[hjorthjort]

I don't know at what level this is used, but I have only ever seen it in my graduate level logic and mathematics courses. (I'm European.)

I like it. Part of a good proof is a rigorous derivation. There is plenty of thing sto be said about what intuition can lead us towards such a proof. But at the end of the day, a good proof is ideally almost machine-checkable. Most proofs (much like code) lives two lives: the one in which they are written, and the one in which they are read. It should be almost trivial for a student to go back, on their own, days or weeks later, and see that each step is valid. And I think prose interspersed between column-style proofs do a better job than what margin notes do. The reason two columns work well is that the step and it's justification are of both condensed and almost always of similar length. Justification (much like code comments) may or may not need a good chunk of space. And surely nothing is stopping anyone from inserting little margin notes here and there in a two-colum proof, right?

[jacksnipe]

Graduate level logic? That’s so interesting. I only took undergrad, but did an ambitious independent study in logic once; we did not use two-column proofs, which seem mostly useful as a pedagogical tool to make the student see where the logical steps in the proof are, and less as a tool for serious work, since prose is really the best tool for communicating the insights that led to the proof.

Definitely did plenty of “one column” symbolic proofs though. I think part of the lack of need is that seeing two steps right next to each other generally makes it very clear what was done to get from one step to another.

Unless it invokes the axiom of choice, in which case fuck me.