Peak oil assumes the price p of oil is a function of the supply s of oil: i.e. p = f(s). It doesn't really account for the fact that as the price of oil increa

Peak oil assumes the price p of oil is a function of the supply s of oil: i.e. p = f(s). It doesn't really account for the fact that as the price of oil increases, people get a lot more innovative at finding new supplies of oil. In other words, s is not some constant, but itself some other function, at the minimum dependent on p: s = g(p). Therefore, p = f(g(p)). Lo and behold, we have a way more complex relationship between price and supply than some naively assume. The fact that the earth has a finite amount of petroleum is irrefutable. Whether or not that matters on any "real" timescale is up for debate.