Justification (theology), justification of sinners Sola fide, through faith alone, the teaching that Salvation in Christianity, salvation comes by unmerited Grace in Christianity, divin ...

s. Jacob's grandson, a spice trader, also named Jacob, moved to

Switzerland Switzerland, officially the Swiss Confederation, is a landlocked country located in west-central Europe. It is bordered by Italy to the south, France to the west, Germany to the north, and Austria and Liechtenstein to the east. Switzerland ...

in 1620, and was granted citizenship in 1622. His son, (Nicolaus, 1623–1708), Leon's great-great-grandson, married Margarethe Schönauer.

Notable academic members

Margarethe and Niklaus had four sons, of whom Johann and Hieronymus became the progenitors of the "greater" and the "lesser" branches of the family, respectively. The four sons of Margarethe and Niklaus were: *

Jacob Bernoulli Jacob Bernoulli (also known as James in English or Jacques in French; – 16 August 1705) was a Swiss mathematician. He sided with Gottfried Wilhelm Leibniz during the Leibniz–Newton calculus controversy and was an early proponent of Leibniz ...

(1654–1705; also known as James or Jacques), mathematician after whom Bernoulli numbers are named, and author of the early probability text '' Ars Conjectandi'' * Nicolaus Bernoulli (1662–1716), painter and

alderman An alderman is a member of a Municipal government, municipal assembly or council in many jurisdictions founded upon English law with similar officials existing in the Netherlands (wethouder) and Belgium (schepen). The term may be titular, denotin ...

of Basel *

Johann Bernoulli Johann Bernoulli (also known as Jean in French or John in English; – 1 January 1748) was a Swiss people, Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is known for his contributions to infin ...

(1667–1748; also known as Jean), mathematician and early adopter of

infinitesimal calculus Calculus 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 arithmetic operations. Originally called infinitesimal calculus or "the calculus of ...

* Hieronymus Bernoulli (1669–1760), m. Catharina Ebneter In addition to

Jacob Jacob, later known as Israel, is a Hebrew patriarch of the Abrahamic religions. He first appears in the Torah, where he is described in the Book of Genesis as a son of Isaac and Rebecca. Accordingly, alongside his older fraternal twin brother E ...

and

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 Graciou ...

, the Bernoulli family of mathematicians is generally taken to include: *

Nicolaus I Bernoulli Nicolaus Bernoulli (also spelled Nicolas or Nikolas; in Basel – 29 November 1759 in Basel) was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. Biography Nicolaus Bernoulli was born on in Base ...

(1687–1759), son of Nicolaus, mathematician, worked on curves, differential equations, and

probability Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an e ...

; originator of the St. Petersburg paradox * Nicolaus II Bernoulli (1695–1726), son of Johann *

Daniel Bernoulli Daniel Bernoulli ( ; ; – 27 March 1782) was a Swiss people, Swiss-France, French mathematician and physicist and was one of the many prominent mathematicians in the Bernoulli family from Basel. He is particularly remembered for his applicati ...

(1700–1782), son of Johann, developer of

Bernoulli's principle Bernoulli's principle is a key concept in fluid dynamics that relates pressure, speed and height. For example, for a fluid flowing horizontally Bernoulli's principle states that an increase in the speed occurs simultaneously with a decrease i ...

and originator of the concept of

expected utility The expected utility hypothesis is a foundational assumption in mathematical economics concerning decision making under uncertainty. It postulates that rational agents maximize utility, meaning the subjective desirability of their actions. Ratio ...

for resolving the St. Petersburg paradox *

Johann II Bernoulli Johann II Bernoulli (also known as Jean; 18 May 1710, Basel – 17 July 1790, Basel) was the youngest of the three sons of the Swiss mathematician Johann Bernoulli. He studied law and mathematics, and, after travelling in France, was for five y ...

(1710–1790; also known as Jean), son of Johann, mathematician and physicist * Johann III Bernoulli (1744–1807; also known as Jean), son of Johann II, astronomer, geographer and mathematician * Jakob II Bernoulli (1759–1789; also known as Jacques), son of Johann II, physicist and mathematician Several more recent prominent scholars are also descended from the family, including: * (1831–1913), art historian and archaeologist; noted for his ''Römische Ikonographie'' (1882 onwards) on Roman Imperial portraits * Ludwig Bernoully (1873–1928), German architect in Frankfurt * Hans Bernoulli (1876–1959), architect and designer of the Bernoullihäuser in Zurich and Grenchen SO * Elisabeth Bernoulli (1873–1935), suffragette and campaigner against alcoholism The surname survives in Switzerland, with 11 entries in the white pages for the city of Basel as of 2024.tel.search.ch
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Family tree of the Basler Bernoullis

Named for members of the family

* Bernoulli differential equation *

Bernoulli distribution In probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli, is the discrete probability distribution of a random variable which takes the value 1 with probability p and the value 0 with pro ...

Bernoulli number In mathematics, the Bernoulli numbers are a sequence of rational numbers which occur frequently in analysis. The Bernoulli numbers appear in (and can be defined by) the Taylor series expansions of the tangent and hyperbolic tangent function ...

Bernoulli polynomials In mathematics, the Bernoulli polynomials, named after Jacob Bernoulli, combine the Bernoulli numbers and binomial coefficients. They are used for series expansion of functions, and with the Euler–MacLaurin formula. These polynomials occur ...

Bernoulli process In probability and statistics, a Bernoulli process (named after Jacob Bernoulli) is a finite or infinite sequence of binary random variables, so it is a discrete-time stochastic process that takes only two values, canonically 0 and 1. The ...

Bernoulli trial In the theory of probability and statistics, a Bernoulli trial (or binomial trial) is a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is ...

* Bernoulli's triangle

Notes

References

External links

Family tree
at the MacTutor History of Mathematics archive.
David Darling ''Encyclopedia of Science'' Bernoulli family
{{DEFAULTSORT:Bernoulli Family Bernoulli Family History of Basel History of mathematics Patriciate of Basel Scientific families Families of Belgian ancestry