**Work in progress** You can convince yourself easily, that mate is only possible in a corner of the board. We distinguish four cases: - The corner is the same color as the bishop and the bishop mates - The corner is the same color as the bishop and a knight mates - The corner is the opposite color as the bishop and the bishop mates - The corner is the opposite color as the bishop and a knight mates For the following analysis we only consider unique positions that are not related by symmetry. Also we don't distinguish between similar positions of a bishop along a diagonal, if the same essential square(s) is covered. ---------- Starting with the first case, bishop same color as the corner and the bishop mates. There are 5 distinct (up to symmetry) mating positions: 1.1a to 1.1e. [![enter image description here][1]][1] Doing a retro-analysis for 1.1a and 1.1b: - White's last move was Bb7+ and the bishop came from c8 or a6. - Black's last move was Ka8 and the king came from b8 or a7. The king was not forced to go to the corner and could have escaped to c7 or b6 instead. Doing a retro-analysis for 1.1c, 1.1d and 1.1e: - White's last move was Be4+ and the bishop came from somewhere along the b1-h7 diagonal. - Black's last move was Ka8. If the king came from b8 or a7, it could have gone to b7 instead of the corner. If the king came from b7, it could have gone to (among others) c6 instead of the corner. So in conclusion, it is not possible to force a mate with the bishop in the corner of the bishop's color. [1]: https://i.sstatic.net/XvXzR.png