Most of the world's nuclear capability was split between the US and Russia, and the umbrella of American protection meant that its allies didn't have to develop nukes of their own.

That appears to be changing.

President Trump has famously been less hawkish about standing up to Russia.

Now, the European Union is reportedly considering a nuclear deterrent of its own, in sharing France's weapons between member countries.

The situation in Asia is even more unsettled.

North Korea is fanatically pursuing its own arsenal of nuclear-tipped ballistic missiles.

On Monday, it test-launched four of the rockets into the ocean, just 200 miles shy of Japan.

And the American President has unconventional ideas about how Japan should prepare:

North Korea has nukes. Japan has a problem with that.

I mean, they have a big problem with that.

Maybe they would, in fact, be better off if they defend themselves from North Korea. Maybe we would be better off— - With nukes?

Including with nukes, yes.

All of this has experts worried about an era of renewed nuclear threat, from jittery states and rogue actors who might seize on the instability.

Among those sounding the alarm is William Perry, who served as Secretary of Defense under President Clinton.

Bill Perry has spent most of his life watching the world prepare for nuclear war, and he thinks we aren't nearly as scared as we should be.

I think the professionals in the field have a pretty good understanding of the impact of the use of nuclear weapons.

But the general public, to me, does not.

And many of our leaders do not.

Perry is 89 years old.

He lectures at Stanford, launched an online seminar last year and travels the world two or three months a year to talk about how close we've come to catastrophe and how close we still are.

He often talks about his "nightmare scenario," where a small amount of enriched uranium ends up in the hands of a terrorists group.

If they had maybe 40 kilograms, they could make an improvised nuclear bomb.

But what would be the consequences?

The consequences of a 15-kiloton bomb would be Hiroshima.

And besides the 80,000, 100,000 casualties, the social, the political, and the economic consequences are just really hard to believe.

How realistic is this, though? Isn't this just some sci-fi fantasy fear?

I think, of all of the nuclear catastrophes that could happen, this is the most probable.

I think, I would say it's probably an even chance this will happen sometime in the next ten years.

An even chance?

Even chance. Sometime in the next ten years.

You may desperately want to dismiss Perry as an alarmist, but he's a renowned expert, often called upon by world leaders.

I met him in Mexico City, where he was attending the celebration of a 50-year-old nuclear ban treaty,

and running a closed-door planning meeting for top nuclear proliferation experts from around the world, known as the "Group of Eminent Persons."

They made us turn off the camera.

The truth is, the chance of a nuclear war is not what it once was.

In the late '80s, there were 70,000 nukes around the world.

Today, there are only about 15,000.

But Perry is not comforted by better odds.

We have the possibility of a regional nuclear war, between Pakistan and India, for example.

Even if they used only half of their nuclear arsenal, those bombs would put enough smoke in the air, and enough dust in the air,

that'll go up and settle into the stratosphere, and then distribute itself around the planet.

It would block the rays of the sun for years to come.

There could be millions of people who die from that alone.

That's a horrific vision. Does it keep you up at night?

The one that really keeps me up at night is the one which is not as probable.

And that is that, somehow, Russia and the United States blunder into a nuclear war.

An all-out general nuclear war, between the United States and Russia, would mean no less than the end of civilization.

That's not being dramatic. That's not being hyperbolic. That's just what would happen.

Today, Russia and the US have 90% of the world's remaining nukes, many of them (are) old, and prone to error, and false alarm.

And they're in the hands of leaders who Perry sees as having cavalier attitudes about their potential.

Are there things you see with President Trump that concern you?

Yes. I think, unlike President Obama, he doesn't have a clear understanding of what the nuclear issues are and what the nuclear dangers are.

Secondly, I think he's demonstrated an impulsive temperament.

The first of them is solvable, we can learn more, if he cares to do it.

The temperament issue, I'm afraid, is... is just there.

And that's why, at the age of almost 90, you're here in Mexico City and not on a golf course.

Exactly right.

One person can only do so much, and I think I can do more than most.

You can scare us better than most.

I can scare you. You deserve to be scared!