Answer:
1. The reasons that Paul Morphy, clearly the premier player of his time, isn't considered officially a world champion is that the concept of a world champion existed at that time in only the most nebulous way, that there was no formal method of establishing a world championship and that Morphy never played anyone .
2. The current world champion is Magnus Carlsen of Norway. The first generally recognized world championship took place in 1886, when the two leading players in the world, Wilhelm Steinitz and Johannes Zukertort, played a match, which was won by Steinitz.
