Although it is likely that many students of calculus are familiar with the idea of ​​L'Hôpital's rule, which concerns the calculation of limits that initially result in indefinite forms such as zero over zero or infinity over infinity taking the derivative of both the numerator and denominator as many times as necessary to calculate a definite limit, most are not at all familiar with the seventeenth century mathematical thinkers who gave rise to this idea . Born in the year 1661, Guillaume Francois Antoine Marquis de L'Hôpital grew up in a military family, as his father Anne-Alexandre de L'Hôpital served in the French army as a lieutenant general of the king's army and his mother Elisabeth Gobelin was the daughter of the steward of the king's army. Although this origin story had its roots in the battlefield, L'Hôpital initially demonstrated a level of aptitude in mathematical studies when he solved one of Pascal's problems dealing with cycloids within a few days. Although L'Hôpital obviously demonstrated both the drive and ability to act as a competent mathematician in the nascent field of calculus, he initially enlisted in the French army, rising through the ranks to lead a cavalry regiment as their commander. captain; yet he also spent the nights in his tent, toiling away on mathematics books while L'Hôpital dedicated his free time and passions to the self-taught study of geometry. Tired of military life and yearning more and more for the attraction he felt for his true vocation, L'Hôpital soon left the army, claiming that his severe shortsightedness prevented him from serving in his position with the necessary effectiveness, but reports on The actuality of this disorder is different. Whatever the case, L'Hôpital soon turned his attention to the growing field of infinitesimal calculus. Say no to plagiarism. Get a tailor-made essay on "Why Violent Video Games Shouldn't Be Banned"? Get an Original Essay As an aristocrat in Paris, L'Hôpital joined many organizations and intellectual circles that were dedicated to devoting their time and energy to discovering how much they could learn about the world around them through science, mathematics, and other curious activities. It was within one of these groups that L'Hôpital initially met Johann Bernoulli, one of the four world leaders in the growing subject of differentiable calculus during the closing years of the 17th century. At the time, Isaac Newton, Gottfried Wilhelm Leibniz, and the Bernoulli brothers Jacob and Johann were considered the four main influential thinkers and leaders in the budding study of differentiable calculus. L'Hôpital, seeing the potential for profit from his interactions with Bernoulli, encouraged him to speak and lecture both in the public forum of these intellectual groups, i.e. in places such as the French Academy of Sciences, of which L'Hôpital was vice-president. president twice, but also as the ancestral home of the L'Hôpital family. It was within these walls that Bernoulli agreed to privately tutor the novice but skilled French mathematician, an arrangement that earned Bernoulli approximately three hundred francs annually for the duration of the interaction but cost him exclusive rights to his mathematical research and discoveries; as one can imagine, this agreement would have fostered subsequent resentment and unrest. In this way, the growing exchange of information between L'Hôpital and other mathematicians and pioneers of the field of infinitesimal calculus, especially Johann Bernoulli, allowed him to rise to prominence in the late 1600s. In the year 1694, L'Hôpital published that which is widely considered the first textbook on the subject.