The Bernoulli family was an extraordinary Swiss family from Basle that produced eight outstanding mathematicians within three generations. Together with Isaac Newton, Gottfried Leibniz, Leonhard Euler, and Joseph Lagrange, the Bernoulli family dominated mathematics and physics in the 17th and 18th centuries, making important contributions to differential calculus, geometry, mechanics, ballistics, thermodynamics, hydrodynamics, optics, elasticity, magnetism, astronomy, and probability theory. Unfortunately, the Bernoullis were as conceited and arrogant as they were brilliant, and engaged in bitter rivalries and rows with one another.
The patriarchs of this mathematical dynasty were Jakob I (1654–1705) and his brother Johann I (1667–1748). (The Roman numerals are to tell fathers, brothers, sons and cousins apart, as the same Christian names kept being used in the family). Next came Jakob's son, Nikolaus I, and Johann's three sons, Nikolaus II, Daniel (1700–1872), and Johann II. Finally, came Johann II's mathematical offspring, Johann III and Jakob II.
Jakob I developed a passion for science and mathematics after meeting Robert Boyle during a trip to England in 1676. He largely taught himself in these subjects and went on to lecture in experimental physics at the University of Basle. He also secretly introduced his younger brother to mathematics, much against the wishes of his parents who wanted the younger brother to go into commerce. The cooperation between the two brothers soon degenerated, however, into vitriolic argument. Irked by Johann's bragging, Jakob publicly claimed that his younger brother had copied his own results. Later, having been appointed to the chair of mathematics at Basle, Jakob succeeded in blocking his brother's appointment to the same department, forcing Johann to take a teaching job at the University of Groningen instead. Johann proposed the so-called brachistrochrone problem and, along with Newton, Leibniz, l'Hospital, and Jakob, managed to solve it – but only after he first came up with a faulty proof and then tried to substitute one of Jakob's in its place! Eventually, Johann was offered a post at Basel as, of all things, the department head of Ancient Greek. But, en route to Basel, Johann learned that Jakob had died of tuberculosis. Upon his arrival he set about lobbying for the vacant position and, in less than two months, got his way. Jakob's most important work, his Ars Conjectandi (The Art of Conjecture), was published posthumously and formed the basis of probability theory.
Sadly, Johann I repeated his father's mistake and tried to force the most mathematically talented of his three sons, Daniel, into a career as a merchant, which he didn't want. When the attempt failed, Johann allowed Daniel to study medicine, in order to prevent his son from becoming a competitor. But all three sons followed their father's path and Daniel, while studying medicine, took lessons in mathematics from his older brother Nikolaus II. In 1720 he traveled to Venice in order to work as a physician but gained such a great reputation during his stay for his work in physics and mathematics that that Peter the Great of Russia offered him a chair at the Academy of Science in St. Petersburg. Daniel went, along with Nikolaus II, who was also offered a position at the Academy. However, after just eight months, Nikolaus fell ill with a fever and died. Distressed, Daniel wanted to return to Basle but Johann I didn't want his son – a potential rival – back home. Instead he sent one of his pupils, none other than the great Leonhard Euler, to St. Petersburg to keep Daniel company. A close friendship developed between the two Swiss mathematicians in exile and the six years they spent together in St. Petersburg were the most productive of Daniel's life.
When Daniel finally returned to Basle, quarrels within the family flared up again after he won the prize of the Parisian Academy of Science with a paper, produced jointly with his father, on astronomy. Upset by Daniel's success, Johann kicked him of the family house. And worse was to come. In 1738 Daniel published his magnum opus, Hydrodynamica. Johann I read the book, hurriedly wrote one of his own with the title Hydraulica, back-dated it to 1732, and claimed to be the inventor of fluid dynamics! The plagiarism was soon uncovered, and Johann was ridiculed by his colleagues but his son never recovered from the blow.