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I am currently an undergrad looking to apply for pure math PhD programs sometime in the future. The thing is, I do not wish to apply for grad program right after graduation but want to work in the industry a few years after graduation.

I am wondering (1) If general GRE test scores matter so much for math PhD applications, (2) how much fo math GRE test scores matter, and (3) up to how many past years' score would be counted, i.e. do some grad school admissions say that they require GRE scores "in the last 4 years" or else you have to take it again.

My question is not intended to garner answers related to whether or not it would be a good strategy to apply few years after graduating instead of applying for it right after graduation. I have already thought deeply about my life and what I want to do. Thank you.

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I suggest that you take the exams during your final year or soon thereafter. The advanced (subject) test is quite difficult and you will probably forget quite a lot (and lose your edge) if you delay too long.

Best to take it when you are fresh, IMO.

And don't be shocked if you think you've done poorly when you finish it. Wait for the scores. The test is very broad - broader than most undergraduate curricula can cover. This is to account for the different focus at different institutions.

You can retake it later if you feel the need, of course.

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From the ETS website, they will report your GRE scores for up to 5 years from your test date.

The other two questions about the relevance of GRE scores to PhD admissions are institution specific and will vary broadly (wildly?).

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