A young person’s guide to the Hopf fibration

I enjoyed this recent arXiv post by Zack Treisman, apparently notes for a summer course for high school students he taught. It leads a beginning mathematician by discovery through the basics of arithmetic of complex numbers, higher dimensional geometry, a word or two on knot theory, and then onto the main topic: the Hopf fibration. I wish someone had told me about these things when I was in high school.

Thanks to several beautiful illustrations by Lun-Yi Tsai and Zack’s charming writing style, it is fun to flip through for mathematicians who are already familiar with these ideas as well. I hope Zack and Lun-Yi make a coffee table book one day.

Hopf