Bernoulli or Bernouilli , name of a family distinguished in scientific and mathematical history. The family, after leaving Antwerp, finally settled in Basel, Switzerland, where it grew in fame. Jacob, Jacques, or James Bernoulli, 1654-1705, became professor at Basel in 1687. One of the chief developers both of the ordinary calculus and of the calculus of variations , he was the first to use the word integral in solving Leibniz's problem of the isochronous curve. He wrote an important treatise on the theory of probability (1713) and discovered the series of numbers that now bear his name, i.e., the coefficients of the exponential series expansion of x /(1- e^-x ). He was succeeded at Basel by his brother, Johann, Jean, or John Bernoulli, 1667-1748, who earlier had been professor at Gröningen and who was famous for his work in the field of integral and exponential calculus and was also a founder of the calculus of variations. He also contributed to the study of geodesics, of complex numbers, and of trigonometry. His collected works were published under the title Johannis Bernoulli opera omnia. His son, Daniel Bernoulli, 1700-1782, was a mathematician, physicist, and physician and has often been called the first mathematical physicist. He received his doctorate in medicine but became professor of mathematics at the St. Petersburg Academy in 1725. He was professor of anatomy and botany at Basel from 1733, later becoming professor of natural philosophy (physics). His greatest work was his Hydrodynamica (1738), which included the principle now known as Bernoulli's principle , and anticipated the law of conservation of energy and the kinetic-molecular theory of gases developed more than 100 years later. He also made important contributions to probability theory, astronomy, and the theory of differential equations (solving a famous equation proposed by Riccati). Among the other noted members of the family are Nicolaus Bernoulli, 1662-1716, brother of Jacob and Johann, who was professor of mathematics at St. Petersburg; Nicolaus Bernoulli, 1695-1726, son of Johann and brother of Daniel, also a mathematician; Johann Bernoulli, 1710-90, another son of Johann (1667-1748) and brother of Daniel, who succeeded his father in the chair of mathematics at Basel and also contributed to physics; his son, Johann Bernoulli, 1746-1807, who was astronomer royal at Berlin and also studied mathematics and geography; and Jacob Bernoulli, 1759-89, another son of Johann (1710-90), who succeeded his uncle Daniel in mathematics and physics at St. Petersburg but met an early death by drowning.

Bernoulli Family

Swiss Mathematicians

Seventeenth and Eighteenth Centuries

The Bernoulli family was one of the world's most outstanding mathematical families. The members of the family who made the most significant contributions were two brothers, Jakob (1654–1705) and Johann (1667–1748), and Johann's son, Daniel (1700–1782).

Family History

Jakob and Johann were among the ten children of a spice merchant from Basel, Switzerland. Jakob was forced by his father to study theology but refused a church appointment when he completed his doctorate. Instead, he accepted a mathematics position at the University of Basel in 1687, a position he held for the remainder of his life.

Johann, required to study medicine, entered the University of Basel in 1683, where his brother Jakob was already a professor. The writings of Gottfried Leibniz (1646–1716), introducing the new field of calculus , had proved to be too difficult for most mathematicians to understand. Jakob, however, mastered their obscurity and taught Johann. The Bernoullis subsequently were among the first to recognize the great potential of calculus and to present numerous applications of this new mathematics, extending its usefulness and popularity.

In 1691, Johann taught calculus to the prominent French mathematician L'Hôpital (1661–1704). Subsequently L'Hôpital published the first textbook on differential calculus, based entirely on Johann's notes but without giving him proper credit. Johann received his doctorate in medicine in 1694 and became professor of mathematics at the University of Gröningen in the Netherlands.

Problems in the Family

Both brothers were making important original contributions and had risen to the top ranks of mathematicians, but they became jealous of each other. Jakob could not accept Johann, whom he had taught, as an equal, and Johann was unable to be professionally gracious. They attacked each other's work publicly. When Jakob died in 1705, Johann returned to Basel to become professor of mathematics, a position he held until his death in 1748.

Jakob Bernoulli was first to use the term "integral" in calculus. He and Johann introduced the calculus of variation. He solved the equation now known as Bernoulli's Equation and applied the methods of calculus to the problems of bridge design.

Jakob's highly significant work, Ars Conjectandi, was published in 1713, after his death. It included the first thorough treatment of probability, a discussion of Bernoulli's law of large numbers, the theory of permutations and combinations, a derivation of the exponential series using the Bernoulli numbers, and a discussion of mathematical and moral predictability.

Johann Bernoulli developed the theory of differential equations and discovered the Bernoulli series. His influential texts on integral calculus and differential calculus were published in the early 1740s. He applied the methods of calculus to numerous practical problems, including a number of aspects of navigation, optics, and kinetic energy. In addition to his influence on L'Hôpital, he taught the noted mathematician Leonhard Euler (1707–1783).

Continuing the Legacy

Johann's son Daniel was born in 1700. Forced by his father to study medicine, he received a medical degree in 1721. After publishing a discussion of

differential equations and the properties of flowing liquids in 1724, he accepted a position at the Academy of Sciences in St. Petersburg, Russia, where he taught medicine and physics. He returned to Basel in 1732 to teach anatomy and botany.

In 1738, Daniel published Hydrodynamica, a thorough treatment of the properties of flowing fluids and the relationships among them. As a result, he is regarded as the founder of the science of hydrodynamics . He also treated the behavior of gases using mathematical probability, introducing the concepts that led to the kinetic theory of gases . He developed the mathematics and physics of vibrating strings and made numerous other contributions in a variety of fields. He accepted positions at Basel in physiology in 1743 and physics in 1750. He died in 1782.

A rather extraordinary incident occurred in 1735 when Johann and Daniel were awarded prizes by the Paris Academy of Sciences for separate work on planetary orbits. Johann became enraged at having to share the recognition with his son and banned him from his house. In 1738, when Daniel published Hydrodynamica, Johann published Hydraulica, which obviously plagiarized Daniel's work, apparently out of jealousy of his son's increasing reputation.

Other members of the Bernoulli family who were significant mathematicians included Johann's other two sons, Nikolaus (1695–1726), who died soon after accepting a position at the St. Petersburg Academy, and Johann II (1710–1790), who succeeded his father as professor of mathematics at Basel; Johann's nephew, Nicolaus (1687–1759), professor of mathematics at Padua; and Johann II's son, Johann III (1744–1807), who became a professor of mathematics at the Berlin Academy at the age of 19. Other grandsons and great grandsons made lesser contributions to mathematics.

see also Calculus; Euler, Leonhard.

J. William Moncrief

Bibliography

Bell, E. T. "Nature or Nurture? The Bernoullis." In Men of Mathematics: The Lives and Achievements of the Great Mathematicians from Zeno to Poincaré. New York: Simon and Schuster, 1986.

Sensenbaugh, Roger. "The Bernoulli Family." In Great Lives from History: Renaissance to 1900 Series. Englewood Cliffs, NJ: Salem Press, 1989.