The Bernoulli Family

The Bernoulli family produced eight notable mathematicians in the 17th and 18th centuries C.E.:

Jacob Bernoulli

1654 – 1705

Swiss mathematician (also known as James, Jacques or Jakob) best known for his work on probability theory and development of the calculus.

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

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

1667 – 1738

Swiss mathematician (also known as Jean or John) 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

1687 – 1759

Swiss mathematician (also known as Nicolas Bernoulli) 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.

Nephew of Jacob Bernoulli and Johann Bernoulli.
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Nicolaus II Bernoulli

1695 – 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

1700 – 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

1710 – 1790

Swiss mathematician (also known as Jean) 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

1744 – 1807

Swiss mathematician (also known as Jean) 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

1759 – 1789

Swiss mathematician (also known as Jacob) who worked in geometry and mathematical physics.

Son of Johann II Bernoulli and the younger brother of Johann III Bernoulli.
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See also

• Eric Temple Bell: Men of Mathematics (1937): Chapter $\text{VIII}$
• George F. Simmons: Differential Equations (1972): $\S 6$
• George F. Simmons: Calculus Gems (1992): Chapter $\text{A}.20$