What often happens to startups, is they begin with some exciting idea, and having looked into it/tried it, it doesn't pan out, and they "pivot" - sometimes slig

What often happens to startups, is they begin with some exciting idea, and having looked into it/tried it, it doesn't pan out, and they "pivot" - sometimes slightly, often wildly. I'm not sure how common this dynamic is in science and maths. Certainly, as you learn more, your ideas and concepts are inevitably refined. (Like: no plan survives contact with the enemy). But I don't know whether that "refinement" is too subtle to count as a "pivot". However, serendipity has a storied past in math and science.