Summer of Math Exposition

The article is nicely written and easy to read and follow. The only problem with the flow is there is a little bit too much emphasis to the author’s own experience/feelings on the topic and personal history. On the positive side, this made the post feel more humanly (or maybe story-like, idk). The downside is, it feel like those parts are there to fill in the relatively short article. I think, the article should have more mathematical content to justify the length of those personal parts. Instead referencing other articles, this post should better give a few examples to keep it more self contained.

This article sparked intuitive thinking and got me asking good questions! I would’ve loved terms to be introduced in the article itself rather than linking it to previous articles in the series (but since the concept was interesting, I did the reading nonetheless!). Also, the section titled ‘Intersection’ was a fun read!

I loved the animation of the tessellation doodle!

I must be missing something because I didn’t understand the link between the doodle and the ‘Defining Convex’ section. You refer to your previous work quite a bit in the article, so I’m assuming that it’s related to that. Maybe if you could give a brief summary of the previous work that you’ve done so that someone new to the Substack can follow it more straightforwardly? I’m glad I had a look at your other articles, they were also very interesting.

I also really enjoyed your section on the connection to other people through time and space.

The article made me feel happy and made me think that there are lots of doodles out there waiting to be discovered. It definitely made me think about including more engaging illustrations in my own work.

I agree with you that the OEIS is always a great place to start any investigation!

Motivation: You explained that you were expanding on previous doodles, but is there anything that is particularly interesting/pleasing/useful about them?

Clarity: I enjoyed the clear writing style. As I said, it was unclear why we were interested in the convex section.

Novelty: It was definitely novel to me, I enjoyed learning about it.

Memorability: I understand how to construct these nice doodles, and I will definitely think about future work being more motivated by nice visuals like yours was. I think it was missing some kind of ‘aha!’ moment where I saw a connection to another area of mathematics or saw how there was a different way of thinking about the problem.

Thanks for your article. I’ve subscribed to your Substack

It would be nice to have a more in depth explanation of why you get precisely the intersection of triangular numbers and the other sequence.

While I can tell that you were very motivated to look into this yourself, that isn’t quite conveyed in the text. The “brain blast” was not conveyed, for me. It is a cool program that demonstrates some interesting properties, but this isn’t as strongly motivated as other submissions I’ve seen.

This is nicely written, but a bit shallow overall. There are quite a few references to other blog posts and outside websites. Which is fine in and of itself. But a lit bit of repetition of the most crucial terms would help a lot. The section “Defining convex” is so short that I have no idea what it wants to tell me. In particular, I have no idea what the depicted sequence is supposed to be and why convexity should be in any form problematic for hex or triangle tessellations. Lastly, we end up with a sequence that is not really analysed. Looking at the winding-strip construction it might not be immediately clear to reader whether the sequence is finite or infinite. Exploring that could have been nice. Lots of little things that could have been done to make the post more accessible.

I was diving into the topic and reached the edge of the pool without even swimming. What I mean by that is the entry was rather short. Very intriguing, very interesting, but way too little content if you ask me. I wish there was a more structure to it, more suspense at the beginning, more mathematical output at the end (formulas, sketches, numbers etc). A little plus for the font though ;)