The Burau representation of the braid group is faithful for n = 4

Also https://www.yahoo.com/news/science/articles/99-old-mathemati.... Someone who has been at this problem for 60 years.

Birman still dropping bangers at 100 is quite something. We knew 3 strands is faithful and it was assumed 4 must be true but the ramifications of this in the face of quantum computing will be really fun going forward.