# Alternating Group

In this post, I want to try to give a mostly-visual proof of an exercise I found in Dixon's book "Problems in Group Theory":

Show that the alternating group A4 has no subgroup of order 6.

I recently saw a video by Michael Penn https://youtube.com/c/MichaelPennMath that explained Cayley's theorem in #grouptheory very nicely and in a way that was very clear to me.

On the other hand, I recently saw a video on the same topic by Richard Borcherds https://youtu.be/AZUDhtnz-Do that explained it in a more abstract way and resonated less well with me. I then wondered why my reception was so different?

While I do like Borcherds' lecture videos in general, I guess that this particular one had a much less clear page layout or flow of thought. It was mixing in too many side tracks. And Penn's black board was very nicely structured in this case.

This also made it again clear to me how individual different people's learning journeys in #math are.

# Groups of order 4

The other day, I wanted to explore all finite groups of low order. This is something that has already nicely been done by the Group Explorer project and in the great Group Theory lectures by Richard Borcherds. I wanted to look into this myself and just started by producing multiplication tables of the first small groups. This always feels a bit like doing a Sudoku to me.

# Creativity

I have written before about creativity and I've thought and read about it a bit recently. There are 2 main things that I have recently discovered: First, the idea that quantity leads to quality. I read this article on Austin Kleon's blog (which I think I found via Matt Ragland's newsletter. This idea is as simple as it is evident, the more you practice, the better you get. But as trivial as it sounds, it is also non-trivial at the same time.