Math Machine – A notebook will show your kid how far they have travelled

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.

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.

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.”