News from the world of maths: Mathematical moments - The mathematical Bernoullis from Basel

Brothers Jacob I (1654-1705) and Johann I (1667-1748)
Their nephew Nikolaus I (1687-1759)
Johann's sons Nikolaus II (1695-1726), Daniel (1700-1782) and Johann II (1710-1790)
And Johann II's sons Johann III (1744-1807) and Jacob II (1759-1789)

The famous mathematical family, the Bernoullis, produced an astounding eight mathematicians over three generations. The sheer number of them, and the family habit of using the same first names, required the numbering system you see above to keep track of them all. And given the family's mathematical success, you would think that each generation was actively encouraged to study the subject. But instead the mathematical members of the family often had to study mathematics and astronomy against the wishes of their parents. Indeed there were enough quarrels, backstabbing and even untimely deaths among the Bernoullis to script a soap opera.

Jacob (I) Bernoulli was the first member of the family to study maths, and taught his brother Johann (I) who had been forced to study medicine. The brothers worked on similar topics, such as calculus (Jacob was the first mathematician to use the term 'integral') and studying families of curves such as the catenary, the curve of a suspended string. However, in what would prove to be typical behaviour in the family, the brothers soon went from collaborators to rivals, publicly criticising each other's intellect and competing to solve the same mathematical problems.

Jacob and Johann taught their nephew, Nikolaus I, mathematics, and Nikolaus assisted his uncle, Jacob, in publishing his works. Nikolaus is known for posing the probability problem the "St Petersburg paradox", which describes a gambling game that no-one would reasonably play, despite a possibly infinite prize.

Nikolaus's cousin Daniel (son of Johann) provided an explanation of the St Petersburg paradox. Daniel, probably the most famous mathematician of the family, did his most important work on fluid dynamics, and gave the Bernoulli principle. However, continuing the family's bitter history, Daniel had a difficult relationship with his father Johann, who did not want him as a mathematical competitor. Johann tried to stop Daniel from studying mathematics, and even attempted to plagiarise Daniel's greatest work, "Hydrodynamica".

Johann I's other two sons were also mathematicians. His favourite Nikolaus II worked on the problem of trajectories, and the mathematical arguments behind Newton and Leibniz's dispute over who had invented calculus. Johann II worked in mathematical physics.

Johann II also had two mathematical sons. Johann III was a child prodigy, and was just 19 years old when he was appointed to the Berlin Academy. He produced work in astronomy and probability, but his accounts of his travels in Germany had a greater impact historically. Jacob II worked on mathematical physics at the St Petersburg Academy of Sciences, and married Euler's granddaughter. Sadly he drowned in the Neva River when he was only 29 years old.

The Bernoulli family, despite its infighting and bitterness, dominated mathematics in the 17th and 18th centuries. Together with their contemporaries Newton, Leibniz, Euler and Lagrange, they laid many of the foundations of mathematics and physics that we still use today.

"There is no philosophy which is not founded upon knowledge of the phenomena, but to get any profit from this knowledge it is absolutely necessary to be a mathematician." - Daniel Bernoulli

Read more about the Bernoulli clan in the MacTutor History of Mathematics Archive...

And about the Bernoullis, the St Petersburg Paradox and the Bernoulli principle on Plus...
The gentlemen from Basel and the Petersburg Paradox
Daniel Bernoulli and the making of the fluid equation
Understanding turbulence
Testing Bernoulli: a simple experiment

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