|Jakob Bernoulli (1645-1705)|
Similar to his brother Daniel, he studied mathematics and
astronomy against his father’s will, but received his degree in
theology. During the next
few years in 1676, Bernoulli continued to study principles of
mathematics, especially the works of René Descartes. Throughout
the years preceding his studies of Descartes’ works, he mastered the
ideas behind calculus and contributed to Leibniz’s work.
He is known for creating the "Bernoulli inequality" and
solving the catenary equation. He
furthered his knowledge of mathematics by studying curves.
With respect to probability,
his diligence in research helped him write a treatise called Ars conjectandi (The Art of Conjecture).
Published in 1713, this work was based on earlier probability
findings. These findings
include Girolamo Cardano’s Liber
de ludo aleae (On Casting the Die), the correspondence between Fermat and Pascal,
and Christiaan Huygens’ De
ratiociniis in ludo aleae (On Reasoning in Games of Chance).
Bernoulli’s work is a great contribution to the study of
probability. It contains an
additional treatise in which Bernoulli discusses a now famous theorem,
The Law of Large Numbers. It
states that "if a very large number of independent trials are made,
then the observed proportion of successes for an event will, with
probability close to 1, be very close to the theoretical probability of
success for that event on each individual trial." (Young, 1998, p.
Bernoulli hoped to continue practical applications of this
theorem in the fields of politics and economics.
He never achieved this due to his death in 1705.
Law of Large Numbers Misconception, so link to quiz? Matt
Picture reproduced from MacTutor History of Mathematics archive with permission.