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human
[The Hobbit] How were the dwarves of Erebor able to mine so much gold? How is this geologically possible?

Erebor is an extremely wealthy kingdom, and from the vast amount of gold seen in its vaults, it looks like Erebor may have managed to accumulate more gold than has ever been mined throughout all of human history and human civilization. 

Estimates of all of the gold cumulatively mined through all of human history put the total sum of gold at around a 20m cube. A cube 20m on every side made out of solid gold.

The dwarves of Erebor appear to have outdone this entirely for one single statue. Just one statue (the casting mold was built but gold had not yet been poured when Smaug attacked) is probably of similar volume to a cube 20m on each side. And again, that is just one single statue. Just one. The vaults of other gold items are in addition to that.

This is a lot of gold, but the dwarves of Erebor appear to have either matched or exceeded the sum total of all gold mined by all of human history, and the dwarves did this with just one city. Total population of Erebor likely does not exceed 100,000 at most. Yes, the interior volume of a mountain is vast, but dwarves need food. You can't grow food underground.

The town of Dale is Erebor's trading post, and foodstuffs are likely purchased with gold to keep the dwarves fed. However there is only so much food that can be carted on wagons. This food can only support a finite population.

So it comes down to Erebor has a small population, likely no more than 100,00 at very most, and yet appears to have matched or even exceeded the gold mining efforts of billions of humans over thousands of years. And not for lack of effort either. Gold is extremely prized amongst humans. Dwarves and humans both share the same greed for gold.

How were so few dwarves able to mine so much gold in such a short amount of time, from just one single area?

What is the geology of Erebor? How is it possible that such rich gold veins can exist in rock?
gpt
Do not make the mistake of assuming that Arda has the same amount of minerals as our Earth. It could very easily have more gold and diamonds than we're used to. That, and the dwarven mines are more vast and go deeper than any human gold mine has done. Another thing to keep in mind is that the mine in Erebor was established in 1999 of the Third Age, Smaug didn't take over for nearly eight hundred years! 2770, to be exact.

And you can easily grow food underground. Fungus, livestock, rats, fish, all of these are perfectly edible and can be grown underground without too much difficulty. Especially if you've had centuries to figure out methods! Why, just look at Dwarf Fortress for inspiration there.

And, finally and most importantly, the Dwarven Kings ruling the Lonely Mountain possessed one of the Seven Rings of Power. These made them exceedingly greedy, but! It allowed them to multiply what they had mined and amplified their skills. Gold breeds gold, in the case of the Dwarven Rings.