# The Bernoulli Family – Quantum Tunnel Podcast

The Bernoulli Family

The Bernoullis were truly a prolific scientific family, in three generations this remarkable Swiss family produced eight mathematicians – three of them outstanding – who in turn had a swarm of descendants who distinguished themselves in many fields.
Jakob Bernoulli (1654-1705) studied theology at the insistence of his father, but abandoned it as soon as possible for science. He taught himself the calculus and became professor of mathematics at Basel. He wrote on infinite series, studied many special curves, invented polar coordinates and introduced the Bernoulli numbers that appear in the power series expansion of the tangent function. In his book Ars Conjectandi he formulated the basic principle in the theory of probability known as Bernoulli’s theorem: if the probability of a certain event is p, and we run n independent trials out of which we get k successes, then the ratio of the successes to the trials k/n tends to the probability p as the number of trials n tends to infinity.
Jakob’s younger brother Johann Bernoulli also made a false start in his career, by studying medicine but he also became fascinated by calculus and applied it to many problems in geometry, differential equations, and mechanics. In 1695 he was appointed professor of mathematics and physics at Groningen in the Netherlands, and on Jakob’s death he succeeded his brother in the professorship in Basel.

The Bernoulli brothers sometimes worked on the same problems, which was unfortunate in view of their jealous and touchy dispositions. On occasion the friction between them flared up into a bitter and abusive fight, as it did over the brachistochrone problem. In 1696 Johann proposed the problem as a challenge to the mathematicians of Europe. It aroused great interest , and was solved by Newton and Leibnitz as well as by the two Bernoullis. Johann’s solution turned out to be more elegant, while Jakob’s one although rather clumsy and labourious was more general.

Johann’s son was Daniel Bernoulli (1700-1782), who also studied medicine like his father and who also gave way to his talent and became a professor of mathematics at St Petersburg. In 1733 he returned to Basel and was successively professor of botany, anatomy and physics. In his famous book Hydrodynamica he discussed fluid mechanics and gave the earliest treatment of he kinetic theory of gases. He is considered by many to have been the first genuine mathematical physicist.

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