Have nuclear weapons resulted in world peace instead?

You are correct. Even nations who despise each other would not use nukes, nor the other outlawed weapons such as invisible nerve gas. Russia and America have large stockpiles of nuclear warheads. It's important that rogue nations like North Korea be kept in check diplomatically, because they have nukes.

The only concern is North Korea where the Dear Leader is seriously deranged and thinks he is invincible. He could make a mistake.

I think it's almost certain that they are the main reason we haven't had a world war since 1945.

No, not really, they've reduced the chances of a world war, where major countries around the world gang up against each other, but they haven't reduced the chances of regional wars. Soon after the last world war, WWII, we then immediately had the Korean War, Vietnam War, Russian Afghan War, American Afghan War, Lebanon, Israel-Arab wars, India-Pakistan wars, etc. So no, it hasn't done a thing to reduce wars.

This was the intention all along. I don't think any of those in charge of countries with a nuclear capability ever stockpiled with the intention of using them. For the most part, this has worked. But it only takes one mad-man to decide to start using their weapons, for all h*ll to break out. Which is why America tends to think only they can have such weapons because 'they can be trusted not to use them'. Yeah right.

So far Nuclear weapons have done what they are designed to do. they have kept the peace because those nations that have Nuclear weapons understand the concept of MAD ..(mutually assured destruction) meaning that if war breaks out between countries and nukes were to be used then neither country would win the war and both would be damaged to point of oblivion. Countries that do not have nuclear weapons , but want them seem the things differently, Iran for instance wants nuclear weapons so it can attack Israel.. North Korea wants nuclear weapons so it can attack south korea and japan and the USA.. hopefully they will learn that Nukes are there to stop war not start it.. if they don't then those nations will end up glowing with the embers of nuclear destruction.

No. They have merely shifted the fighting to proxy wars.

Well if you are talking about the countries who own nuclear bombs, yeah. However, owning such powerful weaponry results in the counties who own nuclear bombs potentially harm other weaker countries (look at the Middle East, very far from world peace right now)