octed's comments

If you wish to thank/support this project and it's creator you should check out the support page: https://hyperessays.net/support/

> I am slowly replacing the Cotton/Hazlitt translation with a contemporary one and adding new notes

So I would assume that the essay you're talking about is from the earlier Cotton translation and has still not been replaced.

This is the first time I've seen AI being used to "modernize" old texts, and it works wonderfully in this case; though a bit of the old-timey charm is lost imo. I used to read a translation that I'd found in my university library which I enjoyed a lot. Very readable but still retained the "feel" of a 16th century book. I don't recall the translator unfortunately.

At the moment I'd advise not worrying much about the construction of the reals. Ideas such as limits, continuity, differentiation, integration, and even fields are much more important for later mathematics and applications (abstract algebra, topology, geometry, physics) than the construction of the reals. Constructing the reals is pretty much something you do a couple of times (traditionally once with Dedkind cuts, as in Spivak, and once more with Cauchy sequences) and then never think about again.

Edit: I'm not sure what you mean by "something I could code." If you want something that you could type in a proof assistant you might have some luck looking at the mathlib library of Lean https://leanprover-community.github.io/mathlib4_docs/Mathlib....

This is not to say that high schoolers can't do abstract algebra (or higher mathematics more generally). In senior year I attended a week-long camp (Arnold had a full semester) in my local uni where we proved the impossibility of squaring the circle, doubling the cube, etc using field extensions. And I was in the older side! Most of the kids there were 10th grades. Though Arnold's class was probably substantially harder than ours. I worked through V. B. Alekseev's book after the camp was over and the exercises were substantially harder than the ones we did at the camp. The material on Riemann surfaces was very hard to understand as well, much harder than the group theory part (I still don't understand Riemann surfaces lol).

In conclusion, AP Calc, and students' performance in it, is a terrible metric for assessing mathematical ability. Sorry for the long rant.

As for the pdf look, you're right. The problem I encountered way back when I was actually building the site was that I didn't know what to put on the extra margins. I could've put footnotes and figures, but that's pretty hard to do if you're generating the site from markdown without a custom markdown engine. I'll see what I can do about it tho, and if you have any suggestions for how I could improve this I'm all ears.

It's pretty new, first post was made in September of 2022. I've been going at the speed of ~1 post per month since then so I got 8 posts.

I mostly talk about stuff I've been learning about. For instance:

1. Lagrangian mechanics I [https://oktagonia.github.io/blog/lanlifshitz_1/notes.html] and II [https://oktagonia.github.io/blog/lanlifshitz_2/notes.html]

2. Group theory (solubility and symmetric groups in particular) [https://oktagonia.github.io/blog/insolubility/p.html]

Besides this, I occasionally write about some of my own explorations as well; stuff that doesn't fit as neatly into a university course format:

1. Going over a random lemma from Newton's Principia [https://oktagonia.github.io/blog/lemma14/lemma14.html]

2. Encoding ternary logic into the lambda calculus (I previously posted on HN) [https://oktagonia.github.io/blog/ternary/ternary.html]

3. Some epistemological ideas (tbh this is not very good and I intend to write a better post about this stuff soon) [https://oktagonia.github.io/blog/pragsol/p.html]

I hope you guys enjoy and give me some feedback if you got some.