Joe Gerhardinger (photo courtesy of Notre Dame Academy)

In the article, Mr. Gerhardinger, who has taught at Notre Dame for 13 years, shares his experiences discussing with his students six key questions: “What exactly is mathematics?” “How is mathematics tied to human history on earth?” “Can we imagine a different human history on earth, and how might that change mathematics?” “Can we imagine a universe with different characteristics than ours containing intelligent life?” “Can we predict the progression of mathematics in any intelligent life in an alternate universe?” and “How might algebra, geometry, and other subjects develop any differently?”

 Mr. Gerhardinger, chair of the mathematics department at Notre Dame, says the discussion draws forth more questions than answers but is still important.

 “Even though I’m leery of taking class time away from mathematics to have such a discussion, I believe that students benefit in many tangible and intangible ways from participating. We have a responsibility to teach our students more than just how to do mathematics, anyway,” he states.