dasgut wrote:Do you think most profs would tell you if they're going to write you a lukewarm reference? Wouldn't they just refuse to write it?
Generally, I think you're right. I think it takes a specific kind of avoidant/non-confrontational personality to sabotage a student with a blah letter without at least hinting that they should look elsewhere for a reference. To be honest, most professors I've had in math-related fields seem to be on the other end of that spectrum of awkward: extremely blunt with no effort to deliver bad news gently. Of course, you would know better than anyone here what the deal is with your letter writers.
Speculatively, what might be a more common issue is accidentally lukewarm references. Surely some well-intentioned professors end up emphasizing strengths and research interests that turn out not to be a good match for particular departments, especially if they are writing one letter for a diverse set of programs or if you have changed paths significantly since you last worked with them. Another possibility is that someone's idea of a glowing recommendation might end up not reading compellingly if they aren't a strong writer or just said generic nice things.
But, in your case, I think you're stressing about this unnecessarily. Per the profiles, Yale thought you were an interesting enough applicant to interview, so your references must have come across pretty well to them, right? If there were any issues raised in the letters that they wanted more info on, they would have dug into those specifically during the interview, so you would have gotten some hints as to any yellow/red flags. Whatever the situation, I think you should enjoy the rest of your weekend! Do your best not to have panic attacks and second-guess things out of your control while waiting to hear from the crazy number of places you applied to.