Having now officially convocated, I feel comfortable posting what I wrote for my valedictory nomination. I was not selected for the honour, but sometimes I like to indulge in a bit of ahistorical fantasy. What would today have been like if I had delivered some polished version of this piece?
Valedictory Address, Mathematics Class of 2015, First Draft
Mr. Chancellor, members of convocation, fellow graduates, and ladies and gentlemen... I must say I am ecstatic to be here, as this means I have seen my last contour integral, if I have any say in the matter.
I have the honour to stand before you today and reflect on your future. It is so energizing to welcome the threshold of your new and exciting life.
The University of Waterloo, is, of course, famous for "the spirit of 'Why not?'" We are the most innovative university in Canada, for God knows how many years in a row now. I suppose it wouldn't be particularly welcome to innovate on that trend, so I expect you graduates to keep up the good work. Now, don't worry; if you didn't live at Velocity for the past five years, I intend to give you a primer right now to ensure the long life of our fine reputation here at the University of Waterloo.
Let's begin with a brief discussion of the properties of the Riemann zeta function, despite your voiced objections—now, I hope you're all familiar with this beautiful enigma, and it does spark some interesting conversations. For instance, earlier in the term I was speaking with a post-doctorate student who was telling me that his calculus students were thoroughly convinced that the sum of all the positive integers is -1/12! Now, I'm not sure what branch of analysis you subscribe to, but surely you must agree that the sum of all positive integers diverges. I can see some of your heads spinning already... no matter, the flashback to first year calculus will end shortly. So this postdoc was telling me his students had told him that their physics professor had taught them this result, and if you're not familiar, an analytic continuation of the zeta function at the point -1 gives us this curious answer of -1/12. Beautiful result from complex analysis. This is useful in making string theory and quantum electrodynamics work, among other things.
So you tell me: which is it? Infinity or -1/12? [pause] I expected a good representation of the two answers: both are correct. We know that the zeta function evaluated at -1 gives us -1/12, but of course, we also know that the implication—that the sum of all positive integers converges, let alone to a negative number—is absurd. One of them must be wrong! Yet there is deep theory that we can use consistently to justify either answer. I can imagine those frosh thinking, "I didn't sign up for this!" Maybe you recall a similar experience.
One thing I've noticed in the time I've spent here is that many of us are attracted to mathematics for its elegance, its logic, its consistency. Sometimes—and perhaps I romanticize a bit—but sometimes I feel as though in mathematics lies the key to truth. And, then Dr. Kurt Gödel comes along, in strict postmodernist style, and softly explains that it is not possible for our mathematics to be consistent and complete. It seems that the further we advance in our studies of the field, the less certain we can be about any truth. We say that Choice is obvious, but then Banach-Tarski devours my enthusiasm. Sometimes it feels as though my refuge is a sanatorium.
You've spent four or five years now collecting knowledge, learning to think critically, perfecting your procrastination techniques, cooking on a shoestring budget, and kicking yourself over and over again for that STAT midterm. For the most part, change in our lives has been gradual, but every so often—and this is something I just adore about mathematics—there's this burst of inspiration, an epiphany, and the answer just clicks into place. Or sometimes, you see things so clearly that everything unravels and you realize that you can't tie the loose threads back together. Change is frightening.
These are moments in which danger lies: we may come tantalizingly close to the threshold of understanding, but then, out of fear and uncertainty, we back away. We lure ourselves into false comfort that mathematics is logical and complete and it holds all the answers: and then it strikes us back with emptiness and paradox. But this is not confined to math: when I see students on this campus faced with issues like discrimination and the challenges of mental health, too often do I see my peers justify injustice by arguing it must have been deserved. Too often do I watch "The Meritocracy" of STEM held up as tautological evidence of its own superiority, while simultaneously watching these pundits tear down another classmate's circular proof. How do you explain this contradiction?
My fellow graduates, I promised you a primer on how to innovate, how to enact change. And so I take this these few, precious minutes to focus on this simple, uncomfortable concept. Because as we all know, a mathematics degree alone is neither necessary nor sufficient for success, but we stand here together to tell the world that it matters, that we can think, that we can solve problems. I know you can solve problems. So let us tackle the hard ones. Let us embrace the cognitive dissonance.
For the last five years of my life, I have experienced contradiction after contradiction that struck me with discomfort, tore my eyes open, spurned me to change, spurned me to action. They tell me that Waterloo students are some of the most apathetic in the country, but when I watch you persist in your studies I know this cannot be further from the truth. You have the fundamentals mastered, but I suggest you consider cross-training. I challenge you: let us embrace the contradiction inherent in the pursuit of any complete and consistent system. The world is waiting for you, and someone is going to ask you to choose between infinity and -1/12. And I hope you pick one, and I hope you justify it to the fullest of your ability, and I hope that you hold in your heart that you are still wrong, and embrace it.