Summer of Math Exposition

I liked the idea to relate set theory and Mersenne prime to this “silly” concept of duck numbers. It’s the perfect excuse to talk about deeper mathematics.

First, I liked the presentation, the editing is really good.

However, the motivation seems lacking. While it’s perfectly fine to sometimes ponder silly topics out of curiosity this particular video simply didn’t click with me for trying to shoehorn a false premise.

Honestly outstanding video. Cool topic, awesome style. You went through the process of refining a mathematical statement, and tied it into a larger picture at the end. Bravo!

This was honestly too esoteric for me. I was actually served this video as a recommendation on YouTube before being given it here to vote on. I just… couldn’t understand what a Duck number was after watching this, and I’m afraid that was the entire point of the video. And I do enjoy the odd question from absurdity. Such questions often are counter to strongly held beliefs and refuting such absurd questions helps us solidify our understanding. But I can’t see that here. Even the idea of further refining what a duck number is feels more like moving the goal post rather than creating a convincing definition of the term. I’m fully willing to admit this is outside of my understanding of number theory. Really good production value, obviously you have good mastery of the topic, it feels novel to me, but I just don’t think I walked away saying “I learned something”

Idea is good, but presentation is hard to follow

The connection to Mersenne primes did surprise me.

Throughout much of the video, I was a bit confused what theorem we were talking about because, as you say at the end, the definition “a number that has a zero in it” is a vague definition. So when you said that it’s proven that every number is a duck number, I didn’t know in what sense every number was a duck number.

I feel like the meat if the video was the part about which numbers have 0s in any base, but this was also misleading because, if I understand correctly, the “duck number theorem” is not a theorem here but a conjecture.

There was some really cool math here, but the introduction could have made it more clear that we would be exploring different senses of what “contains a zero” can mean, rather than showing a specific well-defined theorem.

Fun video!