For me, it is not really very much of an option. I want to be a mathematician. I want to be able to interact with other mathematicians and I need to be able to present my ideas in such a way that they are taken seriously by other mathematicians so that they might bear some fruit.
In order for this to really be possible, I need to enter the world of academia. Some of my specific interests are such that they may or may not be of direct value to a company(I have a greater interest in theory than application, but theory has to come before application), though I have an interest in certain areas of applied math.
In order to achieve my goals, I realized I needed to do certain things, one of them being making myself as knowledgable about math as I could; so I did, and continue to do, just that. I have studied and gone from basic high school algebra when I was a senior in high school, to being the only sophomore in the upper level abstract algebra class, to taking independent study classes this fall as a junior, and soon will be taking graduate level classes(in the winter). I read mathematics texts in my free time. I am currently reading up on Category theory, commutative algebra and mathematical logic, all graduate level material.
Why can I do this? I'm 19 and I'm pretty good at math. I'm passionate about my studies. I have a strong desire to know more. All of these play large roles, but mostly its because I live with my parents who have money so I don't need to provide for myself. My focus can be entirely on academics, so I can stay a safe distance ahead of the curve on math and still pursue my other academic interests and still have time to hang out with friends. I have no real responsibilities, beyond doing well enough as an undergrad to secure a position as a TA so I don't have to pay for grad school.
Now, I could have been like the fellow who lived with his mom in her car during high school, worked hard and got a perfect score on his SAT and a full scholarship to Harvard had I been in that situation. In fact, one reason why I did not put forth much effort during high school was because I knew if I kept up a decent gpa(I was a B student) I could still go to college, because I did not need a scholarship to afford it. I have always had my academic passions, but they were never addressed in my schooling; hence I always viewed school as a distraction from my efforts towards self improvment, even as an undergrad. The main difference now there are exceptions to the rule, there are some truly interesting classes, and I can deal with the few silly Gen eds.
This is my position. I have strong natural abilities, combined with resources, and a desire to pursue a field that generally has both of those as prerequisites. I was lucky, I have a passions and talents (in art and music as well as mathematics) and I can pursue them freely. I take full advantage of my situation, but I recognize and accomplish what I need to do to get to where I want to be. A high level of formal education is a prerequisite to getting to where I want to be. So is making connections with my professors so that I can get good letters of reccomendation for grad school, and not to mention get their insight on any mathematical quandries I might run into. These are all part of the path I need to take to get to my desired destination.