It's tempting to believe we are making real progress in getting rid of the things, but you shouldn't get your hopes too high.
The New Start treaty between the US and Russia sounds impressive, committing the two powers to reducing their deployed strategic nuclear weapons to 1550 each.
That's a 30% cut on what the two powers last agreed, in their 2002 treaty - but it's not as impressive as it seems, because most of their nuclear weapons are not deployed strategic ones.
The two countries have more than 8000 other nuclear warheads awaiting dismantlement, plus an unknown number of tactical warheads that are operationally available.
They admit to having about 2500, but those numbers are completely unverified and probably much lower than reality.
Unofficial estimates suggest Russia and the US really have at least 10,000 tactical nukes.
Add at least a thousand Chinese, British, French, Indian, Pakistani and Israeli nuclear warheads (plus a couple of North Korean ones that sort of work), and there are probably about 25,000 nuclear warheads around the world.
That's fewer than there were at the height of the Cold War, but it's still about one nuclear weapon for every 250,000 people on the planet.
With the right targeting pattern, therefore, you could still kill or maim almost everybody with the existing stock of nuclear weapons.
In practice, of course, they are targeted at particular countries that should expect a much denser concentration of explosions in case of war.
And the New Start treaty will eventually reduce that global total of nuclear weapons by only about 7%.
Besides, the US Senate will probably not ratify the treaty.
It takes a two-thirds Senate majority - 67 votes out of 100 - to ratify a treaty, but all 41 Republican senators have already said they will not support New Start.
Their pretext is a non-binding statement in the treaty that recognises a link between offensive missiles and ballistic missile defence, but in practice it's just Republican strategy to block every White House initiative.
President Barack Obama's commitment to a world that is ultimately free from nuclear weapons seems genuine, but his real strategy right now is not focused on the weapons of the existing nuclear weapons powers.
What he wants to do is strengthen the anti-proliferation regime, and for that he needed some symbolic movement towards nuclear disarmament from the US and Russia.
The problem with the NPT from the start was that the non-nuclear powers kept their promise not to develop nuclear weapons, while the great powers that already had them did not keep their parallel promise to get rid of them.
After 40 years of that, there is an understandable impatience among the non-nuclear majority, and New Start is the best piece of symbolism Mr Obama can come up with. It may not be enough.
Mr Obama clearly hoped the Washington summit of 47 countries this week would provide him with extra leverage at the major review conference on the NPT next month in New York.
He could use it to bring pressure on Iran, a signatory of the NPT that he suspects of working secretly on nuclear weapons.
But it turned out other countries wanted to bring up Israeli nuclear weapons, too.
Only four countries in the world have not signed and ratified the NPT. Three of them, India, Pakistan and North Korea, have openly developed and tested nuclear weapons.
The fourth, Israel, refuses to confirm or deny that it has nuclear weapons, but it is generally reckoned to have at least 200 of them, plus a variety of delivery vehicles.
For almost 50 years, Israel has got away with this creative ambiguity, but it was inevitable that it would be pressed to come clean if any other Middle Eastern country started working on nuclear weapons.
The sheer hypocrisy of turning a blind eye to Israel's nukes while condemning a country like Iran for allegedly seeking them too would become unsustainable. And so it has.
Egypt and Turkey are leading a campaign to have the Middle East declared a nuclear weapons-free zone.
Their real concern is Iran's putative nukes, but it is politically impossible for them to criticise Iran's ambitions while ignoring the reality of Israeli nuclear weapons, so they decided to bring them up in Washington.
As soon as Israeli Prime Minister Benjamin Netanyahu realised that was going to happen, he cancelled his plan to attend the conference and sent his deputy, Dan Meridor, to take the flak instead.
Mr Netanyahu is already in a bitter confrontation with Mr Obama over Jewish settlements in the occupied Palestinian territories.
It would not help to have him stonewalling on Israeli nuclear policy in Washington and personally sabotaging Mr Obama's attempt to strengthen the NPT treaty.
Better to have a subordinate do it instead. Mr Obama's initiative has not yet failed.
Subjects that have been taboo for decades are being openly discussed, and real progress on non-proliferation is becoming a possibility.
- Gwynne Dyer is a London-based independent journalist
