Sometimes, I don't bother struggling. It's all Greek to me (and indeed, a lot of it is. Once you run out of English variable names, you have to go somewhere!). I just nod and smile and hope he's right.
Is that bad of me?
But last week, I was looking at his final figure and it just didn't look right to me. I inquired some more about the particulars, and it still didn't make sense. Usually I would have just let it go at that point, but he was preparing the talk for a conference, and I figured if I couldn't understand it, the conference-goers probably wouldn't either. In fact, the more I thought about it, the more I thought he was just plain wrong.
So I kept pressing. I tried to explain where I thought he was off, and I could see a couple others at the group meeting nodding in agreement. So that helped me believe I had a valid point. Some others were just nodding and smiling, like I do when I don't get it... :) I figured even if I was wrong, he ought to be able to explain my mistake.
We spent 45 minutes discussing how he had gotten from his data to that figure, and the manipulations he had done. It involved 3-D matrices, transformations in space and time, corrections for image perspective, and I think there was a hypercube in there too.
My brain hurt.
And at the end of an hour, the whiteboard was full of drawings, opinions had flown back and forth, and all of us in the group meeting had gotten into the constructive debate. All of our brains hurt. We had attacked the problem and expressed the concept from as many angles as we could think of.
I still thought he was wrong, though I admitted I may be mistaken, and just wanted to thoroughly understand. He still thought he was right. I'm not sure what the rest of the group thought. Probably they were thinking of dinner. We had to let it rest, the meeting had dragged far too long.
But do you know what email I got today? Turns out that student went back and double checked, and I WAS RIGHT!
That makes me happy. I stood my ground, understood at both a conceptual and detailed level another student's work, and spotted an error.