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Johann Bernoulli is one of several noteworthy mathematicians from the
same family. He was influenced tremendously by his brother Jacob, who
was twelve years older than Johann was. He originally toyed with the
idea of going into medicine, writing a dissertation on fermentation
and effervescence. It is not known how he decided to focus on mathematics
rather than medicine, but he was probably influenced by his brother's
math successes. Johann's early significant work was in the expansion
of differential calculus topics. In fact, Johann developed what is now
known as l'Hopital's rule, used to determine the value of the limit
of what is called an indeterminate form. L'Hopital had published a book
on differential calculus that apparently simply rewrote a set of lecture
notes that Bernoulli had developed. When Bernoulli protested that his
work had been plagiarized, l'Hopital offered Bernoulli a significant
cash payment, on the condition that Johann would not publicize the information.
Bernoulli's sons, mathematicians in their own right, knew of this arrangement,
and spoke of it often after the death of their father. Many dismissed
their claims, but in the 1920's a copy of Johann's original notes were
discovered, containing the rule now attributed to l'Hopital. The notes
preceded the publishing of l'Hopital's book by two years, and the Bernoulli
family's claims were vindicated. Bernoulli also worked in applied physics
and mechanics. His tombstone bears the inscription "The Archimedes of
His Age".
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