This video discusses András Máthé's 2006 solution to the famous Angel problem, first described by John Conway in 1982. I encourage viewers to pause if needed, as this proof makes a fair few sharp turns and mental leaps that can take time to appreciate!

The Angel problem went unsolved for 24 years till 4 independent, different proofs appeared in 2006. I gloss over certain minor details/special cases to smoothen the discussion, but the full paper is linked below for anyone who wishes to delve deeper!

Note: as Nicky Case pointed out to me, I forgot to specify something of importance. In the section which counts squares, from 9:05 onwards, we are interested in the burnt squares enclosed within the painted region, rather than all burnt squares. The amount in this connected family is what the quantity 's' refers to, and is what allows the argument to work -- indeed the 'point' of the green paint is precisely to define that region. Apologies for any confusion caused, and hats off to those who noticed!

· Máthé's paper: https://homepages.warwick.ac.uk/~masi...
· Conway's article, where he discusses various counterstrategies: http://library.msri.org/books/Book29/...

Video made using the Python package manim.