Earlier quoted context omitted.
The last 70 or so years have been the most peaceful in human history. How? The American military and economic hegemony. If you want peace, build more aircraft carriers.
Correlation causation
When nukes came into play, the consequences of violating the peace became too much for any sane state to countenance. The US used nuclear superiority to take on the role of global leviathan.
Despite missteps, it used its monopoly on violence as a very big stick that's allowed for a very lengthy peace. If certain idiot regimes keep playing stupid games, we're going to see what happens when the nuclear stick gets used, unfortunately. That might ensure a century or so of peace, if everything doesn't die.