View from the faculty POV: I taught mathematics as an Assistant Professor at Harvard for five years (2000-2005), and this advice seems wrong. It’s very generic and abstract, whereas the actual mathematics department (students, faculty, preceptors) at Harvard at any point in time is made up of real people, most of whom are really interesting fun and genuine math loving human beings. I guided dozens of students in seminars, interesting math research projects, and much more, and many of them really benefited from the environment and went on to truly love mathematics as a long term career.