That’s pretty broad. By eliminating Animal and Vegetable, you leave us with only Mineral, and, the earth being pretty big, it would take quite a while for a small human population to exhaust mineral wealth. Not that we’re not approaching it.
I think, as Quercus said, that you’re defining the problem away. The only resources people could use up before now were animal and vegetable. Tthere has always been a way to dig deeper or look fartyher, or extract more cleveerly mineral resources, but once a plant or animal has been eliminated from its habitat, it’s gone. And, as noted above, these are as much resources as minerals were, maybe more so in earlier times. And no one knew about conserving them earlier, or knew that they’d get used up. So the Aurochs and Moas and Aepyornis – essential food animals, all – disappeared.
Many people before Diamond have brought up the issue of the Easter Islanders cutting down all the trees and trapping themselves. (Heck, Larry Gonick used it as the opening for one of his Cartonn Guides over a decade ago).
Quercus’ tall pine trees are another example. Actually, not just tall pines. The British shipbuilding industry (combined with charcoal burners and grazing animal farming) used up all the tall pines (needed for ship masts) and oak (for structural elements), and by the early 19th century they were importing these from Scandinavia, or taking parts from old ships to build new ones (and often unconsciously transferring rot), or coming up with solutions like binding multiple trees together and “stepping” the masts. That prettyy much sounds like using up a resource, at least locally.
As I noted, we actually did use up many kinds of deposits of minerals, and it’s only our increasing technological sophistication that has enabled us to keep getting the ever-harder-to-reach materials. So gold and copper used to be available as nuggets, then hidden in ores. Then more sophisticated processes like cyanide were needed to get at them. Petroleum from oil shale is a lot harder to get at than pitch oozing up through open ground, but you don’t see a lot of that anymore.
I look at the notes about Nitrogen being used up and say “What!?” It’s 3/4 of the air. Even liquid nitrogen is cheaper on a liter by liter basis than soda. We may have come close to using up easily available nitrogen fertilizer (although I find that hard to believe), but not nitrogen itself.
Here’s a possibility for you – helium. As far as I know, it only occurs on earth trapped atop oil deposits in impermeable domes. It doesn’t combine chemically with anything (except under highly artificial circumstances) and, once released into the atmosphere, it goes up to the top, where it eventually picks up enough energy from collisions to be booted higher in the earth’s and the sun’s gravity wells. All the He used in Macy’s parades is effectively gone. And in your party balloons, too. But Helium is useful in ways nothing else is. You can achieve extremely low temperatures with helium refrigerators (down bnelow 15 K with an off-the-shelf version that has nothing special to it). Using dilution refrigerators and more exotic techniques you can get down well below 1 K. Nothing else really lets you get that low (hydrogen will probably let you get low, but it’s flammable, and you can’t build a hydrogen dilution refrigerator). And I suspect we’ll need to get to such cryogenic temperatures, even in an age of high Tc superconductors.
at one time the Dept. of Mines and universities made an effort to try and trap and recycle helium. We had such a system in my grad school. But even 20 years ago, no one was using it.