February 2016

The concept of zero and the concept of infinity are complete polar opposites, yet they also have attributes that are uniquely the same. While zero can describe an empty set, infinity represents an indescribable amount of largeness—they are polar opposites of the spectrum of quantity. Both can also describe a quantity that never can be reached. Infinity and zero are values that one can approach ever so closely but never actually reach, which is the foundational definition of a limit upon which all of calculus is built. The shape of a circle is based on the idea of infinity and the limit. The circle is created from the simplicity of a triangle. When one continues to add a side and an angle to a triangle, and then to a square, a pentagon, and so on indefinitely, the perfect and beautiful curvature of a circle emerges and grows yet is never fully completed, because infinity cannot be reached. I find these limiting concepts to be so limitless in discovery, elegance and complexity.

An article I read several years ago described infinity as being more like a journey than a destination. That could not be a better metaphor for teaching and learning. Just like infinity, learning is a journey that we encourage students to embark on and but never to be finished with. Beyond diplomas and degrees, we want our students and our teachers to constantly be questioning, pursuing knowledge, and solving problems in order to understand the underpinnings of systems and strategies. I encourage the same for parents. Rather than focusing solely on what your children are learning or doing in school, share with them the things you are reading, articles you find interesting, podcasts you heard that peaked your interest and made you ask questions and want to find out more. In doing so, you model inquiry and help to shape a story about how the academic disciplines they see as discrete entities in their young lives are connected to experience and the world around us.

Just last week, mathematicians and computer scientists discovered the largest prime number now recorded. The number is so large that it can only be expressed in exponential form. I was convinced that the set of prime numbers had to be finite, but once again, the boundaries of what is finite have been expanded and the limitless possibilities of infinity prevail … and I fall in love all over again with the beauty of mathematics.