I am a senior studying math at a private research university. It isn't an Ivy League school by any means, but it is a good school with, as far as I have experienced, a good undergraduate mathematics department. I'm applying for a PhD at several top math programs, such as Berkeley, UCLA, and Michigan, along with some master's programs at top 25-40 schools. I have a pretty strong application - I have taken 12 graduate math classes in various topics, algebraic and differential geometry, algebraic and differential topology, algebra, measure theory, PDE, probability, and more, and done very well in all of them, with a 3.99 subject GPA and a 3.95 overall GPA. I have what I think will be two excellent letters of recommendation, and one good letter. I have three years of research experience, and while nothing has been published yet, my group thinks we might get something out by the end of the academic year.
Here's the problem. I took the math subject GRE in October, and just got back my score. I wasn't expecting to do great, as I didn't get much time to study, it has been a long time since I had used much of the content on the exam, especially the calculus, and I had to wake up at 5 in the morning and drive three hours to get to the test center. But when I got my score back, 600 (36th percentile), I was still a shocked. I didn't think it would be that low, and I know that with proper preparation, I would do far better. Is there anything I can do to "salvage" my applications in which I sent in that score? I already looked on the GRE website, and I cannot cancel the scores being sent. The next math subject test is available in April, long after applications are due. A 36th percentile score seems like the kind of thing that will get my applications immediately filtered out of consideration.
Is there anything I should do? I had the score sent to Berkeley, UCLA, and Michigan, as the other schools I applied to do not accept the subject test this year. I already turned in the Berkeley application, so I assume that it is probably a lost cause as I can't change anything with that now. For the other two, how do I go about addressing this low score? Should I mention it in the statement of purpose, or somewhere else? Is there something else I should do? I apologize for the rambling question, but I was stressed enough without this, and now I am in full panic mode. Thank you for any advice or suggestions.