I mean literal extinction in the long-term. The current mass extinction we are in most closely resembles the Permian-Triassic extinction which was caused by a runaway greenhouse effect acidifying the oceans and warming the atmosphere: https://en.wikipedia.org/wiki/Permian–Triassic_extinction_ev.... It wiped out 96% of known species at the time: https://phys.org/news/2018-09-end-permian-extinction-earth-s...

I don't know if you realize this or not, but humans are capable of living in entirely self-contained biodomes, outer space, and deep under the ocean for months at a time. Humans have invented nuclear energy, a nearly infinite energy source, along with countless other forms of electrical energy. Humans have perfected the science of agriculture and can even grow plants underground and even grow tropical plants in Canada. This is hyperbole. If you had to put the odds at humans going extinct, you'd have to place the odds at something like 1 in a trillion chance, short of an interstellar disaster or nuclear war.

I realize it- months don't really matter when we're talking about the survival of the human race. We have never produced a self-sustaining closed system. The space station, Biosphere 2, and not any of the other closed environments we have ever created managed to stay closed and succeed without outside intervention. We have invented nuclear energy, and then have chosen to not utilize it at scale. The other forms of electrical energy we have created are exactly the problem- we have now realized we were doomed the moment we built the first coal power stations and created this faustian bargain with our environment. We can grow tropical plants in Canada at a huge expense of energy and utilizing fertilizers produced by fossil fuels. This carbon-rich energy let us balloon our population so that now we can't just turn it off- we are stuck. It isn't hyperbole- the soil, the insects, and the marine life that sustain us are disappearing and we have no technology to survive without them.

If that were true, why wouldn't we be doing it now? You could feed the world from the Sahara.

The fact is that ecosystem management is incredibly important technology, absolutely required for things like Mars missions, planetary terraforming, and Not Killing Earth - and we do not have it yet.

Obviously there's more efficient farmland elsewhere that works better than the Sahara. Why would we do it now when we feed 7 billion people under the current system?

Define long-term. You could just as well say the universe will eventually collapse in on itself and that will cause extinction in the long-term. None of the species during the Permian-Triassic extinction knew about things like nuclear power plants etc.

Using Mark Lynas' book Six Degrees and the representative concentration pathways from the IPCC report long term for me is a century. The earliest we would see 5 degrees of warming would be around 2100 under RCP 8.5, the business-as-usual pathway. At that amount of warming we can expect a Cretaceous-like climate where methane eruptions destroy infrastructure in the northern hemisphere, super hurricanes flood the coasts, and hydrogen sulfide from the dead oceans suffocate terrestrial life. Of course, we likely are no longer on the business-as-usual pathway, we are taking some limited steps to mitigate climate change so I would say more likely long-term means 100-500 years, unless we significantly make changes to put us closer to the RCP 6.0 or RCP 4.5 pathways which are merely disastrous instead of fatal.