Summer of Math Exposition

I don’t know how to explain my feeling. It is a really insightful article with literary, and I can imagine how exciting when all of the stuff flood into your mind. But this is a really huge topic and it is hard for readers to fully understand what you are saying without extra illustration, though you have done your best. It’s not your problem and I really like it. I will review it if I want to learn topological Galois theory.

The explanations themselves are fine. The whole framing is a nice idea, but it has no real payoff and it makes the text unnecessarily long. It is definitely possible to write math texts with a strong narrative in a more straightforward way.

Moreover, the whole text reaks of genAI and the thumbnail does not help.

Good entry, and good story too! I have a few points to make, though:

Firstly, the proof itself is really neat and the storytelling is ok; what I loved most were the historical comments on the discovery of the Abel-Ruffini theorem. In the writing side, I do not have many objections to make.

However, I believe more visualization would have been really benefitial when following your arguments; at times it takes some time to picture in one’s mind what you are trying to convey through words. This itself is not bad, yet some plots (and maybe an interactive widget displaying the behavior of the polynomial as the roots move in the complex plane) would have been really insightful when teaching the fundamental argument of the proof.

I think this was a cool explanation into another way to solve the unsolvability into quintics via another approach. I liked the story framing behind it as well and left from reading the essay into an insight into something more interesting about the nature of the solution. Given that it’s a topological proof, it’d be nice to have more visual demonstration around it given its potential.

I quite liked the narrative an you did a good job of providing an intuitive understanding of the results, as well as a way to relate to math as a non-mathematician. However, I would recommend reworking some of the diagrams and making sure they are well integrated into the text and maybe including more since much of the intuition involves visually how points relate to each other.

First, I enjoyed the style - the Diary format, the reflections of the Author on the Weather and Nature? Really nice metaphors - bit different.

Second, I thought the Author did a great job by impressing the Reader with the significance of the Quintic problem and its significance to the history of Algebra.

All I would say is that it was difficult for me as someone who’s not an expert in the techniques being used here to follow the rest. I understand that the Author’s internal monologue does a great job of breaking up the heavy content. Clever!

Again though, I found it hard to hold onto the mathematical story that was being told. I had to pretend I was following, even though I know I’m not. I’m following the Author’s progress of inquiry, rather than understanding any of it.

But I think I did at least grasp one big idea - that permutations can be seen as continuous, rather than discrete, transformations? And I thought that was really cool! I wonder if this is what’s at the heart of Simone Conradi’s work (which he shares extensively in beautiful Twitter gifs)? :)

My only big criticism (if that’s the right word) is that it was extremely long. I have the Browser read this aloud for me, it must have taken a good 45-60 minutes.

I know that the SoME has evolved since its inception, but the initial remit was to make something that could be reviewed in 10 minutes. With the best will in the world, this took well over an hour to read & review.

In fairness, most SoME participants seem to disregard the 10 minute rule.

I’ve no doubt that specialists would love this - the Author’s a great writer! :)