![]() This showed that 0 ÷ 0 does not equal zero, does not equal 1, does not equal infinity, and is not even undefined, but is “indeterminate” (meaning it could equal any number). Johann received a taste of his own medicine, though, when his student Guillaume de l’Hôpital published a book in his own name consisting almost entirely of Johann’s lectures, including his now famous rule about 0 ÷ 0 (a problem which had dogged mathematicians since Brahmagupta‘s initial work on the rules for dealing with zero back in the 7th Century). However, Johann merely shifted his jealousy toward his own talented son, Daniel (at one point, Johann published a book based on Daniel’s work, even changing the date to make it look as though his book had been published before his son’s). After Jacob’s early death from tuberculosis, Johann took over his brother’s position, one of his young students being the great Swiss mathematician Leonhard Euler. ![]() Johann in particular was jealous of the elder Jacob’s position as professor at Basel University, and the two often attempted to outdo each other. ![]() The Bernoulli family was a prosperous family of traders and scholars from the free city of Basel in Switzerland, which at that time was the great commercial hub of central Europe.The brothers, Jacob and Johann Bernoulli, however, flouted their father’s wishes for them to take over the family spice business or to enter respectable professions like medicine or the ministry, and began studying mathematics together.Īfter Johann graduated from Basel University, the two developed a rather jealous and competitive relationship. Unusually in the history of mathematics, a single family, the Bernoulli’s, produced half a dozen outstanding mathematicians over a couple of generations at the end of the 17th and start of the 18th Century.
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