# Mathematician:Jacob Bernoulli

## Contents

## Mathematician

Swiss mathematician best known for his work on probability theory, analytic geometry and development of the calculus.

Also developed the field of calculus of variations.

Developed the technique of Separation of Variables, and in $1696$ solved what is now known as Bernoulli's (Differential) Equation.

Invented polar coordinates.

Elder brother of Johann Bernoulli, with whom he famously quarrelled.

He and Johann, having encountered Leibniz's early papers in his *Acta Eruditorum*, became his most important students.

Solved the Brachistochrone problem, which had been posed in $1696$ by his brother Johann.

Also investigated the catenary and the logarithmic spiral.

## Nationality

Swiss

## History

- Born: 27 Dec 1654 in Basel, Switzerland
- 1687: Became Professor of Mathematics at Basel
- Died: 16 Aug 1705 in Basel, Switzerland

## Theorems and Definitions

- Bernoulli Distribution, Bernoulli Trial and Bernoulli Process
- Bernoulli Numbers
- Bernoulli's Equation
- Bernoulli Polynomials
- Bernoulli's Inequality
- Bernoulli's Theorem, or the Law of Large Numbers

Results named for **Jacob Bernoulli** can be found here.

Definitions of concepts named for **Jacob Bernoulli** can be found here.

## Publications

- 1713:
*Ars Conjectandi*(The Art of Conjecture) (posthumous)

## Notable Quotes

*Invito patre sidera verso*(*Against my father's will I study the stars*)- -- Personal motto, created in memory of his father who opposed his desire to study mathematics and astronomy and tried to force him to study to become a theologian.

## Also known as

**Jacob Bernoulli** is also known as **James**, **Jacques** or **Jakob**.

Sometimes reported as **Jakob I**, or **Jacob I**, so as to distinguish him from Jakob II Bernoulli.

## Also see

## Sources

- John J. O'Connor and Edmund F. Robertson: "Jacob Bernoulli": MacTutor History of Mathematics archive

- 1937: Eric Temple Bell:
*Men of Mathematics*... (previous) ... (next): Chapter $\text{VIII}$: Nature or Nurture? - 1972: George F. Simmons:
*Differential Equations*... (previous) ... (next): $\S 1.6$: The Brachistochrone. Fermat and the Bernoullis - 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next): Entry:**Bernoulli, Jakob**or**Jacques**(also known as**James**)**${}$**(1654-1705) - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.20$: The Bernoulli Brothers - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**Jacques Bernoulli**(1654-1705) - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $6$: Curves and Coordinates: Cartesian coordinates - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**Bernoulli family**