I have sort of an off-the-beaten path story, so I'll play.
I went through my high school years as a rather pugnacious delinquent -- always in trouble, fighting all the time etc. I ended up getting involved with people similar to me and things only got worse. I had never passed a math course with more than a D in my life. This continued for about two years after high school, and I was making money doing assorted odd jobs and sometimes criminal activities.
I was always "philosophical", though. And I say that with quotations because I typically wouldn't describe myself in such a manner, but others have and do. I usually say that I just liked to read. Even though I spent my time on the street, I always was interested in writings about power, (anti)religion, struggle, the human condition etc... And it was my later readings that led me to want for a better life. Once I made the decision to "get out" I spent about 6 months trying to clean up the messes I had made out of my life.
Then, I met a girl. She served as extra motivation to stay on track and I was given a job at a warehouse moving bathtubs by her father. I spent about 6 months there until winter time came and I was laid off. Out of work, I decided I was ready to take school seriously and enrolled in an associates degree program for computer networking. I took to college very well and loved learning. After I graduated I became interested in science and enrolled in a bachelors program for molecular bio. My first semester out I had a calc I class and on the first day I can remember all the students jabbering about how the Prof. was the worst in the school and how hard he was and all that usual stuff. Than he came in and started teaching -- but unlike anything I'd seen before. He was showing us mathematics by doing proofs. I was totally enamored and intrigued. I spent all my time going through the calc book and realized that I didn't care nearly as much about bio as I did about my calculus. I took calc II, and loved it even more. I had this great Prof. again, he was a young guy just out of grad school and he wouldn't teach us like the other prof., but he agreed to show me a select amount of proofs and theorems and work with me during his office hours and it was just awesome. My school didn't have a mathematics major, only a minor. So, I took calc III and spent the semester trying to figure out a way to break it to my parents that I was going to transfer to
study mathematics on what i knew they would deem as a whim.
I finished the semester and transferred to university as a math major, did pretty well my first year out and was enticed into a combined BA/MA program. I'm currently taking a mixture of undergrad and grad courses and absolutely loving every moment of it.
The moral of this obscenely long story is that I probably still can't do long division, yet when I saw the logic that proof based mathematics provides, something just clicked. If I hadn't, who knows where I'd have been. Another noteworthy point is the very radical perspectives I have now. I can remember being in my first classes as university and the class was filled with people who were math whizzes in high school, and to be honest, most of them struggled with topics like set theory and logic (which was, in my school, the first introduction to proof-based maths). I didn't have this problem, simply because I was never a good math student before. It just put a really interesting spin on things for me. I was very lucky, more than a few times in my life; I made a plethora of bad decisions, and (knock on wood) was able to recover from them. That's something that I can't explain. I had four close friends growing up. Two are dead, one's in prison and one has 3 kids with 3 women and a job as a boat yard. And here I am, studying mathematics at university. I'm damn lucky, if you ask me.