Jakob Bernoulli and Johann Bernoulli | Biography

Johann and Jakob Bernoulli, the children of a prominent Basel, Switzerland, couple, were the first in a family line of gifted mathematicians that would endure for three generations. Jakob originally trained as a theologian and was destined to pursue a career in the church, but after studying some of the writings of René Descartes, John Wallis, and Issac Barrow (1630-1677), an English mathematician and theologian, his developing interest in science and mathematics led him away from an ecclesiastical career. After a trip to England in 1676, where he met Robert Boyle and other leading scientists, Jakob decided to devote himself fully to science. In 1677 he began his scientific diary, Meditationes, and thereafter spent two years in France familiarizing himself with the scientific methods of Descartes and his followers. He became interested in the mathematical aspects of astronomy and physics, developing a theory of the origin of comets in 1681 (which turned out to be erroneous), as well as writing a book called De gravitate aetheris the following year, in which he introduced a theory of gravity that was highly respected by his contemporaries. After refusing a church appointment, Jakob eventually accepted, in 1687, an appointment as professor of mathematics at Basel, where he spent the rest of his life.

Johann Bernoulli, the younger brother of Jakob, had originally trained in medicine by order of his father. While Johann applied himself to medical studies, he secretly worked under his brother, Jakob, and became well versed in the fundamentals of mathematics. By the time Johann received his medical doctorate, he had already spent some time as a mathematics tutor in Paris, France. In 1694 he was appointed professor of mathematics at the University of Gröningen, the Netherlands. When his brother Jakob died in 1705, Johann succeeded him as professor of mathematics at Basel.

The Bernoullis made substantial contributions to mathematics. Though the brothers published their work separately, their ways of thinking and interests were so alike that sometimes it seemed that their works had been written by the same person. Among other concepts, the Bernoullis were among the first to present a full treatment of differential calculus as originally devised by Gottfried Leibniz and did much to further the ascendancy of Leibnizian calculus on the European continent. Johann formulated some basic principles of the calculus of variations using Jakob's work on the properties of the logarithmic spiral and transcendental curves. Jean also made important contributions to differential equations, exponential calculus, and complex numbers.

The Ars conjectandi, a highly innovative work on probability theory written by Jakob (but not published until years after his death), discussed what came to be known as the Bernoullian numbers and the Bernoulli theorem, and analyzed games of chance according to variations in players dexterity, expectation of profit, and other variables. Jakob was so awed at the logarithmic spiral's ability to keep reappearing under numerous mathematical transformations that he had it carved on his tombstone along with the words "I shall arise the same, though changed." The next generation of Bernoullis, in particular Johann's son Daniel Bernoulli, would continue to make achievements in mathematics and physics.