History of the Logarithm of Negative Numbers

Not too long ago, I did a blog post on how matlab and python have different responses to logarithms of negative numbers.

It turns out that the history of the logarithm of negative numbers is truly fascinating, and had Leibnitz, Bernoulli, Euler, and the other greats embroiled. Take a look at this article (pdf) by Deepak Bal.

Here is the abstract:

In 1712, Gottfried Leibniz and John Bernoulli I engaged in a friendly correspondence concerning the logarithms of negative numbers. The publication of this correspondence in 1745 sparked an interest in the mathematical community on the topic. In this paper I will discuss the evolution of the logarithmic concept in the time leading up to their discussion. I will then give a synopsis of the correspondence followed by a description of a paper by Leonhard Euler in which he addresses the issue.