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I. Introduction
The Bernoulli family produced many leading politicians, jurists, business men, scientists, and mathematicians. Leon Bernoulli (died 1570), the patriarch of the family, emigrated from Antwerp in Flanders to Basel, Switzerland in the 16th century in order to escape Spain's persecution of Protestants. The family tree becomes confusing very quickly after Leon because there were so many prominent members spanning several generations, and many had Nicholas, James, or John as their given names. Adding to the confusion, James Bernoulli might be referred to as Jakob or Jacques and John Bernoulli might be called Johann or Jean. Some authors have placed Roman numerals after Bernoulli given names, as done with kings and popes, in not entirely successful attempts to disentangle a maze of similar names across generations. The potential for confusion may be viewed as a testament to the family's large volume of outstanding professional accomplishments.
Nicholas (1623-1708), the first prominent Bernoulli mathematician and the great grandson of Leon Bernoulli, provides the historical starting point. He had three sons: James (1654-1705), Nicholas (1662-1716), and John (1667-1748). James made many fundamental contributions to the development of differential equations, calculus of variations, and, together with Gottfried Leibniz (1646-1716), gave rules for differentiation and integration in calculus. James also produced the very first limit theorem in probability theory, later dubbed the law of large numbers.1 He was professor of mathematics at the University of Basel and an outstanding teacher who trained many students including his younger brother John and nephew Nicholas (1683-1759), the son of his brother Nicholas. Bitter professional disputes eventually erupted between brothers James and John. Perhaps John initiated the family feud; but, once started, both men participated with gusto. John made fundamental contributions to the calculus of variations, calculus of exponential functions, and taught Guillaume de l'Hôpital (1661-1704) calculus that resulted in the first book on the subject and what has became known as l'Hôpital' s Rule.2 John, who wanted his sons to pursue non-mathematical careers, begrudgingly taught mathematics to his sons Daniel and Nicholas. Both sons secured appointments in St. Petersburg, but Nicholas died soon thereafter. Although Daniel was unhappy in Russia, he stayed there from 1725-1733 and was very productive, at least in part, because of his...