You took the GREs cold. I'm surprised you did half as well as you did. Why? Because anyone who is not mentally handicaped can pay tutor a large sum of money, do exactly what the tutor says, and get a perfect score. I'm not exagerating -- I have friends who tutor in this business, and every year they sit for the GRE as a requirement for their job, and get a perfect score. It's a teachable skill, and one which has very little to do with the subject matter.
Now consider that most of the other people who took the GRE knew about this weakness. Especially internationally in places like China and India where (1) there are a lot of test takers, (2) a much larger test prep industry, and (3) massive incentives to do well (so as to get into an American or European university). Now keeping all that in mind, you still scored better than 72 / 68 percent of the competition despite having absolutely no preparation whatsoever.
Why are you not congratulating yourself?
I'm not convinced this is a good argument. You're certainly over-stating how teachable the GRE is, and I have a least anecdotal evidence of lots of people who scored above 90% on the general GRE quantitative section without tutors. This includes at least one person who "took it cold." Maybe those are super exceptional folks, but I think the statement that most of the people scoring in the top 30% had tutors is a really strong statement. I have worked for a test prep agency before and there aren't a lot of top tier students in those classes, and i...
I'm sorry if this is the wrong place for this, but I'm kind of trying to find a turning point in my life.
I've been told repeatedly that I have a talent for math, or science (by qualified people). And I seem to be intelligent enough to understand large parts of math and physics. But I don't know if I'm intelligent enough to make a meaningful contribution to math or physics.
Lately I've been particularly sad, since my score on the quantitative general GRE, and potentially, the Math subject test aren't "outstanding". They are certainly okay (official 78 percentile, unofficial 68 percentile respectively). But that is "barely qualified" for a top 50 math program.
Given that I think these scores are likely correlated with my IQ (they seem to roughly predict my GPA so far 3.5, math and physics major), I worry that I'm getting clues that maybe I should "give up".
This would be painful for me to accept if true, I care very deeply about inference and nature. It would be nice if I could have a job in this, but the standard career path seems to be telling me "maybe?"
When do you throw in the towel? How do you measure your own intelligence? I've already "given up" once before and tried programming, but the average actual problem was too easy relative to the intellectual work (memorizing technical fluuf). And other engineering disciplines seem similar. Is there a compromise somewhere, or do I just need to grow up?
classes:
For what it's worth, the classes I've taken include Real and Complex Analysis, Algebra, Differential geometry, Quantum Mechanics, Mechanics, and others. And most of my GPA is burned by Algebra and 3rd term Quantum specifically. But part of my worry, is that somebody who is going to do well, would never get burned by courses like this. But I'm not really sure. It seems like one should fail sometimes, but rarely standard assessments.
Edit:
Thank you all for your thoughts, you are a very warm community. I'll give more specific thoughts tomorrow. For what it's worth, I'll be 24 next month.
Double Edit:
Thank you all for your thoughts and suggestions. I think I will tentatively work towards an applied Mathematics PHD. It isn't so important that the school you get into is in the top ten, and there will be lots of opportunities to work on a variety of interesting important problems (throughout my life). Plus, after the PHD, transitioning into industry can be reasonably easy. It seems to make a fair bit of sense given my interests, background, and ability.