One of classical music's great mysteries is J.S. Bach's unfinished piece in The Art of the Fugue musical work; specifically the Fuga a 3 Soggetti piece which ends rather abruptly . Probably many authors, artists or composers leave unfinished work before they're ready to meet their maker, but what leaves this specific unfinished work even more puzzling is that the author, J.S. Bach, finished it with the musical motif B-A-C-H (B♭–A–C–B♮ is the english notation). Did Bach intentionally leave his name as the last motif just so he can laugh in his grave while we, centuries later, still squeeze our minds thinking about it? Hard to say, but it did indeed inspire many composers after him to try to finish the work, more than 80 attempts in fact [ 1 ]. Since Bach is famous for his mathematical precision in composition, this blog will approach completing the fugue as a mathematical puzzle to solve. I will take a probabilistic approach using Markov chains, try state of the art AI ...