CALCULUS Understanding Its Concepts and Methods

Johann Bernoulli
(1667--1748)** **--- Historical sketch

In Fermat's Historical sketch, you met a lawyer who was also a famous mathematician. In this one, you meet a medical doctor who was also a mathematician and who, like Fermat, has been cited by many as one of the major founders of calculus, along with Newton and Leibniz. Johann Bernoulli earned a doctorate in mathematics (under his brother Jacob), while Fermat was an amateur. Each was a consummate scholar in mathematics and as well as in a great many other fields.

The Bernoulli family was surely the most prolific clan of mathematicians of recorded time. Here is the part of the family tree for three successive generations that contain mathematicians beginning with Jacob. Mathematicians are in bold type, all of whom made significant contributions to the field: sons, grandsons, and great grandsons of Nicolaus (1623--1708) and Margaretha.

Many people use the example of the Bernoulli family to argue that mathematical talent is inherited. But is it then also true that mathematicians inherit shorter lifespans, since the average lifespan of the mathematicians in this family tree was but 61.25 years, while the average lifespan of the nonmathematicians was 68.5 years? The truth is that there seems to be no solid evidence either way concerning the inheritability of mathematical talent.

But back to Johann Bernoulli. He was born in Basel, Switzerland in August of 1667, the tenth child of Nicolaus and Margaretha, who had fled Belgium to avoid persecution during the Religious Wars of Europe at the time (they were Lutherans in a Catholic society). Johann's father was in the spice business, and his parents tried to persuade him into a business career. But he defied their urging and studied both medicine and mathematics at the University of Basel, where his brother Jacob was a mathematics professor. He graduated in medicine and became an MD in 1690. Then he studied mathematics under Jacob and wrote his doctoral thesis on the mathematics of muscle movement, obtaining his doctorate in 1694. By the way, Jacob had studied under Gottfried Leibniz for his doctorate, making Johann a mathematical grandson of Leibniz. Johann then taught at the University of Groningen in the Netherlands, teaching there until 1705 and taking his brother's position after the latter's death.

With his huge mental data base, Johann Bernoulli was able to penetrate many
fields and aspects of mathematics, proving many deep theorems, and he is
reputed to have been a great teacher. (In fact, it was his classroom material
was that was used---with his somewhat questionable consent---by
de l'Hôpital to write the first known
calculus textbook, which contained Johann's quotient of derivatives method for
evaluating the indeterminate forms
and
and hence became called l'Hôpital's
rule). As for mathematics itself, he is known for advances in the calculus
of exponential functions, solving the "brachystochrone
problem"** (**determining the path of fastest descent of a
weighted particle between two points in a gravitational field), and numerous
other efforts. With his brother Jacob, he worked on the mathematics of
infinite series. He also contributed greatly to the mathematics of shipboard
navigation and to geodesics.

As for Johann's lasting influence on the world of mathematics, one need only look to the Mathematics Genealogy Project at http://www.genealogy.ams.org/html/search.phtml to find that he had only one doctoral student---the esteemed Leonhard Euler---but 32,926 mathematics doctoral descendents (students, students of students, students of students of students, etc.) as of the time this is written, to say nothing of his biological sons and grandsons who became mathematicians.

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Bernoulli differential equation

Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.