Summer of Math Exposition

I like the vibes. But it would've been way easier to read if the content was in a narrower column and wasn't Times New Roman.

I liked the stream of consciousness that the author shows. It gives a window onto a mathematician’s thinking. (Albeit an amateur’s thinking). That this was done by an amateur opens the door for others to come and play with sequences too. One cannot forget that the non-periodic monotile was found by an amateur!

Probably overly verbose, but I appreciated the attempt at full clarity. I lost the "why" about 2/3 of the through, where it started to really feel like scattershot.

Thank you for this article. I think you've done quite a fine job with independently discovering these sequences that it's hard to believe your claim as a math hobbyist! It reminds me of the playfulness in math to that of Jon Conway, may he R.I.P.. I hope you continue to expound upon what you've written, and meet the goals you've stated for the next SoME. That being said, I do not think this is an exposition quite yet. I say this because of the article's formatting and introductory statements. For e.g. why is it standard or essential to check the OIES? Perhaps there are other math hobbyists reading who may and may not know. And while I myself need to practice this, please be gentle with yourself for the work you've done in math. The tree diagrams will be achieved because much enthusiasm and work are seen in what you've presented. Would you consider writing a section about the Collatz Conjecture (CC) and without loss of generality (wlog), assume a position that talks about CC for the sequences you've discovered and verified with the OEIS? Cheers and my best to you!

Very nice introduction to the problem. I much appreciated your explanation.

The article is easily understandable by an average reader. The text is long, and it would be better if it could be made shorter in scope so that readers' attention is not lost.

This entry is good for it's approachability (level required and lack of specialization) and as an illustration of the process of exploration. However, I believe that some of the reasoning using infinities is erroneous which calls into doubt some of the intermediate conclusions. Overall, this would be better for the audience if it restricted to a smaller nugget which can be explained in a self-contained manner, leading to a clearer introduction and a more satisfying conclusion. And of course, ensuring that the phenomena are airtight.

I did not read this full entry, and so I am not going to be critiquing it. I hope you don't mind that I say a few words about why I stopped. In a sentence: the article does not make much attempt to motivate the topic. Your personal motivation appears to be "it's simple and fun :)" This is 100% fine, please don't misunderstand me! But I don't personally find Collatz to be particularly interesting in its own right. Of course, I wanted to give your writing a fair shake, so I read the first couple sections, but I didn't find much I could latch onto. So I was planning to skip this table and move to the next sequence, since your first sentence implies you'd be looking at a few. This didn't pan out as I was hoping, since those were also all in service to this main idea. By the time I got to "Check All the Numbers!", I caught myself doing more skimming than reading, so I decided to call it off. As a parting thought, I will say that you have a very distinctive mathematical voice, one that I happen to like quite a bit. You're also making heavy use of algorithms that have a sort of "dynamic" feeling: we take these numbers and *do* things with them. So while I think a lot of math topics are better explained with text and a few well-chosen pictures than with video... this particular piece is a textbook example of exposition that (I strongly suspect) I would have enjoyed more with narration and animation. I do appreciate the ad-stripped YT sources, and I'm sure others will too ^_^