Date: Mar 21, 2000 1:39 PM
Author: Alfred Ross
Subject: Re: [HM] L'Hopital, Pythagoras, Ptolemy and Hilbert

Johann's first publication was on the process of fermentation in
1690, certainly not a mathematical topic but in 1691 Johann went
to Geneva where he lectured on the differential calculus. From
Geneva, Johann made his way to Paris and there he met mathematicians
in Malebranche's circle, where the focus of French mathematics was
at that time. There Johann met de l'Hopital and they engaged in
deep mathematical conversations. Contrary to what is commonly said
these days, de l'Hopital was a fine mathematician, perhaps the best
mathematician in Paris at that time, although he was not quite in
the same class as Johann Bernoulli.

Now de l'Hopital was delighted to discover that Johann Bernoulli
understood the new calculus methods that Leibniz had just published
and he asked Johann to teach him these methods. This Johann agreed
to do and the lessons were taught both in Paris and also at de
l'Hopital's country house at Oucques. Bernoulli received generous
payment from de l'Hopital for these lessons, and indeed they were
worth a lot for few other people would have been able to have given
them. After Bernoulli returned to Basel he still continued his
calculus lessons by correspondence, and this did not come cheap for
de l'Hopital who paid Bernoulli half a professor's salary for the
instruction. However it did assure de l'Hopital of a place in the
history of mathematics since he published the first calculus book
Analyse des infiniment petits pour l'intelligence des lignes courbes
(1696) which was based on the lessons that Johann Bernoulli sent to

As one would expect, it upset Johann Bernoulli greatly that this work
did not acknowledge the fact that it was based on his lectures.