I very nearly added a caveat about ideas in philosophy, politics, etc. The reason I didn't is because, really, those ideas don't actually change the world. People acting on them is how the world changes. In maths the discovery of something leads people to work on further discoveries - standing on the shoulders of giants as it were - so again it's the work that changes things. Ideas can definitely be a catalyst, but of themselves all that can be said is that they motivate people to change the world rather than change the world themselves.
Although, all that said, I've not given it a huge amount of thought. I could be wrong.
And even in math, its not as if the idea is all there is, and then boom, done. New math concepts take a significant amount of work as well, and the execution can be a significant factor as to whether the idea lays in obscurity, or is picked up and used by the wider body of the math community. There have been plenty of groundbreaking math concepts that were thought of, but nobody followed through to see whether they worked, what the implication were, or how they could be applied.
Although, all that said, I've not given it a huge amount of thought. I could be wrong.