Kylie Brous’ essay, “The Mystery of Negative and Imaginary Logarithms,” appears in the new volume of Lucerna available at https://honors.umkc.edu/get-involved/lucerna/
For more about Kylie’s work, keep reading.
What is your Lucerna project about?
My project is an explanation of eighteenth-century mathematician Leonhard Euler’s examination of Johann (Jean) Bernoulli and Gottfried Wilhelm Leibniz’s letters to one another about the existence, or thereof, of negative and imaginary logarithms. I took Euler’s original work, translated from Latin to English by Todd Doucet, and explained it using modern math.
Why are you interested in this topic?
I find logarithms interesting, and in math classes, one is always told, “You cannot take the logarithm of negative number.” The surface level reason made sense, but I always wondered about the deeper reason.
What have been the benefits and challenges of this project?
The benefit of this project was it made me both a better mathematician and allowed me to satisfy my curiosity. Having to explain eighteenth-century math in modern terms made me figure out information that I would not have had to do otherwise. This project also let me explore the why as to why negative and imaginary logarithms do not exist or the possibility that they do exist. The two main challenges were getting stuck constantly and then having to figure it out only to be told that I did it wrong and the sheer amount of work that this entailed. This paper is not one that I could do two days before it was due; I had to start five weeks in advance and keep doing little-by-little to produce a high quality paper.
What is your advice for students who are interested in publishing their work in Lucerna?
My advice would be to work closely with your professor. They can make sure that not only is your paper factually correct, but that it is robust enough for Lucerna. Also, do not get discouraged when your professor crosses out a whole page of work. That work still taught you valuable information that you may be able to use elsewhere; failure is part of the process. Finally, make sure that you are interested in your topic since you will spend more hours than you will want writing and editing the paper.
What are your professional plans or goals?
My plan is to be a high school math teacher who teaches courses at or above the algebra 2 level. I plan on either getting my master’s degree in math immediately after I graduate and then teach high school or go right into teaching and get my master’s degree in education later.
