Comment by abetusk

Be careful to differentiate working on important problems and being paid to work on important problems. I've heard (though I can't find any sources) that one of the reasons Einstein took the job at the patent office was because it was such a low effort job that he had time to work on his more important ideas.

Also note that some of the major breakthroughs in the past decade or two have been by mathematicians and scientists that are outside of the "system" (Grigori Perelman, Yitang Zhang (though maybe he's not as much of an outsider)). Maybe a bit outdated but Riemann and Galois also fall into that category.