Jakob Bernoulli
1645-1705
The first member of his distinguished family to attain international notoriety, Jakob Bernoulli contributed greatly to mathematicians' understanding of calculus and probability theory. He maintained a correspondence with Gottfried Wilhelm von Leibniz (1646-1716), and was one of the first scholars to fully grasp the latter's "infinitesimal calculus," as that branch of mathematics was then called.
The Bernoullis came from Holland, which at the time was controlled by Spain, and fled Spanish oppression, winding up in the Swiss town of Basel. Against his father's wishes, Jakob studied mathematics and astronomy, but it was in theology that he earned his degree in 1676, at age 31. He then went to work as a tutor in France, where he became acquainted with the writings of René Descartes (1596-1650), and in 1681 traveled to Holland and England, where he met physicist Robert Boyle (1627-1691).
Upon his return to Basel in 1682, Bernoulli established a school for science and mathematics, and published a number of articles in Europe's two leading scientific journals, Journal des sçavans and Acta eruditorum. In a 1684 article, he showed his grasp of calculus at a time when the discipline was new, and in subsequent pieces expanded on the base of understanding he had developed. It was Bernoulli who in 1690 coined the term "integral calculus" to describe the branch concerned with determining a function where a derivative is known.
Jakob Bernoulli. (Corbis-Bettman. Reproduced with permission.)Bernoulli took a position as professor of mathematics at the University of Basel, where he would spend the remainder of his career, in 1687. Two years later, he published his famous Bernoulli inequality, a theorem already derived—unbeknownst to Bernoulli—by Isaac Barrow (1630-1677) in the latter's Lectiones geometricae. He also solved a problem of long standing concerning a catenary, a shape that results when a flexible, nonelastic cable is suspended between two fixed points. Mathematicians had traditionally maintained that a catenary is a parabola, but Bernoulli showed that it was not.
Another shape that intrigued Bernoulli was the brachistochrone, a curve of quickest descent between two points A and B, where B does not lie directly beneath A. The latter problem received the attention of both Leibniz and Bernoulli's younger brother Johann (1667-1748). So intense was the rivalry between the two brothers that Johann claimed Jakob's brachistochrone solution as his own. This set a pattern for intrafamily competition, much of it centering around Johann, that would continue into the next generation, locking the latter in a struggle with his son Daniel (1700-1782), most famous member of the clan.
As for Jakob and the shapes that interested him, one of the foremost was the logarithmic spiral,the shape made by the cross-section of a chambered nautilus. Among its most interesting properties is self-similarity: any section, if properly scaled, is congruent to other parts of the curve. When he died, having never married or fathered children, he had this spiral engraved on his headstone, along with the motto Eadem mutato resurgo (Though changed, I arise again the same.) His Ars conjectandi (The Art of Conjecture), published posthumously in 1713, is considered one of the foundational texts on probability.
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