**(August 6, 1667 – January 1, 1748)**

Johann Bernoulli is Daniel’s and Nikolaus’ father, as well as Jacob’s brother; all of whom were acclaimed mathematicians from the renowned Bernoulli family. He was tutored by his elder brother Jacob, and also learned from Gottfried Leibniz. On his part, Johann nurtured the greatest of all mathematicians, Leonhard Euler. It was him who discovered Euler’s profound mathematical abilities (as a lad), and persuaded Paul Euler (the boy’s father who was a local pastor and a family friend to the Bernoullis) to let Leonhard study mathematics in lieu of theology. A grateful Leonhard grew-up to adore his mentor, and maintained lifelong friendships with his sons. Like his brother Jacob, Johann was revered across Europe for his brilliance. He founded the Calculus of Variations which Joseph-Louis Lagrange later revolutionized. He also made lasting contributions to Differential Geometry, Optics, Oscillation and Elasticity. Indeed, most of the works which made Guillaume de l’Hôpital famous are actually Johann Bernoulli’s. The underlying secret arrangement could be summarized thus: L’Hôpital (who was a wealthy aristocrat) pledged steady income to Bernoulli, provided that Bernoulli correspond with him in details regarding all his new math discoveries which must not be shown to others, and which he (L’Hôpital) may use as he prefers. Agreed, they sealed the deal. But as L’Hôpital gained fame by publishing those works, a jealous Bernoulli sulked. L’Hôpital’s untimely death in 1704 allowed Bernoulli to expose their secret deal. Several letters, manuscripts and other evidence which were discovered in 1921 (in Basel, Switzerland) supported Bernoulli’s claims.

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Thanks for this critique. It stirred my math memories.

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My opinion is that a thin line separates Jacob and Johann Bernoulli’s maths strength.

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L’Hôpital’s rule should be changed to Bernoulli’s rule.