I haven't dabbled in the math and shorthand stuff, but did switch to analogue for a while, doing a Zettelkasten-like system of my own, using folded A4 paper, with IDs, thread chaining, indexes, linking, etc. A pencil and a ruler plus the paper were all the tools I used. I used it for journaling, writing, keeping lists of books, writing reviews and notes, task management, indexing my collections of psychical objects, and other assorted uses. My verdict is: analogue has definitely been more productive than digital for me. It is slower in every way, so /speed/ is not how it did it. It was more through /focus/, friction making switching away from things more expensive, more accurate estimation and prioritization of tasks, and some kind of psychological effect from the meditative effect of preparing the documents, lining the paper manually, and drawing some flourish and some attempts at calligraphy in the titles; having beauty and care imbued into the work; craftsmanship of sorts. I tried it even on other people, for example helping my wife with a long-term project by dedicating a paper to record her achievements, writing them down very carefully and slowly, with some ornaments around the paper, etc. It had a very visible effect on her excitement and dedication to get to her goals, and she was always coming back to ask me to write down the next thing she's proud of. I don't think this effect would be achieved by writing a bullet list in a plain text file.
The negatives of analogue are overblown usually. Most governments ran on paper machines, but too many salesmen wanted to sell us the "Digital Transformation" the past few decades. Search is not a big issue, because you can have an index, and write keywords in it, backups are not a big issue, because you can scan your documents, copy them, and even OCR them if your writing is acceptably readable, or even manually copy them by hand if the writings are important (every time you manually copy, you have a chance to improve what you wrote; an article re-written from scratch three times is usually of way higher quality than one written once). Hyper-linking does not require a digital tool; you can have IDs and use them as links, and finding the right document can be fast if you have a good ID schema to sort your documents by. Even copy-paste works in analogue if you really want, by... you know, copying with a printer, and then pasting with some glue. Or just link using IDs. I use simple nylon plastic sleeves as folders, give folders IDs too, and link to them from an index page that explains what things are in that folder. Usually the index paper is kept as the first paper in the folder itself, then a link to that index paper is made from a more central index (e.g. index of personal government documents, index of sentimental letters, gifts, and trinkets, etc.). Moving paper around is also easy. Throw it on a scanner, make a copy, put it in your clipboard, and take it with you on a bus ride. If you want to move an original document from your main data store to some other place (e.g. from home to office), you can write that down in a special "move index" file, in which such moves are tracked.
Another thing I noticed with analogue, is that my brain became better at things, making it faster than using a computer. For example, it takes me a few minutes to search online maps to make a trip plan to where I wanted to go, but since I'm using analogue instead of digital (I got rid of my phone completely too, by the way) I had to write the directions down on a paper and take it with me, as I couldn't access them on demand whenever I needed them otherwise. Well, not for long, because my brain suddenly started remembering the roads for next time, whereas I went places dozens of times using digital maps before, and never memorized the roads. Same for phone numbers, I used family members' numbers hundreds of times using a mobile phone, never memorizing them, but without using a digital contacts manager, I had to write them down, and then I find the paper and read it when I needed to call them using landline, and less than half a dozen times later I was just remembering the phone number off the top of my head. Much faster than searching any digital tool :D
After a year or so, I went back to my digital systems to see if the lessons I learned can be helpful there. I ventured forth implementing my (8th, over the past decade) home-grown digital organization system, in Emacs Lisp, focused on a chunked single plain-text log, with internal linking, tag-based indexing, very fast leader-key-based shortcuts to do everything, etc. The results so far, around 3 months in, are not very good. It is much better than any of the seven digital systems that I built before it, and any of the dozen 3rd party digital tools I've tried, but it just doesn't "hit it". There's something really missing in the digital world. The faster the tools are, the easier the shortcuts, the lower the friction, the worse it becomes. The results are measurable reductions in total productivity, even though /it feels/ like I'm faster, and I spend less time organizing and planning, and everything just "emerges" from the system. Yet, I'm measurably less productive. I see I lose a lot more time on distractions, small side tracked tiny tasks that hairball into massive time wastes, more likely to not be productive due to not "feeling it"; i.e. low-energy, lack of excitement about things I want to do, etc.
Now, of course, there are like a million confounding factors in those experiments, so I can't really make any absolute judgments. But I'm starting to build a model that has two distinct approaches to productivity, one focused on improving the tools and workflows, modifying the outside world, and the other on sharpening the mind and mental state, modifying the world within. Doing analogue things in the real world, because it's slow as heck, because it has friction, because it allows your brain many many free cycles to generate random associations in the background, because you see many things at the same time (try spreading 20 related cards / documents on a big desk or the floor, very hard to simulate what happens there on a computer), because it costs so much time and effort, it all pulls your mind together, gives a fine point to your attention, and a sharp edge to your priorities.
Or that's my hypothesis about what happened with me at least. To learn more, lots of information around Zettelkasten is good food for thought, and I recommend the book Paper Machines by Jacques Derrida, which I found very interesting (though I haven't finished the entire book yet).
