Where do great ideas come from?

As a mathematician, most of what constitutes my work is having new ideas and then formalize them and write them down so that they can be shared among other people. An idea per se is a very abstract object. Sometimes it can be a very simple concept but the details to talk about it might make it look very complicated.
When we do recognize great ideas, maybe from a book, from a paper or from talking to someone, we feel that spark of genius in it. The question comes often. Where do great ideas come from? Well, I wished more of that was taught in class. We attend tens of classes in college and graduate school but the only thing we learn is about other people ideas and not about the process that lead them to develop them. Learning this might be a very painful process.
In general, the person that is supposed to teach you that should be your advisor. Although your advisor might not be good at that or simple might not realize the importance of teaching that. Or maybe for every person is different and it is just not something that can be taught. To some extent, you have to find your own way.
My advisor told me that his way to come up with something interesting. When he was in graduate school he was at looking at data and examples and trying to figure out what you could do or might want to do with it. Many papers he wrote came out of this process. So he decided to do the same with me. Mainly, he gave me large datasets and told me to go and play.
Yes, to play, because playing is were ideas come out from. And playing also means to have fun because if you are not having fun then you are not playing.
And indeed I have been playing recently with this massive dataset of genotype data from nine related individuals and this week I feel I really nailed down a cool idea. Now it will take at least two weeks to shape an algorithm to make it work and probably at least a month to write a paper about it and hopefully convince other people about how cool it is.
I spent today a lot of time trying to find out papers through Google scholar that might relate to what just came to my mind but I couldn't find any, yet. That makes me really excited since it motivates me even more to pursue this 100%. But ultimately, in my case, where this idea came from and why has nobody thought about it before?
I have spent many weeks now looking at the data over and over again, seeing what information was lying there, testing algorithms, seeing how they run and why they don't run well sometimes. Confusion added up to confusion until I realized that there was a simple solution lying ahead. Well, simple as compared to the level of mess that had been building up in my head recently. Now my goal is to share with other people and I guess they will judge how simple it is. All ideas look simple to the person that first thinks of them.
Now I have got to go. I feel like I have found my little gold mine and there is a lot of work to do. In this case it also means that there is a lot of fun to go through. I haven't been so excited since the days when I realized that my polynomial factoring algorithm was factoring some special kind of polynomials faster than any other algorithm ever devised for that purpose. I am feeling that my office is the place where the most exciting stuff is going on, even if there is just me there. With my little dream that I might put down something interesting and there might be smart people willing to listen to me because I have something smart to say.
I have known myself for a quite awhile now. That, basically, is really all that I want.