How are you defining the word “world”???
Since 1974 I have had a reasonable expectation of living a very long time, perhaps longer than the sun. If that happens, then oddly no, because if we get through the next 2 decades with exponential technology, then we should have established a sufficiently cooperative base to society that technology will allow us to manage the sun and any other threats posed to the earth itself or us.
Would anyone knowing me now, recognise me then? That is doubtful.
As automated technology allows us to deliver universal abundance of an expanding set of goods and services (including all those essential to human life and travel), then the world of scarcity and money will come to an end. So in that sense, the world as many know it now will end. And the world that emerges will be so much more secure, with greater freedom; that it will take many a while to adjust.
And all of that is predicated on most people actually realising that markets and money use a type of value that is based in scarcity, and cannot give a positive value to anything universally abundant (like oxygen in the air – arguably the most important thing to any of us, yet of no market value); so that sort of value really isn’t very useful in an age where automated machinery allows us to produce whatever is reasonably needed by anyone, anywhere.
Part of that process will be understanding that in evolutionary terms, all new levels of complexity are predicated on new levels of cooperation, and that is a relatively complex topic, with whole ecosystems of complexity within it at every level.
So the planet seems safe.
And we people seem to have a much better than even chance of living a very long time, with very high degrees of freedom; and getting such freedom will demand responsibility from each of us, and it will demand change (escape from the economic slavery of our current systems). And freedom without any boundaries always leads to destruction. All forms of complexity require boundaries, the more complex the system the more complex and flexible the boundaries need to be to sustain that form. We humans are the most complex thing we yet know of (AI is coming, but not quite up to our level yet), so we and our cultures have boundaries that must limit freedom if we are to survive – no logical way to escape that, ever! Freedom always demands responsibility if it is to survive, and such responsibility is always more complex and deeper than any set of rules can codify.
And within those limits reside infinite possibilities, so plenty of room for individual identity, creativity and diversity. No real chance of boredom. The earth is a big place, the solar system much larger, the galaxy much larger still.
And one of the responsibilities that all must accept with increased security is limits to family size. For most people, that will mean one child, if you and they want to stay on the earth.
I think there is a very good chance that the world will still be here in 10 billion years time, and just maybe some of us will still be around someplace nearby, provided we can get past the idea that evolution is all about competition, and that competitive markets are of general benefit to people. Neither of those ideas is anywhere near reality, and the belief held by many in both currently generates existential level risk, and both are extremely complex topics.