Beyond the Classroom: Mathematics in Service

Mathematical expertise demands effective thinking and learning methods, and these techniques transfer well to other domains. In this article, I discuss how my own training as a pure mathematician influenced my performance in three disparate domains: electrical engineering, art appreciation, and learning Italian. In electrical engineering, the focus is on how mathematical reasoning and thinking processes impact knowledge acquisition and problem solving. Appreciating and analyzing art raises the question, "How do we know for certain?" Acquiring fluency in another language is akin to gaining mathematics proficiency, and here, I explore the human side of persistence. The article combines narrative, reflection, analysis, and teaching ideas to suggest how, when teaching our subject, the mathematics community might pass on our core strength: our thinking and learning methodology.