## The History of Mathematics## Mathematics After the Middle Ages |

## Why was the Bernoulli family important to mathematics? |

The Bernoulli (also seen as Bernouilli) family of the 17th and 18th centuries is synonymous with mathematics and science. One of the developers of ordinary calculus, calculus of variations, and the first to use the word integral was Jacob Bernoulli (1654-1705; also known as Jakob, Jacques, or James). He also wrote about the theory of probability, is often credited for developing the field of statistics, and discovered a series of numbers that bear his name: the coefficients of the exponential series expansion of x/(1 - *e*^{-x}).

Not to be outdone, his brother Johann (1667-1748; also known as Jean or John) contributed to the field of integral and exponential calculus, was the founder of calculus of variations, and worked on geodesics, complex numbers, and trigonometry. His son was not far behind: Daniel Bernoulli (1700–1782) was considered the first mathematical physicist, publishing *Hydrodynamica* in 1738, which included his now famous principle named in his honor (Bernoulli’s principle); and he brought out two ideas that were ahead of his time by many years: the law of conservation of energy and the kinetic-molecular theory of gases.

The Bernoulli legacy did not end there, with family members continuing to make great mathematical and scientific contributions. There were two Nicolaus Bernoullis; one, the brother of Jacob and Johann (1662–1716), was professor of mathematics at St. Petersburg, Russia’s Academy of Sciences; the other, the son of Johann and brother of Daniel (1695–1726), was also a mathematician. Another Johann Bernoulli (17101790) was another son of Johann (and brother of Daniel), who succeeded his father in the chair of mathematics at Basel, Switzerland, and also contributed to physics. The younger Johann also had a son named Johann (1746–1807), who was astronomer royal at Berlin and also studied mathematics and geography. Finally, Jacob Bernoulli (1759–1789), yet another son of the younger Johann, succeeded his uncle Daniel in teaching mathematics and physics at St. Petersburg, but met an untimely early death by drowning.