I took the math subject GRE in 2010, two years before I got my bachelor's degree. I hadn't taken Complex Variables or Topology or even Linear Algebra. Right before the exam, I quit school for the fourth time. I had not prepared at all, I was depressed with suicidal tendencies, and I stopped working every time the proctor walked by.
I got a 680 (58th percentile).
My school told me they were disappointed and hoped I would do better, but I got into their Ph. D. program anyway because they didn't even require subject GRE scores (definitely not an Ivy League school).
So, seven years later, I have a master's degree. My life is stable. I got a Ph. D. level pass on the qualifying exams. I definitely know a lot more math. I've published a paper proving something conjectured in another paper. I wanted to take the math subject GRE again to prove I could do better. I spent months preparing. I went over all the material for hours a day. I did tons of exercises. I took timed practice exams, acing the old, easy tests, and getting 90+ percentile scores on the rescaled practice tests (mostly arithmetic errors), which I guess are still easy.
Scores just came in this morning: 720 (64th percentile).
So, how can my proficiency in Mathematics increase so much, while my math subject GRE score has increased so little? What exactly is the math subject GRE exam measuring? And most importantly, how do I get it?