> It's not simply throwing energy away into solving useless math problems; it's spending energy to create infrastructure.
But it is also an arms race of energy spent. And the more valuable BTC becomes, the more energy a rational agent will use to mine it. Unlike mining gold, BTC mining does not have a fixed cost.
Gold mining doesn't have a fixed cost either. Different locations have different costs per gram of mining and refining gold, and whether it is worthwhile or not to mine in a given location depends on the price of gold.
And the yields from mining have decreased by orders of magnitude over the last several decades as technology increases have made it more possible, while less efficient, to extract additional known deposits.
But it is also an arms race of energy spent. And the more valuable BTC becomes, the more energy a rational agent will use to mine it. Unlike mining gold, BTC mining does not have a fixed cost.