JOHANN(I) BERNOULLI
BORN: July 27, 1667 in Basel, Switzerland
DIED: January 1, 1748, in Basel, Switzerland
BORN: July 27, 1667 in Basel, Switzerland
DIED: January 1, 1748, in Basel, Switzerland
Johann(I) was the son of Nicolaus Bernoulli, younger brother of Jakob(I) and Nicolaus(I) and father to 3 sons, of whom the most notable one is Daniel(I). His other two sons were Nicolaus(I) and Johann(II).
Johann's calling in life, as proposed by his father, Nicolaus, was to become a merchant and take care of the family's trading interests. However Johann avoided this by studying medicine and becoming a physician. Although this wasn't what his father had in mind, it kept Johann away from mathematics.
It appeared that his father's choice of careers for him had permanently dissuaded the young Johann from becoming mathematically minded, but after writing his doctoral thesis in 1690, he became so heavily involved in studying the calculus that he did so until his death in 1748.
It was Johann's older brother Jakob who tutored him in mathematics in the beginning.
It was considered that Johann was a jealous man who not only didn't get along with his brother, but it is said he was responsible for his son Daniel leaving home for winning a prize for which Johann had competed as well.
There was a bitter resentment between the two brothers, but they still chose to share ideas and work together. They also worked with Leibniz and between the three of them came up with the contents of many of our basic calculus textbooks we use today.
Johann is credited with being the first person to use the sqrt(-1) term
in any practical way. He achieved this by using it when intergrating
rational functions by transforming compound differentials into simple
ones and reciprocally. He even transformed the imaginary simple ones
into real compound differentials.
An example of this is given by Fauvel and Gray,(1987):
Transform the differential a.dz:(bb-zz) into a logarithmic differential
a.dt:2bt and reciprocally.
Set z =(t-1)b:(t+1), and you will have a.dz:(zz-zz) = a.dt:2bt. Reciprocally
take t = (+z+b):(-z+b) and you will have a.dt:2bt = a.dz:(bb-zz).
Corollary: One transforms the differential a.dz:(bb+zz) in the same way into -a.dt:2bt.sqrt(-1), an imaginary logarithmic differential, and reciprocally.
In 1691, Johann was introduced to the Marquis de l'Hopital, who after careful scrutiny and a test, as described by Fauvel and Gray (1987). The test given to Johann involved solving a problem the way l'Hopital knew how to do it, and then Johann showed how he did it and in doing so earned the respect of l'Hopital who proceeded to ask Johann if he would visit the Marquis to give him lectures on the new integral calculus and the differential calculus of which he had heard very little about. l'Hopital had heard little about the calculus due to the war going on in Europe at the time, which slowed the transmission of information dramatically.
Over the next 6 months, Johann did give his lectures to l'Hopital. While tutoring l'Hopital, Johann signed a pact saying that he would send all of his discoveries to l'Hopital to do with as he wished, in return for a regular salary.
This pact resulted in one of Johann's biggest contributions to the calculus being known as l'Hopital's rule on indeterminate forms. Johann had found that if f(x) and g(x) are differentiable functions at x = a such that f(a) = g(a) = 0 and the limit (x->a) f'(x):g'(x) exists then, lim(x->a). f(x):g(x) = lim(x->a). f'(x):g'(x).
So although Johann "discovered" this relationship, it was l'Hopital who got the credit for it. l'Hopital had published Johann's lectures as he understood them some 50 years before Johann did himself. This may have had something to do with the fact that Johann may not have wished to publish anything on the calculus before he had completed his work, giving some indication as to the complexity of the calculus.
In his lifetime, Johann had also studied the following topics:
The brachistochrone is the curve of quickest descent of a weighted particle, and along with the brachistochrone problem, Johann also studied the tautochrone problem. This is the curve on which a weighted particle will always arrive at a fixed point, lower than the initial position, in the same time, independent of its initial position. The answer to both problems is the cycloid, and this principle was used in the construction of clocks. However this practice is now obselete as there was too much friction involved and the clocks kept losing time.
Johann's professional career included being appointed to a chair of mathematics in Groningen, the Netherlands, in 1695, but after the death of his brother, Jakob, he returned to Basel to take over the position Jakob had held as professor of mathematics at the university there. Johann held this position until he died at the age of 81 in 1748 in Basel, Switzerland.
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