This seems to have gone a bit too far in the other direction, I felt like I was wasting my time reading a whole page for an insight that could have been conveyed in one line.
(I wrote the Fundamental Theorem of Algebra post.)
I don’t necessarily disagree; I wrote the original thing as a proof of concept and wasn’t expecting it to be perfect first time out. However, I do have the extra notion—given my design ideas presume things are being delivered electronically, as seems to be the case with most math papers these days—that one could expand or condense different parts of the proof so the amount of detail would be selectable.
Also, however, regarding the fiddly details, some of the insights conveyable in one line are in the original proof are written as the original whereas some of the denser things that DID need expansion were originally mashed together as one line with cryptic variable names. This can happen with math papers quite often due to the demands on rigor. One proof redesign I was working on but never posted (at least not yet, I should dig it out) was that the set-theory definition of ordered pairs (x,y) actually works; it’s head-slappingly obvious but the demands of mathematics require every small detail accounted for.
Also also, a lot of this is dependent on personal preference. One commenter didn’t like extra emphasis the indents-for-suppositions but I’ve found them extremely helpful in reading proofs.
This seems to have gone a bit too far in the other direction, I felt like I was wasting my time reading a whole page for an insight that could have been conveyed in one line.
(I wrote the Fundamental Theorem of Algebra post.)
I don’t necessarily disagree; I wrote the original thing as a proof of concept and wasn’t expecting it to be perfect first time out. However, I do have the extra notion—given my design ideas presume things are being delivered electronically, as seems to be the case with most math papers these days—that one could expand or condense different parts of the proof so the amount of detail would be selectable.
Also, however, regarding the fiddly details, some of the insights conveyable in one line are in the original proof are written as the original whereas some of the denser things that DID need expansion were originally mashed together as one line with cryptic variable names. This can happen with math papers quite often due to the demands on rigor. One proof redesign I was working on but never posted (at least not yet, I should dig it out) was that the set-theory definition of ordered pairs (x,y) actually works; it’s head-slappingly obvious but the demands of mathematics require every small detail accounted for.
Also also, a lot of this is dependent on personal preference. One commenter didn’t like extra emphasis the indents-for-suppositions but I’ve found them extremely helpful in reading proofs.