To be honest, I understand the decisions made. My recs were good but not great. The main weakness in my application was a poor grade in Analysis, I suspect, and a general lack of grad-level classes. My overall math GPA was 3.8, but I guess it wasn't enough to overcome one bad semester.
For top 10 programs, it's probably a bit of a long shot. Perhaps I'm just jaded from my experience but my stats:
Math major from a top 10 undergrad with 3.72 GPA
Perfect 170 on quant of the general GRE and a respectable 164 on the verbal
800 (81%+) on the Math subject test GRE
Have a bit of research experience with one publication as second author and a senior thesis
I was rejected across the board and will probably be attending a Masters program. I hate to play the race card card but being an Asian male didn't help my cause. Being DWF may be helpful, but it's far from a free pass: you'll still need to be qualified.
How high? Probably not to be honest, though, at least at top schools. I have a 170 Q and 800 (81%) subject test, and at this point, it's likely that I won't have any offers. I did my undergrad in math at a top 10 undergrad and got a 3.72 GPA, too. A poor grade in Analysis and lack of grad-level coursework probably raised a few red flags about my app.
I'm looking to apply to top Math/CS programs next fall. I just got back my GRE scores.
VR: 164 (93%)
QR: 170 (99%)
AW: 4.0 (49%)
I get the impression that they are mostly used as a cutoff. I am mainly concerned about the AW score. Is it too low? I could probably stand to bring my VR score up as well since I was scoring 165+ on practice tests, but it's probably high enough already that it doesn't matter.