With Kate leaving, Vincent is forced to pick up the pieces of what she left. He tries to find her for two months before he gives up. She ran away from him and he's left heart broken and devastated. He didn't know what happened before she ran - what caused her to leave. Vincent stays in depression for another two months before he finds a letter. A letter from Kate. It didn't state where she was or why she left. She didn't even write it for him. Though what it said caused him to jump back on the track of finding her. Of solving the puzzle she left for everyone.