I’m not sure. These lists of open problems definitely contain stuff we would like to know, but it’s not like mathematicians were spending their entire time after the millennium problems, say. For example, in the past 15-20 years there have been several breakthroughs in fluid PDEs, I think the area has been reignited by the connection with convex integration found by De Lellis and Szekelyhidi. This is why lots of people were thinking about the millenium problem on Navier-Stokes, it seemed ripe for solution. But the reality is that mathematicians has been pursuing research directions in a more creative and unstructured way than any problem list has ever captured. This idea that math is a list of problems to be solved and then we are done belongs very much to non-mathematical circles