15/05/2019

The Bernoulli family are the royal family of mathematics.

Jacob Bernoulli – Wikimedia Commons

Reproduction of Marcelo Viana's column in Folha de S.Paulo.

Recent advances in neurology show that the human brain is a plastic structure that can be profoundly shaped. The organ at birth matters much less than how it is reorganized throughout our childhood and adolescence through learning. Therefore, no one is born "in the sciences" or "in the humanities"; this is determined by education .

That's certainly why a vocation for mathematics is much less hereditary than one might imagine. The Frenchman Jacques-Louis Lions (1928-2001) was an excellent mathematician, and his son, Pierre Louis (born in 1956), is a Fields Medal recipient. But such situations are rare.

Interestingly, I know of more cases where the vocation "passed" from father-in-law to son-in-law. There are even dynasties: Jacques Hadamard (1865-1963) was the father-in-law of Paul Lévy (1886-1971), who was the father-in-law of Fields Medalist Laurent Schwarz (1915-2002), who in turn was the father-in-law of Uriel Frisch (born in 1940). I have no reasonable explanation for this phenomenon.

But mathematics has at least one great family. Originally from Belgium, the Bernoulli family emigrated to the Swiss city of Basel, where the first generation that interests us was born. Of four brothers (and six sisters), two achieved renown in mathematics: Jacob (1654-1705) and Johann (1667-1748). Daniel (1700-1782), Johann's son, was another first-rate mathematician. His cousin Nicolaus I (1687-1759), his brothers Nicolaus II (1695-1726) and Johann II (1710-1790), and the latter's sons, Johann III (1744-1807) and Jacob II (1759-1789), also made significant contributions to mathematics.

The works of the Bernoulli brothers cover important and very diverse topics. Jacob made pioneering advances in probability theory – the law of large numbers, Bernoulli processes – in addition to discovering the constant 'e' and the so-called Bernoulli numbers.

Johann worked on differential equations (Bernoulli's equation) and the calculus of variations.

Daniel formulated Bernoulli's principle of hydrodynamics, in addition to studying the St. Petersburg paradox, an important problem in probability and economics (decision theory) formulated by Nicholas I.

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