Impact of solving a Millenium Prize Problem [closed]

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I just learned about P vs NP and the Millenium Prize Problems.

I understand that one Grigory Perelman solved one of the problems but rejected the USD1m prize.

That made me wonder something:

Suppose a computer scientist discovered an algorithm to solve one of the remaining problems (to make it relevant to Stackoverflow, let's use the Travelling Salesman Problem as an example (TSP)) , would it not be wiser for him/her to patent the algorithm and retire rather than settle for that prize money? After all, solving one of maths' important questions should be a big deal.

Or does solving the problems have no useful purposes for the average people other than to advance maths? I doubt this is so because the TSP problem seems to have real-world benefit.

I would appreciate any enlightenment on this complexity (no pun intended) of human behavior.

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You'd have to publicly disclose the algorithm in order to patent it, so you might as well collect the prize money too. There's also the possibility that such a breakthrough could be theoretically significant, yet still intractable for all practical purposes. (E.g., a polynomial algorithm for some NP-complete problem is found, but the runtime is still O(n^100)...good luck monetizing that!)