Summer of Math Exposition

Bit long. But overall very nice.

Motivation - The clear and straightforward writing style makes the motivation clear within the first few paragraphs. The motivation is tied nicely with a brief history of the complex plane and then driven forward with natural questions that are explored with graphics and interactive features.

Clarity - Clear explanations throughout, building up to more complicated ideas naturally through discussion, examples, and figures.

Novelty - easy to read format and clear explanation of the topic.

Memorability - simple yet clear explanations

A good ending, with good exposition.

I Kinda like the intro it throws the motivation in there by directly connecting the progressively larger spaces. It feels like I would learn something from reading this or it could be the start of a great youtube video.

Due to the history lesson and dense information I am missing references. In terms of clarity I would make a list of all of the jargon terms then you should kill your darlings which are simply there to be technically correct. Otherwise this text requires too much prerequisite mathematical knowledge to be directly useful. How this writing feels is like a great record of what is technically true and for that you would return to it, but only when you’ve learned the prerequisite concepts elsewhere.

You could probably break this up into a series and do one entry per number system. By doing so you would give your work more room to breath. The subject is esotherical that is what makes it novel. The downside of that is the need to bring more people into a rather deep subject swiftly.

What would stick with me are the interactive visualisations. Like you put a ton of work into making those look nice and work well. Since you already have most of the scenes you could also break them down into sub parts to explain them deeper. This is already done to great effect at the start, so that looks good. But you stray away from this build up, probably because you require a lot of complex operation properties to explain the differences between the spaces.

Interesting approach to construct the algebras from the geometric perspective. I liked the construction of the quaternions and octonions based on the anti-symmetric property and other relations derived from the orthogonality, as once it’s established that basis vectors must be orthogonal, the other follows suit. I think I was slightly confused with the whole velocity analogy there and it was a bit confusing on why 3 dim algebras are not possible or how an orthogonal vector must generate a whole velocity field in 3 dimensions.

Nice discussion of the history.