Having more than one mathematician in a family is not unheard of. There have been many father-son and father-daughter duos in the history of mathematics, e.g. Theon and Hypatia, Farcas Bolyai(1775-1856) and Janos Bolyai(1802-1860), George David Birkhoff(1884-1944) and Garrent Birkhoff, Emil and Michael Artin, Elie and Henri Cartan, etc. The Riccati family in Italy managed to produce three mathematicians, but the their contributions to mathematics do not compare to that of all eight of the Bernoulli mathematicians.
The first generation of Bernoulli mathematicians include brothers Jacob I(James, Jacques) (1654-1705), Nicolaus (1662-1716), and Johann I(John, Jean) (1667-1748), second generation are brothers Daniel I (1700-1782), Johann II(1710-1790), and their cousin Nicolaus II (1687-1759), and the third generation are brothers Johann III(1746-1807) and Jacob II(1759-1789). It would be exhausting to discuss the accomplishments of all the Bernoulli mathematicians, so our focus will be on the brothers Jacob I and Johann I, who contributed a substantial amount to the fields of mathematics we know today as elementary calculus and the theory of probability.
Before the Bernoulli family was known for its mathematicians, the father of mathematical dynasty Nicolas Bernoulli(1623-1708) was known for being a successful spice trader and businessman. His family was originally from Holland, but they left Antwerp to avoid religious persecution. At the time, King Philip of Spain began enforcing the Roman Catholic beliefs in their country, but the Bernoulli's were Calvinist Protestants so they migrated to Basel, Switzerland in 1583 and settled on the bank of the Rhine. Basel was one of the main trade routes at the time, a University town since 1460, and a center for early printing and Renaissance scholars. Nicolas married into one of the town's oldest families and established himself there a prosperous merchant(Burton, 473).
The first mathematician of the Bernoulli family, Jacob I was born in 1654. As he grew, his parents insisted he study philosophy and theology, which Jacob always resented. He received a theology degree in 1676, and then moved to Geneva where he began working as a tutor(Bui, Online). Jacob eventually made his way to France where he studied with some of Rene Descartes' disciples. In 1681, he traveled to the Netherlands, and then to England where he met Robert Hook(1635-1703) and Robert Boyle(1627-1691)(Bui, Online). Of course, as a result of these travels he was able to correspond with mathematicians for many years.
In 1683, Jacob returned to Switzerland to teach mechanics at the University of Basel. He was offered an appointment to the Church because of his background in theology, but he rejected the offer because he enjoyed teaching mathematics and theoretical physics(Bui, Online). Between 1682 and 1704, Jacob published five treatises on infinite series. But in 1690, his solution to the isochrone problem was published in the Acta...