I did not see this mentioned so far, so I'll suggest that perhaps older mathematicians are more inclined to offer statements of solvable problems to their stude

I did not see this mentioned so far, so I'll suggest that perhaps older mathematicians are more inclined to offer statements of solvable problems to their students and colleagues rather than jumping in and trying to knock it out all by themselves. (And after all, simply setting up a problem in a form that points to a plausible solution is at least half the battle.) Surely by the time they reach 50, mathematicians will have the experience to know that mathematics is a collaborative field, and that working alone to get ahead is the less efficient tactic for proving theorems. Some of the most productive mathematicians seem to work with armies of graduate students, and even though an older mathematician may be at the height of their abilities, they will likely be even better at stating unsolved problems that just need more eyeballs.