Because there were several men from the Bernoulli family who found success in the fields of math and science, it can be easy to get one confused with another, and to forget exactly who did what and when.
The first generations of the Bernoulli family tree - those which founded the family, though were not themselves prominent in mathematical history - begin with Leon Bernoulli, who first settled the family in Basil, Switzerland, and Nicolaus Bernoulli (the first of four Bernoulli's who would share this name), who became the progenator of the famous dynasty.
The First Generation of Mathematicians
Nicolaus Bernoulli (1623-1708), became the father of three sons, Jakob (1654-1705), Nicolaus (1662-1716) and Johann (1667-1748). Of these three sons, Jakob and Johann would become the first in the family to gain cultural prominence, while Nicolaus (the second) would not gain fame himself, though his son would.
These two first Bernoulli mathematicians, Jakob and Johann, both achieved great things in mathematics. Jakob, through correspondence with Gottfried Leibnitz, who had invented the mathematics of calculus independent of Newton toward the end of the 17th century, became one of the first to master this new form of mathematics and wrote an important work on the subject. In addition, Jakob became a prominent number theorist, pondering the laws of large numbers
Johann, on the other hand, is probably most famous today as having been the teacher of one of history's greatest mathematicians, Leonard Euler. Like his brother, Johann became familiar with the calculus of Leibnitz, and became an important voice in opposing Newton's claim to have been the rightful inventor of this new mathematics. Later in life, Johann and Jakob became entwined in a jealous professional rivalry which saw them competing to solve difficult mathematical problems.
The Sons of Johann Bernoulli
While Jakob Bernoulli's branch of the family mathematical tree ended with himself, Johann saw the legacy survive in not one or two but three sons; Nicolaus II, Daniel and Johann II.
Of the three sons of Johann, Daniel Bernoulli is surely the best remembered, as it is he for which the Bernoulli Principle is named, as a result of his definitive and unprecedented work in the subjects of probability and statistics, which would eventually prove to serve great purposes both in mathematics and in the practical sciences. Daniel was a close friend of his father's greatest student (apart from himself), Leonard Euler, and even joined him in a teaching post in St. Petersberg for a time in the 1720's.
Daniel Bernoulli's greatest work is surely Hydrodynamica, which blurred the line between mathematics and physics.
The other sons of Johann, Nicolaus II and Johann II both became important mathematicians as well (and Johann II would continue on to have three more mathematician sons, Johann III, Daniel II and Jakob II, himself), though their names are not as well remembered in history as their famous brother.
Also in this generation of Bernoullis was the son of Nicolaus, Nicolaus I (1687-1759), who, like his cousins and uncles, became inspired by the new calculus, corresponded with Leibnitz, and became an important teacher of differential equations and geometry in Padova, Italy
Within just this one family, eight individuals became prominent mathematicians in their day, and several of their names, Johann, Jakob and Daniel chiefly, will surely be remembered throughout history as having been some of the great revolutionary figures in the early days of calculus and statistics.
The Bernoulli family, depending on how one looks at them, must surely be either a great argument in favor of the importance of genetic inheritance, or of the importance of mathematical training early on. One way or another, within this family one finds an almost unprecedented amount of knowledge.
References:
The Bernoulli Family The Internet Encyclopedia of Science.
The Bernoulli Family. Thinkquest.
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