foundational bricks
When I was young, I don’t remember exactly when, I encountered an idea, that if we ask a question carefully, properly, correctly, then the answer will be obvious. The answer will emerge, on wings, from the ashes of the question being asked.
I’ve never been able to entirely shake this idea. It snuck in under the radar, an idea that took root before I was old enough to know better. I’m sure there are other dandelions, kudzu vines, that are part of my internal firmament.
But something that’s interesting about this idea, is that it still to a small extent shapes how I got about my professional life as a mathematician. I work on questions whose answers are not yet known, looking for those answers. Some of the questions are ones that I’ve developed, others are questions that I’ve learned of from others. But still, questions.
Mathematicians are aesthetes to some extent; this is illustrated in a strong way in Proofs from the Book by Aigner and Ziegler, the collection of the most elegant, the sharpest proofs of classic results. It begins, because of course it does, with Euclid’s proof that there are infinitely many prime numbers, and explores from there.
As beautiful as they are, the aesthetics of the Book are different than what I’m thinking about there, though they are related. And so, for the mathematical problems I’m thinking about, the question remains: what is the statement of the question that makes the answer the obvious statement.
I’m not sure such statements exist. Questions can be complicated, mazes with twists and turns and minotaurs, wielding their axes of reason and argument. There may well not be a statement that makes the answer to these complicated questions the next obvious thing.
And yet. And yet, for me the echo of that old belief still persists. And this perhaps is actually the thing I’m thinking about today. That there are these foundational bricks that we each have, ideas and beliefs and rumors, perhaps, that we each acquired when we were too young to know better. That we heard before we had the weapons, swords and shields, to defend ourselves.
multijimbo 