And the compromise is to study economics.
A similar strategy worked successfully for my friend. As a student, he was very enthusiastic about math and programming, but a big part of that was influence of his friends, me included. Later he saw evidence that he was in these topics, let's say, above average, but not great enough. (He would be able to write simple programs, and he would get the job, but the more complex parts would be too abstract for him.) He tried studying informatics, and dropped out.
So he switched to economics, choosing some study that also included maths. Hanging out with different kinds of people he discovered he had good social skills (he didn't notice that while hanging out with nerds). These days he is a consultant, and his specialization could be described as applying database tools to examine or improve economical stats of companies. (Imagine a huge company which has a lot of data in dozen different systems, including Excel sheets; those systems are not connected, they don't even use a similar structure, and the company actually doesn't even know which divisions or products are profitable. So my friend comes, and uses different tools to connect all those data sources together, and then creates easy-to-read reports. Which is not as easy as it seems, because those data sources describe the data differently, so he must examine the underlying territory to understand what can be connected with what. Also he must reduce all the available information into cca seven very simple graphs, so that even the most stupid managers could understand that easily.) So, he has some IT things there, enough to make him feel happy for living his dream of working in IT, but no lambda calculus or anything like that. On the other hand, travelling and debating with clients is okay for his extraverted nature.
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.