I am currently an undergraduate student taking an Honours Pure Mathematics degree with an additional major in Astrophysics and I plan to go to a good graduate school (as good as I can get into) for Pure Mathematics to research either Geometric Topology or Convex Geometry.
I know that academia is a cut-throat world where only "the best" end up on top and the ability to get a professorship is becoming harder and harder as time goes on. I enjoy Pure Mathematics and Theoretical Physics and would not want to do anything else with my life just because I could not do anything else since I find them too damn interesting. What I do not enjoy is the grade-driven-here-is-the-next-thing-for-the-exam learning that doesn't give anyone the big picture. I have been working non-stop to make sure I perform in my courses, undergraduate research, etc. and I am just wondering if there is any way to learn about these topics at a slower pace or just have more time to think about the topics eventually. I understand I will have to at least get through graduate school and get a PhD (otherwise there would be a chance I'd turn out as a crackpot), but I'm just really tired of having so much information crammed into me without having the time to think about what I am learning. I want to do my own additional research on topics I see connections between, and think more about the big picture of how the different fields of Pure Mathematics and Theoretical Physics are related. There are so many unfinished papers that I have started throughout my undergraduate on embeddings of low-dimensional manifolds, determining knot invariants by unique methods, etc. but I just have no time to think about what I want to think about when there's that Real Analysis assignment due the day after my midterm in E&M which I had to stay up all night studying for because I had three quizzes the previous week in blah blah blah blah... for years on end.
Essentially, my question is this: Is there any other way that someone (after getting a PhD or a few post-docs) can do research at their own pace and just completely go after their interests without having to justify what they are doing to funding agencies, being swamped with administrative work (such as marking exams and writing grants), etc.?
I know that is asking a lot out for a life style, but I would even be interested in leaving academia altogether to just do my own independent study somewhere and travel around to different universities to collaborate whenever I have new findings or need some new inspiration or ideas. Are there any easy part-time jobs one could do to support such a lifestyle? Julian Barbour would be someone who I look up to in that respect, I believe he did this exact thing by making a living translating Russian academic papers into English.
Any comments, helpful suggestions, about how it would be possible to live an non-traditional academic lifestyle where people still take you to be credible and you can publish your work in journals. I just want to avoid working working working my entire life without a chance to reflect and then just die.
It may not be necessary to wait until you've reached the end stages of your career to have time to explore your research.
If you are able to get fellowships to fund your graduate career—or to find a suitably understanding advisor—then it may be possible to "slow down" your graduate career. In such a case, you'd be able to handle things at your own pace (within reason). That's how I managed to take my time doing my Ph.D., and it allowed me to work on problems I was interested in, rather than other problems.
Similar funding does exist at the professional level, such as "named" fellowships at the US Department of Energy (DOE) laboratories, and through grants like the MacArthur Fellowship (also known as the "genius grant"). It is certainly not easy and straightforward to do, but it could be a way to get the freedom to work without additional responsibilities.
Outside of academia, I don't think the situation improves much. For instance, at the DOE laboratories, you're only able to pursue your own research if you're able to secure your own funding to do so (or have moved so far up the chain that you are a laboratory "fellow," and can do what you want). Similarly, in industrial research institutes, I suspect similar issues apply (you might not have to worry about writing grants the same way you do in academia, but you'll still be expected to "justify your existence" on a fairly regular basis.