The Universe of Discourse

Almost-trivial theorems

A couple of years back I wrote an article about this bit of mathematical folklore:

Mathematical folklore contains a story about how Acta Quandalia published a paper proving that all partially uniform k-quandles had the Cosell property, and then a few months later published another paper proving that no partially uniform k-quandles had the Cosell property. And in fact, goes the story, both theorems were quite true, which put a sudden end to the investigation of partially uniform k-quandles.

I have an non-apocryphal update in this space! In episode 94 of the podcast “My Favorite Theorem”, Jeremy Alm of Lamar University reports:

My main dissertation result was a conditional result. And about four years after I graduated, a Hungarian graduate student proved that my condition, like my additional hypothesis, held in only trivial cases.

(At 04:15)

In the earlier article, I had said:

Suppose you had been granted a doctorate on the strength of your thesis on the properties of objects from some class which was subsequently shown to be empty. Wouldn't you feel at least a bit like a fraud?

In the podcast, Alm introduces this as evidence that he “wasn't very good at algebra”. Fortunately, he added, it was after he had graduated.

The episode title is “In Which Every Thing Happens or it Doesn't”. I started listening to it because I expected it to be about the ergodic theorem, and I'd like to understand the ergodic theorem. But it turned out to be about the Rado graph. This is fine with me, since I love the Rado graph. (Who doesn't?)

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