How will the world end?

Nuclear war despite the fearmongering is highly unlikely. Mutually assured destruction is a fate every country that is capable of creating nuclear warheads understands, it's more of a deterrent. Modern warfare between nuclear-capable countries is fought with ballistic missiles and footsoldiers. Much more likely to kill us all would be a global financial collapse (either due to great depression-like wealth gaps or climate change) and subsequent degradation of society or an outbreak of a rapidly evolving disease.