The dark house of math

When I was in high school, I saw a NOVA episode about Fermat's last theorem and it's final proof. In there, Andrew Wile gave a quote about how doing math was like wondering around a dark house. It made a big impression on me, and a few years ago (fall, 2010) when I was trying to explain some things to one of my classes, I embellished on the idea to try to give them some feeling for research. It's phrased in terms of math, and could also be applied to scientific pursuits, but I think all of us can recognize some of our experiences in the idea.

Studying mathematics is like walking into an unfamiliar house on "a dark and stormy night" when everything has lost power. At first, it's just empty and dark. You know your in the house but you cannot see or feel anything. You start to move through the house just like you would your normal house like you know where you are going. For a moment, you feel like your at home. But as you start to walk, you start to bump into things: your toes get stubbed on things you didn't see, you can not tell doors from walls... After bumping into a few things, you start to get a little scared, lost, and confused. You hesitate. You realize you don't know where you are, and that this house is DIFFERENT from your house, that things are in different places, and that you might get hurt if do the wrong thing.

And we all start to act a little differently. Those of us here for the first time are at a total lose about what to do.

It would be great if you could find a light, BUT DON'T KNOW WHERE THE LIGHTS ARE! You might might panic a little, decide to back out of the house the way you came in. But that won't get you want you want, because you'll be back out in the storm and you'll still be lost if you try to go back in.

Some of us are fool-hard. We plow ahead like we know what we're doing, trusting to our luck will keep us from falling down the basement stairs before we find a light.

Sometimes somebody shows us the way. But sometimes there is nobody around.

So you start moving around the house a little more carefully. You take small steps, so that you don't stub your toes. You bump into things softly, and feel your way around them. Some of the things you bump into feel like chairs and tables, but some of them are unrecognizable. Eventually, we find some light switches or window shades, which help us find our way around the room. And now you can start to see how the pieces of the room puzzle fit together, and you check and find that some of your surmises were right, but others were wrong. But light switches for one room aren't of much in the next dark room. If you are really lucky, you find something like a flashlight, that you can take with you from room to room.

Doing research is finding more, better flashlights, maybe even with different colors.

Doing magic is hiding the flashlight and leading people around the house in the dark.

Doing teaching is handing out flashlights.