# Mathematician:Bernoulli Family

## Mathematicians

The **Bernoulli family** produced a number of notable mathematicians in the $17$th and $18$th centuries:

##### Jacob Bernoulli $($$\text {1654}$ – $\text {1705}$$)$

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.
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##### Nicolaus Bernoulli $($$\text {1662}$ – $\text {1716}$$)$

Brother of Jacob Bernoulli and Johann Bernoulli, and father of Nicolaus I Bernoulli.

It is unclear exactly what, if anything, **Nicolaus Bernoulli** contributed to mathematics.

The accepted report is that he was a painter, and an alderman of Basel.

However, some sources, notably 1937: Eric Temple Bell: *Men of Mathematics*, appear to conflate him with Nicolaus II Bernoulli.
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##### Johann Bernoulli $($$\text {1667}$ – $\text {1748}$$)$

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.
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##### Nicolaus I Bernoulli $($$\text {1687}$ – $\text {1759}$$)$

Swiss mathematician who worked on probability theory, geometry and differential equations.

Most of his important work can be found in his correspondence, particularly with Pierre Raymond de Montmort, in which he introduced the St. Petersburg Paradox.

He also corresponded with Leonhard Paul Euler and Gottfried Wilhelm von Leibniz.

Son of Nicolaus Bernoulli and so nephew of Jacob Bernoulli and Johann Bernoulli.
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##### Nicolaus II Bernoulli $($$\text {1695}$ – $\text {1726}$$)$

Swiss mathematician who worked mostly on curves, differential equations and probability theory. He also contributed to fluid dynamics.

Studied as a lawyer, and became involved in the priority dispute between Newton and Leibniz, and also the one between Johann Bernoulli and Brook Taylor.

Posed the problem of reciprocal orthogonal trajectories in $1720$.

Son of Johann Bernoulli and the elder brother of Daniel Bernoulli and Johann II Bernoulli.
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##### Daniel Bernoulli $($$\text {1700}$ – $\text {1782}$$)$

Dutch / Swiss mathematician who worked mostly on fluid dynamics, probability theory and statistics.

Considered by many to be the first mathematical physicist.

Son of Johann Bernoulli and the brother of Nicolaus II Bernoulli and Johann II Bernoulli.

Famously suffered from the jealousy and bad temper of his father Johann Bernoulli who, among other unpleasantnesses, tried to steal his *Hydrodynamica* and pass it off as his own, naming it *Hydraulica*.
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##### Johann II Bernoulli $($$\text {1710}$ – $\text {1790}$$)$

Swiss mathematician who worked mostly on the theory of heat and light.

Son of Johann Bernoulli and the younger brother of Nicolaus II Bernoulli and Daniel Bernoulli.

Father of Johann III Bernoulli and Jakob II Bernoulli.
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##### Johann III Bernoulli $($$\text {1744}$ – $\text {1807}$$)$

Swiss mathematician who worked on probability theory, recurring decimals and the theory of equations.

Son of Johann II Bernoulli and the elder brother of Jakob II Bernoulli.
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##### Jakob II Bernoulli $($$\text {1759}$ – $\text {1789}$$)$

Swiss mathematician who worked in geometry and mathematical physics.

Son of Johann II Bernoulli and the younger brother of Johann III Bernoulli.
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## Also known as

Some sources suggest that the name may also be spelt **Bernouilli**.

## Sources

- 1937: Eric Temple Bell:
*Men of Mathematics*... (previous) ... (next): Chapter $\text{VIII}$: Nature or Nurture? - 1952: H.T.H. Piaggio:
*An Elementary Treatise on Differential Equations and their Applications*(revised ed.) ... (previous) ... (next): Historical Introduction (footnote) - 1972: George F. Simmons:
*Differential Equations*... (previous) ... (next): $1$: The Nature of Differential Equations: $\S 6$: The Brachistochrone. Fermat and the Bernoullis - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.20$: The Bernoulli Brothers - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next): Entry:**Bernoulli family** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**Bernoulli** - 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**