(1667 – 1748)<\/p>\r\n\r\n
The accomplishments of the Bernoulli family are legendary in the history of mathematics. Never before or since has one family produced eight extraordinarily gifted mathematicians in the span of three generations.<\/p>\r\n\r\n
The Bernoullis originated in Antwerp but fled to Switzerland in 1583, when their Protestant faith in Catholic Belgium endangered their lives. In Basel, John\u2019s great-great-grandfather established himself as a merchant. Three succeeding generations of Bernoullis tended the family business, and in the process garnered enormous wealth. That they were so successful suggests a latent mathematical talent.<\/p>\r\n\r\n
Born in Basel on August 6, 1667, John Bernoulli was among the first of his family to be recognized as a mathematical genius. John\u2019s first mathematics teacher was his equally gifted older brother, James, who was then a professor at the University of Basel. At first, John deferred to James and relations between the two were amicable; however, as John\u2019s knowledge burgeoned, so too did his desire to surpass his brother James in reputation.<\/p>\r\n\r\n
John\u2019s progress in mathematics was thus spurred by his intensely competitive nature. James, in turn, struggled to maintain his own mathematical supremacy. Eventually, all pretense of affection was abandoned and the brothers were at war; their respective mathematical discoveries were the shots they fired at one another. They shamelessly plagiarized each others work and publicly ridiculed each other\u2019s errors. John was especially unscrupulous: on one occasion he stole his brother\u2019s paper outright and attempted to submit it as his own for a prize. When the great mathematician Leibniz, a diplomat by profession, sought to intervene, James accused him of favoring John. From that time on, James allied himself with those who favored Newton\u2019s claim of priority over Leibniz in the discovery of the calculus.<\/p>\r\n\r\n
John was so relentlessly competitive that when the French Academy awarded to John\u2019s son Daniel a prize that John had expected to receive himself, John drove Daniel from his home in a jealous rage.<\/p>\r\n\r\n
An incident involving the French mathematician Guillaume F. A. L\u2019H\u00f4pital was even more infuriating. John Bernoulli had consented to tutor L\u2019H\u00f4pital in the calculus and had also agreed to sell L\u2019H\u00f4pital the rights to Bernoulli\u2019s research. Bernoulli taught L\u2019H\u00f4pital primarily through correspondence. His letters to his student explained the calculus in careful detail and kept L\u2019H\u00f4pital apprised of new theorems as they emerged. Bernoulli\u2019s collected letters were published by L\u2019H\u00f4pital in 1696 as the first calculus textbook, the Analyse des infiniment petits<\/em>. Because L\u2019H\u00f4pital had purchased Bernoulli\u2019s letters and the rights to Bernoulli\u2019s discoveries, L\u2019H\u00f4pital\u2019s name, not Bernoulli\u2019s, appeared on the title page of the text. In addition, Bernoulli\u2019s method of finding limiting value of fractions of the type 0\/0 became known as L\u2019H\u00f4pital\u2019s Rule. Bernoulli was incensed that his letters and one of his most important discoveries had been attributed to the man he had tutored. Bernoulli publicly accused L\u2019H\u00f4pital of plagiarism as soon as L\u2019H\u00f4pital was dead and therefore unable to explain the terms of their agreement.<\/p>\r\n\r\n Despite Bernoulli\u2019s failings, he was a brilliant mathematician and an exceptional teacher. Among Bernoulli\u2019s students was the spectacularly gifted and prolific mathematician, Leonhard Euler. Bernoulli is said to have inspired Euler to devote his life to mathematics; this was, arguably, Bernoulli\u2019s most significant achievement.<\/p>\r\n\r\n John and his brother James were, after Newton and Leibniz, at the forefront of the development of the calculus. The formula for the radius of curvature of a curve, the exponential calculus, and the determination of orthogonal trajectories, are among their many contributions. John was also instrumental in effecting the adoption on the Continent of Leibniz\u2019s calculus over that of Newton.<\/p>\r\n\r\n John Bernoulli died in Basel on January 1, 1748, at the age of eighty.<\/p>\r\n\r\n \r\nhttp:\/\/www-history.mcs.st-andrews.ac.uk\/Biographies\/Bernoulli_Johann.html<\/a>\r\nLinks<\/h3>\r\n
References<\/h3>\r\n
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