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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?

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    $\begingroup$ it's mostly multivariate calculus and then some somewhat obscure but elementary things picked from various fields: number theory, topology, probability, partial differential equations, abstract algebra, etc. You can spend your whole life mastering a very particular field, say frames for Hilbert spaces and their applications, or shallow water waves, or elliptic curves, and never progress past some 'low' percentile in the subject test. It is a test which covers a broad swath of material that most people only need to know part of. $\endgroup$ – Tony S.F. Oct 13 '17 at 12:48
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    $\begingroup$ Not an answer since I don't know anything about that exam. My question: why bother? You seem to be on track to doing real mathematics at a level appropriate for you. Maybe if you'd spent that exam preparation time on your research you'd have published another paper or two. $\endgroup$ – Ethan Bolker Oct 13 '17 at 12:48
  • $\begingroup$ @EthanBolker there is nothing wrong with wanting to achieve a goal you set for yourself, i.e. in this case the OP wanted to do well to prove to themselves that they could do better (stated in the post). Life is not just about writing papers, you could use the same argument you just made to say, "why would any mathematician want to do X?" where X does not contribute to their research. $\endgroup$ – Tony S.F. Oct 13 '17 at 12:50
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    $\begingroup$ @TonyS.F. Why isn't the analogy instead 'Why do people who are professional pianists do something piano related that doesn't help towards improving their professional career in piano?' ? It would be like a professional mathematician seeing if they can ace a secondary maths exam final because they scored low in their secondary maths exam final. $\endgroup$ – BCLC Aug 30 '18 at 12:23
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    $\begingroup$ @BCLC the generality of allowing non professional things encompasses the case when the hobby is slightly related to the profession. Sure, if it makes it more clear for you then consider the question "Why do some professional pianists learn about woodwork and carpentry and piano making?". The answer is still the same, though. $\endgroup$ – Tony S.F. Aug 30 '18 at 12:31
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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

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  • $\begingroup$ AmagicalFishy, your post seems to refer to GRE general. Does your post refer also to GRE subject? $\endgroup$ – BCLC Aug 28 '18 at 6:48
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    $\begingroup$ @BCLC Yes, it does (unless there's some significant difference between the physics and mathematics subject tests, and other subject tests). $\endgroup$ – AmagicalFishy Aug 28 '18 at 13:18
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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.

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  • $\begingroup$ Did you perhaps mean 'but don't mistake bad test scores for bad proficiency' ? Idk, I think good test scores would indicate good proficiency. Just not vice-versa $\endgroup$ – BCLC Aug 28 '18 at 14:46

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