I really like these diagrams, as an answer to your question: http://matt.might.net/articles/phd-school-in-pictures/ http://matt.might.net/articles/phd-school-in

I really like these diagrams, as an answer to your question: http://matt.might.net/articles/phd-school-in-pictures/ http://matt.might.net/articles/phd-school-in-pictures/ You can't predict breakthroughs. A scientist might spend their entire career following their research to a dead end. That's not a failure, in my opinion. It just shows how much we already know, and I think we should honour those scientists just as much as the lucky ones.