To some, the Clay prizes spell a vulgarization of mathematics. There are better ways to use the money to foster mathematical research. The Clay Institute has allocated a portion of its income toward a variety of lesser prizes, grants, workshops, and so forth. These activities are certainly welcome, but will hardly cause a stir in the media. There are many important unsolved problems in mathematics.
Subjective judgment decides which problems are more likely to be fruitful in the long run.
No one at the beginning of the 20th century would have predicted that the most significant mathematical development of the century would be the digital computer, insofar as it has affected the lives of everyone on earth. Then there is the question of what constitutes a mathematical proof. Formalists, logicians think they know. But they don't, really. Consider, for example, the famous four color problem.