What happened to mathematicians after solving their "career problem"?

Many mathematicians have dedicated a good part of their career towards solving a specific problem, whether directly or indirectly. Some examples on top of my head: Richard Hamilton and the Poincare conjecture Andrew Wiles and Fermat's last theorem Thomas Hales and the Kepler conjecture (proof and formal verification) And perhaps very recently: Diego Cordoba and the Navier-Stokes equations How did the careers and research-focus of these mathematicians shift after their career-problem was solved? Did anything particularly interesting happen?