Political and social chaos has been with us for a very long time. Given the revolutions of the past and present, class warfare, and scheming of those seeking power, the human race has shown a remarkable resilience and managed to survive thus far.
The new factors in the equation of the balance of mankind and the rest of nature are the technological advances that have changed how political and social chaos can develop, and the advances in industry that have the potential to inflict serious environmental alterations. Threats of nuclear war, biological catastrophe, and climate change now bring into question as to how humanity can continue to survive.
Personally, I think that with the growth of true threats to survival, there has been growth of human ingenuity as well. We have yet to release a Frankenstein's monster of technology upon the world. Despite the stockpiles of nuclear weapons, there has been no global warfare. Medical research is in a renaissance of advance. Climate change remains a concern, but I believe that we are an adaptable species, as we have adapted before and will again.
The larger question is how will humanity survive, which is what is asked. It's very likely that the resources of today may no longer be available in a century. But consider the resources available today that were not available a century before. As stated before, we are an adaptable species, and when one window of resources closes, it's likely that other windows will be openable.
Of course, the speed that everything progresses at has increased. Will we be able to adapt in time? Perhaps not for a lot of us, but consider that in the 14th century, the Black Death wiped out over a third of Europe's population. Yet Europe survived and prospered. We may again have a catastophe that has similarly devestating effects, but I feel confident that after the catastrophe, humankind will prosper.
Why do I place this faith in humanity? Because I must. Without the belief that we will continue to grow and overcome the pains of social chaos as we mature as a species, we might as well not have any faith at all. I'm not talking religion (although that may or may not be a part in its current forms), but simply the same belief that we will survive just as much as the sun will rise the next day.
Just what I believe.