Nikolaus Bernoulli

1695-1726

Swiss Mathematician

The first and favorite son of Johann Bernoulli (1667-1748), Nikolaus Bernoulli was destined to be overshadowed by his younger brother Daniel (1700-1782). However, working in collaboration his brother Daniel, Nikolaus contributed to the formulation of the famous St. Petersburg Paradox, a question of probability.

The Bernoullis were a distinguished family of Swiss mathematicians and scientists dating back to Nikolaus's grandfather, Nikolas (1623-1708). Grandfather Nikolas had three sons—Jakob (1654-1705), Nikolaus (1662-1716), and Johann (1667-1748). Jakob, a professor of mathematics in Basel, Switzerland, died without leaving any notable offspring of his own. Nikolaus, often referred to as "Nikolaus I" to distinguish him from the two other men of that name in the family, had a son named Nikolaus (1687-1759), typically designated as "Nikolaus II". Adding to the confusion is the fact that this Nikolaus, a professor of mathematics at Padua and later of law and logic at Basel, contributed to the study of probability and infinite series—as did "Nikolaus III," eldest son of Johann.

"Nikolaus III" was born on February 6, 1695, in Basel, but later the family moved to the Netherlands, where his father Johann took a position as professor of mathematics at the University of Gröningen. Nikolaus, who always enjoyed a close relationship with his father, was five years old when Daniel—against whom the jealous father would place himself in competition throughout his later career—was born. Five years later, the family moved back to Switzerland, where Johann took over the mathematics chair vacated by his recently deceased brother Jakob.

Like his younger brother, Nikolaus proved himself an exceptional student, but unlike Daniel, Nikolaus's brilliance did not excite his father's envy. At the age of 13 Nikolaus entered the University of Basel, where he studied both mathematics and law. Seven years later, at age 20, he became a licentiate in jurisprudence.

Nikolaus also worked with his father, acting as his assistant in correspondence. He was particularly involved in writing letters to address a dispute between Isaac Newton (1642-1727) and Gottfried Leibniz (1646-1716), and exchanged letters with the English mathematician Brook Taylor (1685-1731). During this time, Nikolaus also worked on problems involving curves, differential equations, and probabilities.

In 1725, at about the time Daniel—by then emerging as the most outstanding member of the talented family—received an appointment to the St. Petersburg Academy in Russia, Nikolaus was likewise assigned to a post there. In Russia, the two brothers worked on the "St. Petersburg Paradox," which involves a coin toss game in which a player bets on the number of tosses needed before a coin turns up heads. Given that he will receive 2ⁿ dollars if the coin comes up heads on the nth toss, he is theoretically incapable of losing money.

On July 31, 1726, just eight months after arriving in St. Petersburg, Nikolaus died of what was then called a "hectic fever." Thus a promising career was cut short at the age of 31.

JUDSON KNIGHT