It's not about discovering new materials, or technologies, or physical phenomena.
It's about exploring new social contracts. Here on Earth we are stuck with whatever social arrangements we've developed over the millennia, we can tweak here and there, but we can't start with a blank slate.
For me this would be the grand prize: figuring out better ways for people to live together.
When America was a frontier, this exploration yielded significant fruits...
This is a nice idea if the frontier is accessible by foot, horse, or boat.
If the frontier is accessible only via corporate-owned spaceship, then the frontier will inevitably be a corporate-owned dictatorship.
The (hypothetical) colonists would develop loyalty to their own silly, strictly hierarchical government that was imposed on them. (For some strange reason, many Americans still have loyalty to a 200 year old document. And others have loyalty to 2000 year old documents.) As usual, some people will benefit greatly from the hierarchy and fight to the death to preserve it. Some other people might fight to the death to overthrow it. Perhaps they'll have a civil war, which likely won't end well for anyone, given that survival on Mars would be tenuous in the very best of circumstances.
Note that "terrorism" on Mars could be an extinction-level event for colonists.
Not to mention, if the Mars colonists get uppity, then Earth can send a fleet of warships to put down the rebellion. Hell, Earth could just launch unmanned missile strikes at Mars. Wipe the slate clean and start over.
If things eventually do escalate to interplanetary warfare, Mars has the significant advantage of having a much shallower gravity well. It's much cheaper for them to send missiles to Earth than vice versa, so perhaps the MAD threat will be enough to keep them safe.
Have you seen [gestures broadly] the world? People are people regardless of where you put them. There's no reason to believe that Mars will magically become a political paradise, simply because it's a long distance away from here.
> Mars has the significant advantage of having a much shallower gravity well.
But vastly fewer people, vastly smaller manufacturing base, and vastly more difficult living conditions.
Obviously it won't be a paradise. But the natural environment will select for hard-working individuals with grit, determination, and community spirit.
What do you mean by this?
Natural selection AKA "survival of the fittest" only works over the course of thousands or millions of years. Otherwise, Mars would be pretty much stuck with whatever people it (hypothetically) had. Especially if you're talking about a colony that decides to make itself independent of Earth.
On Earth, we can be selective of who we would (hypothetically) send to Mars. But wouldn't we select loyalists to ourselves? Unless... we make Mars a penal colony. ;-)
Also, "community spirit" can mean obedience to the strict existing hierarchy, for the preservation of the community.
The initial group of settlers will self-select themselves; not many of us are willing to live in such harsh conditions.
Kids that grow up in this environment are likely to develop grit and cooperative spirit, and they will see first-hand how it is necessary just to survive.
Alternatively, they may grow up dispirited and disillusioned, because they had no choice in the matter. Maybe they'll want to leave Mars and go to Earth. Or maybe they'll just be pissed off and lazy, wanting to watch the world burn, so to speak.
If you want to keep the kids in line, you'd better have a totalitarian government that restricts their access to information, to prevent them from discovering that life on Earth is so much better than their own miserable lives.
"Mommy, I want to go outside and play!" "Sorry honey, but outside will kill you. Now eat your manufactured nutrient packs and drink your recycled urine."