This happened when I was 12 years old. I was trying to solve a problem at a mathematical contest which involved proving some identity with the nth powers of 5 and 7. I recall thinking vaguely "if you go to n+1 what is added in the left hand side is also in the right hand side" and so I discovered mathematical induction. In ten minutes I had a rigorous proof. Though, I didn't find it so convincing, so I ended with an unsure-of-myself comment "Hence, it is also valid for 3, 4, 5, 6 and so on..."

When I was in high school, creationism seemed unsatisfying in the sense of a Deus Ex Machina narrative (I often wonder how theists reconcile the contradiction between the feeling of religious wonder and the feeling of disappointment when facing Deus Ex Machina endings). The evolution "story" fascinated me with its slow and semi-random progression over billions of years. I guess this was my first taste of reductionism. (This is also an example of how optimizing for interestingness instead of truth has led me to the correct answer.)