Johann Bernoulli (27 July 1667 – 1 January 1748) was a Swiss mathematician who studied reflection and refraction of light, orthogonal trajectories of families of curves, quadrature of areas by series and the brachystochrone. 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 de l'Hôpital and they engaged in deep mathematical conversations. Contrary to what is commonly said these days, de l'Hôpital 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. De l'Hôpital 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. Bernoulli received generous payment from de l'Hôpital for these lessons. After Bernoulli returned to Basel he still continued his calculus lessons by correspondence, and this did not come cheap for de l'Hôpital who paid Bernoulli half a professor's salary for the instruction. However it did assure de l'Hôpital 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 him. As one would expect, it upset Johann Bernoulli greatly that this work did not acknowledge the fact that it was based on his lectures. The well known de l'Hôpital's rule is contained in this calculus book and it is therefore a result of Johann Bernoulli.