Scientific advances and inventions are

only based on luck.

often rejected, inventions leading from them proven to be fraudulent.

often developed gradually, building on previous advances.

things that must occur quickly.

I can already say it's not option 1 nor 4 as these go against everything science is. I'd say it's option 3 since it takes a bit and though yes they can be rejected, many scientists build off another individual studying the same material for a lead on where they should look. I hope this works for you and I'm not wrong. It's just that option 3 is most understandable in my mind with common sense of previous schooling.