Asking for recommendation letters for math PhD applications
Many, if not most, successful PhD applicants in mathematics have no research experience, and even when an applicant does have "undergraduate research experience, " it's usually not worth much as an indication of talent. If the first three letters are from the same project, it's probably better to skip one of them and go with the course professor instead. Rank, or at least reputation, of the recommender does matter, but what's most important is what they have to say about you.