Result of solving an unsolved problem? I know that when some of the previously unsolved problems were solved they created new fields in mathematics. May someone explain to me what would be the result of a major problem like the Hodge Conjecture being solved vs a "smaller" problem like "Do quasiperfect numbers exist?" in today's society.
Thank you in advance.

Most of the time, the actual result isn't important as the theory. The reason why problems are unsolved is because either the math doesn't exist yet, or some connection between current fields has not been established yet. 
Either way, creating new math and connecting existing math are the real reasons why solving open problems is important. 
For example, if the word of god came down and told us that yes, indeed the Hodge conjecture was true/false, it would be nice but not nearly as groundbreaking as a proof for it.
