Summer of Math Exposition

The article begins strong but the middle section requires improvement. To an audience unfamiliar with the concepts, the exact formalism could be omitted or an option to skip could be provided. Overall, the presentation is very good.

This was an amazing piece! Very clear, easy to understand for beginners, well-motivated, and fresh. I have no additional feedback since this was so amazing. I can’t wait to read more of your creation! Spectacular job!

such an outstanding dissemination of mathematics! love the piece

Nice way of explaining it but I felt the article lacked motivation - why would we choose to think about infinity in this way? Good clarity and the illustrations are nice.

This is a quick introduction to some basic ideas surrounding infinities: Hilbert’s hotel and bijection, cardinality, ordinals, cantor’s theorem. As a teaching resource, this could be used to generate some interest in learning more about these topics, but I would not use this as a primary resource to learn about any of these topics as it is not formal or deep enough. This topic has also been covered many times at this point, so this submission suffers on the novelty axis.

Would be nice to explain Cantor’s thm in more detail, and try to intuit the proof - I think the reader is currently left perplexed when you say “|A| < |P(A)| holds for infinite sets too” - what does size mean for infinite sets?

I don’t have much to say. I love your writing style. I’m always a fan of reading math content with creative writing, way past the boring tone of most books and papers out there.

The topic you chose has been touched countless times, but I don’t care. Everyone is free to write about the topic they like, and more so if you do it in such a beautiful way.

I love how you acknowledge at the end that it’s perfectly fine if the reader couldn’t grasp everything. I can’t tell if there was something that could be improved in your way of explaining the topic, because I myself know this was always hard to understand… Math understanding ultimately comes with practice.

I am very impressed by this article!