Have you seen the number three?

“Have you ever seen the number three walk across Jakeman Field?” Anyone who has had the pleasure of taking the Rev. David Curry’s Theory of Knowledge class has been confronted with this seemingly simple question. Of course, no one has ever seen a three walk across Jakeman Field! Three athletes throwing about a rugby ball, three cadets standing in line, three students from Vair Mac on their way to class trudging through the snow: we have seen all of these things on Jakeman Field, but never the number three.  

And therein lies the challenge of the Rev’s question: we use the number three all the time, and we feel confident in its use (as we should!), and yet, even among philosophers of mathematics and science there is no consensus of what three is. Certainly, there are definitions, properties, and effects of number, but none of these things can definitively conclude upon what number is.  

Regardless, number exists in some magnificent and mysterious way! I know this because over the past two weeks groups of students from grades nine through twelve have taken on some wonderful and difficult mathematical problems by writing the most recent University of Waterloo Math contests. It has been a joy watching students toss about complex numerical abstractions. I am proud of the students who step up to take on these competitions. These contests are not easy; they are designed to challenge students’ thinking and feed their drive for mathematical knowledge, magnificent and always unfinished.