<p>I just took the October Math GRE Subject exam and I really didn't do as well as I wanted to. I probably got a 65% score, around that range give or take 5% in either way. I wouldn't be surprised if I get a 50 or 55% score just to be brutally honest. I'm horrendous with these ETS tests. I didn't do so great on the SAT either.</p>
<p>I was thinking about applying to 3 top 10 schools, 3 really good schools and 10 "midrange" schools along with a few safeties. I know this is a lot of schools to apply to, but I have saved up enough money to pay for all the apps, GRE scores, etc.</p>
<p>I have good research experience, I am currently almost done with a paper on an open problem where I did a LOT of the work and most of the proofs. Actually, I did almost all the proofs. The only thing my professor did was guide me and tell me what assumptions or proven facts I could use. But I really did do a lot of the work and my professor definitely sees is this way as well. The professor I am working with a very famous in his field, and the problem I solved was an open problem he listed on one of his papers.</p>
<p>Would a publication make up for the bad GRE Math score? I will have good to really good letters of recommendation, I have a good GPA (3.8 on a 4 scale), I have taken a wide range of math courses and I have also an honors thesis on a mathematical physics topic and a technical report from an REU I attended. One of my recommenders is very famous, but I haven't been lighting the world on fire with my independent study with him. However, I think I am just being very tough on myself and he is a very kind man. And I also have a month left to impress him.</p>
<p>Where do you guys think I should apply for Math PhD, given my profile?</p>