Utilizing history in the classroom is an important technique that helps improve learning. When we are lucky, we discover new mathematics in the process. When we are very lucky, that mathematics can be used in the classroom, which is what happened in this project.
Lagrange first brought the problem of reduction of order to d'Alembert's attention, a problem d'Alembert called "... so beautiful to me that I've looked for a solution myself." Lagrange already had a solution and it didn't take long for d'Alembert to find his own. D'Alembert often rushed to publication to guarantee priority to the detriment of clarity. However, on the topic of reduction of order, the tables were turned. D'Alembert lost priority to Lagrange, but his method is so clear it remains with us today.
The authors would like to thank all the people who made suggestions that greatly improved this paper. In particular the referees and editor made many helpful comments, and Dr. Timothy Wilkerson of Wittenberg helped review several of the French translations.
Sarah Cummings (Wittenberg University) is a 2015 graduate of Wittenberg University in Springfield, Ohio, where she was a Mathematics major and French minor. She was thrilled to see her two passions, math and the French language, come together in this project unraveling the history behind methods for reduction of order. Sarah is currently living in Chicago, Illinois, and is a first year graduate student in DePaul University’s Predictive Analytics program.
Adam E. Parker (Wittenberg University) is associate professor of mathematics at Wittenberg University. He has undergraduate degrees in mathematics and psychology from the University of Michigan and earned his mathematics Ph.D. in 2005 from the University of Texas at Austin under the direction of Dr. Sean Keel. He teaches a wide range of classes and often tries to incorporate primary sources in his teaching. This paper grew out of just such an attempt. In his free time he enjoys sports, cooking, and repairing mechanical watches.