Science and math are a repeating story of civilization-level of knowledge reaching a threshold at which some breakthroughs become easy to figure out, followed by a bunch of smart people making those breakthroughs simultaneously.

I.e. the famous scientists were not that smart - they were just the smartest and therefore first to react to the waterline of knowledge in their domain rising high enough.

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.