As beautiful as mountains are they are pretty useless productivity wise. How can they be engineered to be as productive as the plains and flat land that most nations owe their productivity to.
Terraces, Tunnels, gravity Transport:
Mountains, worthless? Perish the thought! But there will be some work involved, often fairly manual work. The good news is, there are definitely some serious energy advantages that can be gotten from being in the mountains. Ask the Swiss how worthless their mountains are.
- Gravity can be with you: The good news is, there are a variety of transport means that let you move things OUT of mountains fairly easily. Everything from a lumber sluice to an aqueduct relies on water flowing from high to low. Lowlands are at a disadvantage WITHOUT the mountains. And entire industrial processes have been based around things moving along cables. As long as the heaviest stuff is going down, not up, you have the advantage.
- Power: If you want to look to hydroelectric power, there isn't a better place than in the mountains. Almost by definition, you want some kind of geographical irregularity so a dam can trap the water. The classical reason is for water (which you then have hoarded up in abundance), but electrical power is hugely productive for all sorts of applications.
- Trees!: While lowlands have been denuded of trees over the years, the very slow movement in rough terrain means you have LOTS of trees growing in mountains. They're often bigger, sometimes harder, and you have them in abundance. A little good common-sense responsible harvesting at the front end and replanting at the back end will mean that the folks actually living in those mountains have trees to cut down in perpetuity.
- Mining: All that exposed rock means ready access to mineral wealth. On the plains, who knows what's beneath? You might have to dig hundreds of miles of tunnels (or have access to advanced geological surveys) to find the stuff. In the mountains, you can SEE it all laid out for you. You don't have to dig through a half mile of overburden to get to the good stuff.
- Terraces: The Inca are most famous for it, but lots of cultures have made irregular lands bloom by simply making little flat parts out of it. High mountain lakes give access to some really amazingly sophisticated irrigation systems even in the hands of "primitive" stone-age cultures. Modern industrial processes don't lend themselves as well to terraces, which is why you don't see vast mountain farmsteads today.
- Defense: All the resources in the world don't help you if the plains invaders march in and loot your settlements every year. A mountain settlement can be defended at a few chokepoints with a handful of men. A good mountain home in an old mine can even protect you from nuclear weapons, so your settlement may be protected no matter WHAT period you're living in. Control of mountain passes can mean you control trade along critical routes.
To me one obvious method to increase agricultural productivity of mountains would be terracing.
Here is a link to images of Inca argricultural terraces.
And terraces have been used in other parts of the world.
A non agricultural way to increase the productivity of mountains would be to dig more quarries and mines in them.