Watchmaking is a dying art, but more people than ever want a wildly expensive and complicated watch. With a new Manhattan school, Patek Philippe is trying to bridge that divide.Inside the Manhattan workshop where the most complicated, expensive, and shouted-out-in-rap-songs watches in the world are serviced, everyone is wearing white Crocs. 31 pairs of the sanitary ur-ugly shoe are tucked away underneath desks where Patek Philippe’s platoon of watchmakers are hunched over, toiling away on one of the 10,000 pieces that pass through the workshop annually—either for routine servicing or because it was taken to another repair shop that used a paper clip in place of an actual part. Through a door in the back is a smaller room with a projector at the front of it and six sweet-faced, enthusiastic men mostly in their early 20s. They comprise the entire current class of Patek Philippe’s watchmaking program, which the brand built and offers to students for free.