But it should be recognized that obsessive devotion to a single problem can destroy a professional career. An example, based on the experience of a real-life mathematician, can be found in mathematician and film maker Apostolos Doxiadis's novel Uncle Petros and Goldbach's Conjecture. Large prizes feed right into the star system, which is now endemic and getting worse. They emphasize the individuals and not the accomplishments as such. Large prizes underline commercial values.
Theorems can become commodities.
The heros they bring forth will be one part Tiger Woods and one part Sammy Glick. The Fermat problem was solved only recently, almost a century after the announcement of Wolfskehl's prize. The competitive aspects of prizes can lead to publicly expressed acrimony. I know of three, perhaps four, serious instances of it during the years of my professional career. Recall that the Trojan war was begun because of the decision of a prize contest.