How old are you? 78% percentile of what demographic?
But more importantly, why are you in mathematics in the first place? What's your motivation for being there? From an effective altruism standpoint I don't see academic math or physics a very valuable field.
I think it's much better to take the skills you learned in math and then go into some field like biology, engineering or programming and actually apply the knowledge to important real world problems.
That said when it comes again to math skills I'm not sure whether tests measure the right thing. Contributions to math as a field are not done in a few hours. They are done by working focused on a problem for days, weeks and months. That needs certain skills.
There also the model that advancing the field is basically about knowing a bunch of techniques and a bunch of problems. If you are the only person who knows a certain mathematical technique and a certain mathematical problem that's solvable with that technique you advance the field.
That means it's very much about your ability to spend a lot of time learning complex mathematical techniques. It's more about endurance than about solving a bunch of problems in the time span of a test.
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).
Don't make the mistake of assuming that the work you do when you learn a field is the same as the job in the field.
While university classes on programming might involve memorizing fluuf that's not about what working as a programmer is about. Trying to understand how baldy documented legacy code or API work is something different than solving mathematical problems but it's also a highly intellectual challenge. Designing software architecture is also highly intellectual.
I think it's much better to take the skills you learned in math and then go into some field like biology, engineering or programming and actually apply the knowledge to important real world problems.
+1
For example, psychology is too important to be left to the sort of people who typically become psychologists in my opinion.
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.