L’Hopital Rule – interesting history

Last week on Tumblr I got into an interesting conversation on L’Hopital Rule and I wanted to share with you some of the interesting facts I have found about it. First of all, this rule was one of my favorite during high school and also in the first year of university. If nothing else worked for the limit, we always used L’Hopital Rule, as if this was the ultimate perfect rule.

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I always thought that the person that came up with was indeed very intelligent. From this you can imagine that I was a little shocked to find out that not L’Hopital found this rule, but Johann Bernoulli. It turns up that these two have met towards the end of 1691, when Bernoulli was just 24 and new in the mathematics world. In that time, L’Hopital was already a member of an important circle at the Congregation of the Oratory which contained many leading mathematicians and scientists of Paris. It turns up that L’Hopital observed the potential of Bernoulli and wanted to learn from him. Therefor, he employed Bernoulli to give him private lessons for a short period of time.

So far so good… Now the story gets to a controversial point. Some time in March 1694, L’Hopital sends a letter to Bernoulli with an incredible proposition:

I will be happy to give you a retainer of 300 pounds, beginning with the first of January of this year. … I promise shortly to increase this retainer, which I know is very modest, as soon as my affairs are somewhat straightened out. … I am not so unreasonable as to demand in return all of your time, but I will ask you to give me at intervals some hours of your time to work on what I request and also to communicate to me your discoveries, at the same time asking you not to disclose any of them to others. I ask you even not to send here to Mr Varignon or to others any copies of the writings you have left with me; if they are published, I will not be at all pleased. Answer me regarding all this …

No copy of Bernoulli’s answer was found, but from other letters it is easy to observe that he accepted L’Hopital’s proposition. In another letter from 1695, Bernoulli writes:

You have only to let me know your definite wishes, if I am to publish nothing more in my life, for I will follow them precisely and nothing more by me will be seen.

At first glance I was quite shocked about it and felt that I was mislead and I was annoyed by the story. But if I think more about it, there is nothing wrong in this. Bernoulli accepted to be paid for his work, there is nothing wrong in that. I don’t feel 100% happy for this, but it was his choice and I am convinced that nowadays there are many scientists all over the world that discover incredible things, but we just know the company they work for. From this point of view I agree with Truesdell’s opinion about this story:

We should not judge L’Hôpital’s procedure too harshly. While perhaps financial necessity compelled Bernoulli to accept the arrangement initially, it continued after he had settled in his professorship at Groningen in 1695. L’Hôpital, being a noblemen, was accustomed to pay for the services of others, and what he did would not have been considered wrong had Bernoulli been a politician, a lawyer, perhaps even an architect. Certainly it was nothing for L’Hôpital to be proud of. Careful examination of the letters in which L’Hôpital reported his mathematical progress to Leibniz and Huygens shows that with one or two possible exceptions L’Hôpital did not lie, but rather referred to Bernoulli in a condescending tone without acknowledging any debt whatever to him and in matters of provenance wrote in such a way as to suggest without actually asserting.

Source: L’Hopital Short Biography 

What do you think about this story? Do you agree with Truesdell’s opinion or do you think we should blame L’Hopital?

Hope your enjoyed this post. Thank you for your help and support, you are the best and I appreciate everything that you do. Have a great day.  You can find me on Facebook,  Tumblr,  Google+,  Twitter   and  Instagram. I will try to post there as often as possible.

Don’t forget that maths is everywhere! Enjoy! ~LThMath

4 thoughts on “L’Hopital Rule – interesting history

Add yours

  1. This is a very interesting story and thank you for sharing it. Although it all sounds at least shady from today’s point of view, there is probably no reason to judge L’Hopital for this if he never insisted on the lie that the work done by Bernoulli was done exclusively by L’Hopital. It makes me think how interesting it would be to read all the letters they exchanged.


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