Summer of Math Exposition

I like that you’re showing that math can be both fun and messy and still be valid and that it’s not just all about memorizing formulas, etc. I’m not sure a formal definition of functions and bijections was strictly necessary to get the idea of different sized infinities across. I don’t think it’s bad that you included it but it felt a little out of place to me, pulled me out of the puzzle a little bit.

This one was amazing. It’s like a YouTube video where you control the pace. Great story. I love how it tries to take you through a few paths. Why can’t I assign 10 points here?!

Love the graspable example to illustrate the wandering/hunting way thinking works (not just math :-) )

I liked the idea of using a slideshow, that was very creative.

I know my vote might be biased (which vote is not?). Surely many people reviewed more entries than me, but from all those I read myself so far, this one was the best. It kept me engaged at all time. I realize this might be because of the nature of the presentation (i.e. it’s a puzzle you must try to solve), but the way you progress until we get the final solution, and you even explicitly say at the end that this was your thought process while solving yourself… It just feels natural.

There are two things that were a bit confusing for me.

The analogy of a computer spitting random numbers didn’t hit. It’s interesting but I don’t directly see why it’s helpful. I was confused as to what happens if the computer gives a random number it already gave before. Then you can think, OK, doesn’t matter, just give another one until it’s new. And then it’s confusing as if this can go on forever. I myself know this analogy is not necessary to solve the problem, since near the end I can tell that we just need to define a valid bijection ourselves, and I need nothing related to random numbers for that.

I understand by myself that a bomb not hitting for a particular choice of initial position and speed directly rules out that choice. However, I don’t really understand what memoryless means. I totally didn’t understand the definition you gave.

Anyway, overall, as I said, I really value that it was engaging and it presents math as a spontaneous, non-linear activity, where you have to figure out your own path. Thank you.

could make a smoother transition from describing the puzzle to defining bijections

Loved this puzzle as a motivation for studying countability!

Has a lot of potential - great problem to introduce countability with.

It would have been nice to emphasize beyond doubt why the search is guaranteed to work, and use that as motivation / reinforcement for the concept of countability. I wasn’t really sure what you meant by “memoryless” and the section on the “choose a random number” strategy seemed irrelevant. Also there are some grammatical errors.

Great simple explanation for cardinality and infinities. It also captures the maths exploration as a combination of “what if”s and trying random things that eventually fit together in some way.

i already knew the solution.. but very well explained the way we can compare two infinite sets using bijection also i loved the way you included the part of doing math as a fun story with twists and turns, a story that can be different for anyone going through the process

This was a clear explanation and nice, fun application of a mathematical principle. To make it better, you could use more graphics and show how this applies in the everyday activities or other applications.

This is an excellent discussion about infinity. I initially could not solve the puzzle but after going through the solution it made perfect sense.

I actually disagree with the use of the term “larger” with regards to infinity. I think you should stick to saying, one way map and two way map. And I had a big argument with everyone in the “logic and foundations” section on the Some discord.

But I find the topic of infinity very interesting and of course the presentation gave the official definition which is important for students.

Overall this is a fun and interesting way to present a difficult topic.