We've all had that moment as children when we realized something about the physical world (or mathematics, that also counts) based on our own experience and thinking, even when it is the most trivial, basic stuff. Those moments are like little "discoveries", and are, I believe, very special and important. It's the first time we realize we don't have to be told something to learn it, and they inspire us to think more critically. So, what are some of your own such experiences? To me, I think the first thing was realizing what bubbles are. Yes, very basic, but as a preschooler, I didn't realize that they were just air inside water. After that, I think it was the realization that when you rotated say a pencil or a marker, the end that is further from the point that you rotate it covers a greater distance than the points that are closer to where you rotate it, and it does so in the same time, so it moves faster. In maths, the earliest thing I can remember was when I observed that the difference of the squares of two successive natural numbers is the sum of these numbers, followed by the observation that the difference of the squares of any two natural numbers is actually the sum of the numbers multiplied by their difference. I didn't know algebra back then, so I didn't prove it, but when we eventually learned the identity a^2-b^2=(a+b)(a-b), it all came back to me, and I have to say it felt pretty good!