American wins $1 million math prize
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I haven't done research myself, but I've spent a fair amount of time around researchers in math and the basic sciences and my experience strongly suggests that the purpose of the Nobel etc, insofar as they have any, is not to advance the careers of the recipients (who don't need the help if they're deserving) or to drive the recipients to do better research (the consensus is that, if anything, earning a major prize dampens a researcher's potential, though of course that has selection bias written all over it); the purpose is really to give those researchers who've already reached the top of the playing field something to aspire to. (I used to think these prizes were net losses for science, but over time it's become clearer to me that the role they play is actually fairly important.)
All of this is to say: the actual distribution of prizes is more a necessary evil than anything, and delaying conferral to the end of a person's career minimizes the bad effects of a prize and maximizes the good ones.
The genesis of the rule that it be awarded only to mathematicians no older than forty is evidently the statement that “… while it was in recognition of work already done, it was at the same time intended to be an encouragement for further achievement on the part of the recipients and a stimulus to renewed effort on the part of others”.