[9] After graduating from Basel University, Johann Bernoulli moved to teach differential equations.

Later, in 1694, he married Dorothea Falkner, the daughter of an alderman of Basel, and soon after accepted a position as the professor of mathematics at the University of Groningen.

At the request of his father-in-law, Bernoulli began the voyage back to his home town of Basel in 1705.

[10] In 1724, Johann Bernoulli entered a competition sponsored by the French Académie Royale des Sciences, which posed the question: In defending a view previously espoused by Leibniz, he found himself postulating an infinite external force required to make the body elastic by overcoming the infinite internal force making the body hard.

Entering the challenge, Johann proposed the cycloid, the path of a point on a moving wheel, also pointing out the relation this curve bears to the path taken by a ray of light passing through layers of varied density.

L'Hôpital authored the first textbook on infinitesimal calculus, Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes in 1696, which mainly consisted of the work of Bernoulli, including what is now known as l'Hôpital's rule.

[14][15][16] Subsequently, in letters to Leibniz, Varignon and others, Bernoulli complained that he had not received enough credit for his contributions, in spite of the preface of his book: I recognize I owe much to the insights of the Messrs. Bernoulli, especially to those of the younger (John), currently a professor in Groningen.