# Mathematician:Johann Bernoulli

## Contents

## Mathematician

Swiss mathematician best known for his work on development of the calculus.

Taught Guillaume de l'Hôpital, who then went ahead and published his lecture notes without crediting him.

Pioneered the technique of Integration by Parts.

Younger brother of Jacob Bernoulli, with whom he did not always see eye to eye.

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

Started his career by studying medicine, but after receiving his M.A. in medicine, he realised his mistake and turned to mathematics.

Also studied physics, chemistry and astronomy.

Contributed extensively to the field of optics.

Wrote on the theory of tides and the mathematical theory of ship sails.

Enunciated the Principle of Virtual Displacements in the field of mechanics.

Posed the Brachistochrone Problem: to find the curve down which a particle will take the shortest possible time between two points. This was solved by Jacob Bernoulli.

Father of Nicolaus II Bernoulli, Daniel Bernoulli and Johann II Bernoulli.

## Nationality

Swiss

## History

- Born: 27 July 1667, Basel, Switzerland
- 1695: Appointed Professor of Mathematics at Groningen in Holland
- 1705: Succeeded Jacob Bernoulli as Professor of Mathematics at Basel
- Died: 1 Jan 1748, Basel, Switzerland

## Theorems

- The actual discoverer of what is now known as L'Hôpital's Rule
- The Sophomore's Dream

## Publications

- 1739:
*Hydraulica*

## Also known as

**Johann Bernoulli** is also known as **Jean** or **John**.

Some sources report him as **Johann I** in order to distinguish him from Johann II Bernoulli.

## Notable Quotes

*With justice we admire Huygens because he first discovered that a heavy particle falls down a cycloid in the same time no matter from what point on the cycloid it begins its motion. But you will be petrified with astonishment when I say that precisely this cycloid, the*tautochrone*of Huygens, is our required*brachistochrone*.*

## Also see

## Sources

- John J. O'Connor and Edmund F. Robertson: "Johann 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 - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): A List of Mathematicians in Chronological Sequence - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.20$: The Bernoulli Brothers - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): A List of Mathematicians in Chronological Sequence - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**Jean Bernoulli**(1667-1748) - 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**