THE BERNOULLI FAMILY
One of the most distinguished families in the history of mathematics and science is the Bernoulli family of Switzerland, which from the late secenteenth century on, producced an unusual number of capable mathematicians and scientists. The family record starts with the two brothers, Jakob Bernoulli(1654-1705) and Johann Bernoulli (1667-1748), some of whose mathematical accomplishments have already been mentioned in this
book. These two men gave up
earlier vocational interests and became mathematicians when Leibniz' papers
began to appear in the Acta eruditorum.
They were among the first mathematicians
to realize the surprising power of the calculcus and to apply the tool to a
great diversity of problems. From 1687 until his death, Jakob occupied the
mathematics chair at Basel University. Johann, in 1697, became a professor at
Groningen University, and then, on Jakob's death in 1705, succeeded his
brother in the chair at Basel University, to remain there for the rest of his life.
The two brothers, often bitter rivals, maintained an almost constant exchange
of ideas with Leibniz and with each other.
Johann Bernoulli was an even more prolific contributor to mathematics
than was his brother Jakob, Though he was a jealous and cantankerous man, he
was one of the most successful teachers of his time. He greatly enriched the
cajculus and was very influential in making the power of the new subject
apprecianted in contincntal Europe. As we have seen, if was
his material that the Marquis de I;Hospital (1661-1704), under a curious
agreement with Johann, assembled in 1696 into the first calculus textbook.
In this way, the familiar metgod of evaluationg the indeterminate form 0/0 became
incorrectly known in later calculus texts as I'Hospital's rule.
Johann Bernoulli had three sons, Nicolaus (1695-1726), Daniel(1700-
1782), and Johann II (1710-1790), all of whom won renown as eighteenthcentury
mathematicians and scientists. Nicolaus, who showed great promise in
the field of mathematics, was called to the St.Petersburg Academy, where he
unfortunately died by drowining, only eight months later. He wrote on curves,
differential equations, and probability. A problem in probability, which he proposed
from St. Peresburg, later became known as the Petersburg paradox. The
problem is:If A receives a penny when a head appears on the first toss of a
coin, two pennies if a head does not appear until second toss, four pennies if
a head does not appear until the third toss, and so on, what is A's expectation?
Mathematical theory shows that A's expectation is infinite, which seems a
paradoxical result. The problem was incestigated by Nicolaus' brother Daniel,
who succeeded Nicolaus at St. Petersburg. Daniel returned to Basel seven
years later. He was the most famous of Johann's three sons, and devoted most
of his energies to probability, astronmy, physics and hydrodynamics. In
probability he debised the concept of moral expectation, and in his Hydrodynamica,
of 1738, appears the principle of hydrodynamics that bears his name in all present-day
elementary physics texts.