Over at Good Math, Bad Math, Mark explains “Proof by Contradiction,” a common mathematical technique that doesn’t translate all that well to politics. Whenever proof techniques come up, I always think about one of the very few things I remember from my graduate class on Math Methods.
We were talking about some sort of complex analysis technique– I don’t remember what it was– and the professor was drawing diagrams and doing contour integrals on the board to demonstrate whatever it was that he was talking about, and at one point he drifted into Proof by Invocation:
“So we integrate along this curve, and we see that we just integrated through the singularity. But we know that everybody– including Feynman!– has done this, so we continue on…”
I guess it all worked out in the end, but that was a singularly unconvincing step in the lecture. (I wrote the comment in the margin of my notebook, which is why I remember it to this day. And no, Jonathan Vos Post was not guest-lecturing that day.)
So here’s the dorky question:
What’s your favorite dubious proof technique?
What justifications have you seen people use, either in class or in research papers, that just don’t make any sense if you think about them?