I’ve just uploaded to youtube a video I made with Katie Steckles to demonstrate why zero-knowledge protocols exist and how one works.
Katie is a habitual liar, so we followed the zero-knowledge protocol described in the paper, “Cryptographic and Physical Zero-Knowledge Proof Systems for Solutions of Sudoku Puzzles” which you can download from http://www.mit.edu/~rothblum/papers/sudoku.pdf
By following this protocol, Katie can prove that she isn’t lying to me about being able to solve the puzzle, without revealing anything about how she solved it.
The paper I mentioned, “How to explain zero-knowledge protocols to your children” is an excellent explanation of the ideas behind zero-knowledge proof.
Inspirations is a short movie by Cristóbal Vila, inspired by the work of MC Escher. While it isn’t particularly great considered purely as a work of art, it could be considered as an excellent advertisement for maths. It’s jam-packed with references not just to Escher pieces but to all sorts of famous mathematical art and ideas. I think it would take a lot of careful pausing and looking to find all the references.