Spending tax dollars specifically to "mine" the "asteroid belt" has got to be the dumbest thing I've ever heard.
Where did I say anything about "spending tax dollars"? Like all colonization in human history, colonization only works if there is some economic incentive for it. There is no economic incentive going to Mars, no matter how many tax dollars you spend.
If you only depend on economic investment to drive basic science, then scientific advancement would come to a dead stop. You can only obtain that money via national investment; through politicians that can sell to their taxpaying voters its money worth spending on something that may not give a certain return on profit.
The Apollo program was not pursued primarily for scientific advancement. It was a gov't subsidization program for the aerospace industry, so they could attract more talented minds to an industry primarily there to develop more accurate, reliable nuclear weapon delivery systems. Apollo was the snowjob sold to the American people, to convince them to spend 10% of the GNP towards sending SPAM to the Moon, in the name of science. (See how the real world works?)
The lesson here is to sell the taxpayer to spend their tax dollars to send Man to Mars. Then spend even more money to colonize Mars. The payoff? A nicer place to live (after 10 billion people living in civilization's metabolic waste make Earth a lot less nicer place to live), and the guarantee that humanity can survive a cosmic catastrophe.
There is an economic incentive to mine asteroids.
Its only a pipedream for government bureaucrats with a science background. There's nothing out in the asteroid belts which we can't mine on Earth (or Mars). Even if it were, the cost to use rockets & maintain miners in space long enough to extract the minerals would cost more than the rare minerals mined. And even if it were the case, I'd still not have any interest in paying money so the Koch Brothers can get richer. Let them spend the billions of dollars to develop the technology. They're the ones profiting from it.
Well, if you believe that, then going to Mars is the wrong thing to do. Mars is a dead end, just like the moon was.
Mars is anything but a dead end.
1) Its far away enough from Earth to survive a disaster that ends life on Earth.
2) Mars probably has enough gravity to avoid the debilitating physical deterioration caused by long term zero gravity.
3) Mars has H2O and probably enough O2 to make a colony self sustaining (not so with the Moon).
4) Mars is big enough to have something worth mining.
5) If you can make it on Mars, you can make it anywhere in space.