Mathematics:

It will require either,
1)Using fewer resources per person
2)Discovering more resources
or3)Reducing the number of people.

1) is only a bandaid, as they can only be reduced by so much.
2) is highly problomatic, and has finite limits.
3) seems to be the only solution, but would require Draconian measures currently abhorrent to much of the world.

What many fail to realize is that 1 AND 2 will happen, if not voluntarily, then automatically...and it won't be pretty.