I'm not so sure. I agree we will eventually reach a point where the global birth rate (and later population) goes down, but I don't think we're close to it yet. I suspect we'll hit 8 or 9 Billion before we start to shrink back again.
And if we continue to extend the average age, then we may never shrink in numbers (barring a major catastrophe or mass-migration).
That would be a very interesting outcome. It seems rare that things that grow exponentially just level off at some point (I'm thinking of economic bubbles), or even slowly decline. I'd be happy with anything but a massive collapse.
And if we continue to extend the average age, then we may never shrink in numbers (barring a major catastrophe or mass-migration).