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Jakob Bernoulli, known as one of the Bernoulli brothers, a mathematician, and a Swiss probabilist, was born in the Netherlands in 1583 to Johann Bernoulli, a mathematics professor at the University of Gröningen.  He was the first of the Bernoulli brothers to actually find international fame in the world of mathematics.

     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. 52).  

     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.  

Additional Links:
MacTutor - J. Bernoulli
Malffati Problem and Jacob Bernoulli by Antreas P. Hatzipolakis
The Bernoullis- Germantown Academy Mathematical Biographies
Mathematicians of the Seventeenth and Eighteenth Centuries - J. Bernoulli

Activity #3:

Law of Large Numbers Misconception, so link to quiz? Matt

Picture reproduced from MacTutor History of Mathematics archive with permission.