What does the subject GRE measure? 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?
 A: I know this is an old question, and excuse me for what some might consider an overly pessimistic attitude, but:
The GRE is measuring your ability to take the GRE. ETS is a private institution whose interested in maintaining the nigh forced purchasing of their product. To quote a comment in this thread:

More bluntly, it's a self-perpetuating racket by ETS who makes a bloody fortune on useless testing and selling "preparation materials" to train the subjects of their supposedly valid testing methods. Deductive logic test: if the GRE is a measure of inherent qualities, then preparation should not significantly affect a subject's score.
Ⓐ True
Ⓑ False
Ⓒ Either way, ETS makes more money

A: Please check your implicit assumptions. It is an assumption that any test score "measures" some objectively knowable quantity in a statistical sense. For example, the claim that "IQ" tests measure intelligence. At best, there is a positive correlation between such test scores and abilities that would be considered signs of intelligence. The best measure is behaving intelligently no matter what test scores indicate. The real question is "what do you want to do and why?" and only you can answer that for yourself. One good use of tests is what you did by taking practice tests and see where you are missing abilities. They can show where you can try do better.
If your goal is to increase your mathematics proficiency, then you are on the right path. Use the tests to highlight weaknesses, but don't mistake good test scores for good proficiency. They are only positively correlated. It all depends on the actual test. A bad test can be useless. Finally, don't mistake "school mathematics" for real mathematics. It is an easy mistake to make until you have a lot of experience with real mathematics.
