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I LOVE physical notebooks, paper, and ink. Physical notebooks do not crash, they do not lock up, they do not have DRM on them, they are not impacted by "updates" to pens or inks. Sure they can be difficult to "backup" and can be lost, but these are small cons against the much larger pros.

From math, to science, to world building, and even to learning a notebook can be your best friend. A quote that has always stuck with me about notebooks has been from Robert M. Pirsig's "Zen and the Art of Motorcycle Maintenance":

> “For this you keep a lab notebook. Everything gets written down, formally, so that you know at all times where you are, where you’ve been, where you’re going and where you want to get. In scientific work and electronics technology this is necessary because otherwise the problems get so complex you get lost in them and confused and forget what you know and what you don’t know and have to give up.”

Related: https://wiki.c2.com/?LogBook and GreyPatter https://news.ycombinator.com/item?id=29661167 (My productivity app for the past 12 years has been a single .txt file (2020))

This is an insane amount of verbiage to say "your kids should have a notebook for every field they study". Actually it doesn't even generalize it that far, it just obsesses on insane minutae of why it's good to have a notebook for math. Is this LLM spew?

You can go to any drugstore or office supply shop and find cheap spiral-bound notebooks. Your school's supply list is probably asking you to do this and even specifying a size. Is your school not doing this? Are you home-schooling?

Given your abhorrence of verbiage, here is some LLM spew instead:

In Search of Lost Time by Marcel Proust is a monumental novel about memory, time, and the subtle shifts of consciousness. Through the narrator’s recollections—often triggered by sensory experiences like the taste of a madeleine—Proust explores love, art, jealousy, and the passage of life in early 20th-century French society.

Seeing math on Lined Pages is unsettling to me. I agree with author that Blank Pages tend to become a mess, and that Gridded Pages are too "noisy", that's why Dotted pages are perfect and prefered for Journals, especially ones with very light dots. I wonder why I don't see more of those in math.

Yeah, I also found dotted notebooks to be the sweet spot. It's cleaner than a lined or gridded notebooks and especially helpful if they're already numbered.

The tweaks they found in the article is basically a proto-version of the Bullet Journal but just with its index system.

Physical notebooks are nice but as I have to come to know throughout the years, they are also kind of "disposable" and cannot survive long-term if you have to do any amount of moving. You wish you could keep all of your journals/notebooks in an archive but seems infeasible when you don't have your own house or your house is just too small. The rising rent and house prices just makes this all the worse.

I agree lined paper is inappropriate. I like dotted pages for my planning as I'm drawing a lot of boxes and arrows etc. I think squared paper is great for maths, though. You just have to find one with light and pleasing lines. Just spend a bit extra and get something decent. In the UK I use Pukka or Rhodia. They both do dotted now if preferred.

I've had similar ideas throughout the years of my personal mathematical journey:

- When I took my Discrete Mathematics course, I began to keep a separate notebook to compile proofs that I found to be particularly clever or, I thought, illustrated a particular concept/approach clearly. It was partially inspired by Erdős' concept of The Book.

- I did something similar for "Leetcode" problems but in this notebook I would only document solutions I personally came up with for when I feel like having solved the problem gave me considerable "XP" if not outright leveling me up. They ended up mostly dynamic programming problems and clever applications of number theory---I never really felt like I grokked these topics even now so it was useful when I detected similarities to past problems.

- Lately I've decided to give signal processing a deeper shot and a grid notebook has been my invaluable companion for the task. The last two notebooks were very neatly organized but this one is more like lab/field notes but for mathematics. It's gritty and dirty in there. There isn't really much point learning signal processing only from books so I'm always in front of my computer (with a lecture video or an interactive Python script) when I'm working on this notebook. Being able to formulate hypotheses/intuition, writing down thoughts to be considered later, annotating graphs/proofs where things don't make sense to me yet---it has been an extremely liberating learning experience. I've only been on this endeavor for a few weeks but I can definitely say it has allowed me to interact with the material at a deeper level.

The only way my signal processing effort could be better was if I had a teacher whom I can ask my noted-down questions to. I know the suggestion is gonna come up and I'll be lying if I say it hasn't crossed my mind so I'm just gonna address it unprompted (pun intended): I don't bring my questions to a LLM because I'm not yet smart enough to detect bullshit in this field of study. I don't think setting-up my own agent to ingest my notes would make any sense because then I would have to structure my notes and the core reason why it's been so liberating/has enabled me to interact deeper with the material is because I gave myself the freedom to be unstructured.

I am trying to get better at signal processing too. Are there any resources that you find particularly useful?

I understand your point about LLMs. Especially those like GPT 4o can lead you astray by not being sufficiently precise, confusing things, and plotting things incorrectly. (I experienced this in the DSP context.) I feel stronger models could be more useful, especially when paired with a good system prompt. I read people set up NotebookLM with their textbooks for studying, but I don't know how reliable it is.

This reads like so much of common sense and how we learned and practiced math through out our own school years decades ago.

A little baffled at why so much verbiage is dedicated to it.

Kids having notebooks dedicated for each subject for the academic year is news how?

All supplies and stationery stores include tons of notebooks in standardized dimensions. For math, we used grids in elementary school and then graduated to blank white pages from middle school. Teachers and schools would clearly mandate this -- and given how common and prevalent this practice was, it was almost tacit knowledge that no one needs to explain it or write about.

Not just for math kids--good for anyone.

I have a "daybook" thats always with me. Each day gets a header with the date. I treat it as a "cache" for what I'm working on. Math problems for school, jotting down ideas for programming, having a dialog with myself while debugging (also a good tool).

When one gets full you put it on the shelf. Fun to look back on what you were working on a month/year/5 years ago

Is this kid home schooled or are there really schools that aren't giving kids workbooks? We had workbooks for every lesson, with squared paper for maths (don't do it on lined paper, that's silly). The first time I had to buy my own (which I obviously did, and still have) was in uni.

Not mentioned in the article but I highly recommend using pencil, not a pen, and erasing stuff. Scribbled out mistakes aren't useful later.

I appreciated this, though I see a number of others here did not.

There's more to this than merely "notebook good". It's interesting to view how a child relates to a notebook through the lens of a parent trying to make it more effective. The conclusion may be obvious, but the journey was insightful.

My son uses Math Academy. My son has a folder of paper that's printed on one side and destined for the recycle bin. He uses when he can't solve the problems in his head.

I don't see any good reason to retain this stuff:

- his progress is tracked in Math Academy

- he doesn't need a reference sheet, as anything he needs to reference is stuff he will memorize using Math Academy or Anki

First I expected this to be online.

Then I expected it to be a notebook for sale.

Now I'm just puzzled.