Answer with Caution

An idea pops into your head as you walk up to the board, staring at the problem, but you hold back, not wanting to embarrass yourself in front of the class. You pause for a few seconds, thinking through exactly what it is that you want to accomplish, and then pick up the chalk, writing down two lines to open up the proof.

You look back at the class, and then at Professor Luck, who nods reassuringly, and you pause to take a look at the board again. There’s a tricky thing going on here that you can’t quite pin down - you need to make sure that two moving parts are converging in the way that you want. Scratching your head, you sketch out a few things on the board. You’re making progress, but the going is slow as you try to hash things out in your head.

Eventually, you seem to come to a roadblock. You write down two potential avenues that you could go down, and then turn to face the professor. As you’re about to ask for help, a hand is raised from the back of the classroom. It’s the guy with the nasally voice again.

“Yes, Vignesh?” Professor Luck asks.

“I think the second thing that Alex wrote is correct. If he simply uses the inequality we established last class, then I think that we start to get somewhere interesting.”

“That’s a good point. Why don’t we try that, Alex?”

You fumble at the board for a few seconds, trying to figure out what inequality they’re talking about, but you can’t figure it out - you weren’t here last class.

“I’ve been in the hospital, Professor Luck,” you say. “I wasn’t here last class. What’s the inequality that I should be using?”

“You’ve been in the hospital?” Professor Luck exclaims. “I’m so sorry to hear that! It’s impressive that you’ve gotten as far as you have! Here, let me finish up the proof - though I’m sure it’ll make sense to you once I write down the next line or two.”

With that, she nods at you, and you take a seat. Professor Luck gets up to the board and continues writing, and you want to hit yourself in the head for not seeing the steps that she outlines next. It makes so much sense in hindsight. She takes a little while longer to flesh out some details, which you copy down, while some of the people in the seats next to you just sitting with blank stares.

“That wraps up the proof. As I mentioned, this is a hard problem, so we’ll go over this proof again first thing next class, because it’s going to require some more explanation - but thank you very much to Alex, who did a spectacular job setting up the first few parts of it. I’ll post the homework for next class in an hour or so,” Professor Luck says. “Don’t forget, I have office hours right after class now! Stop by and chat if you have any questions or are finding anything tricky.”

With that, the class begins to filter out of the room, and Christina punches you in the shoulder.

“Nice job, Alex,” she says. “What you did there was pretty cool. Anyways, got to run now - have another class.”

“See you,” you say, before she’s gone. As you leave the classroom, you realise that you need to decide how to spend the hour before your next class begins.

Christina +5