There are reasons to be cautious – of course there are – but let us recognise that historic change is under way in Iran. To enumerate the reasons to be cautious, we know that Hassan Rouhani, the new President, stands an uncertain distance away from wielding the ultimate power of decision in Iran, and that the most powerful person remains Ayatollah Khamenei, the Supreme Leader.
We know Mr Rouhani's expressions of goodwill towards Jews, expressed unexpectedly on Twitter, may not mean that Iran is about to accept Israel's right to exist. We know that "Ahmadinejad set the bar very low", as Ali Ansari, the director of the Institute of Iranian Studies at St Andrew's University, put it: any change of president was likely to be for the better. And we know that Iran's rulers continue to sponsor terrorist and sectarian forces in Syria, Iraq, Lebanon and elsewhere.
But this is a big moment. The presidents of the United States and of Iran have spoken for the first time. The Iranian government has said that it wants to talk about its nuclear programme in the hope of lifting economic sanctions that are now having a serious effect. The economic crisis, which has pushed inflation up to 40 per cent and unemployment to 20 per cent, is probably the driving force behind Mr Rouhani's new approach.
If this is the case, it would be worth noting that it was not the threat of military action that brought Mr Rouhani to the phone. The US President has been criticised by American hawks for his weak and inconsistent foreign policy, but we should be grateful that the counsels of patience prevailed over his intention to launch punitive strikes against Assad's regime in Syria at the start of this month. President Obama should have learned that the bellicosity of his predecessor served only to inflame the nationalism and anti-Americanism that gave the theological conservatives in Iran their authority.
We should also praise Baroness Ashton, the European Union's foreign affairs representative, who kept the nuclear talks going through a long period of Iranian intransigence.
That what Mr Rouhani is attempting is real and difficult was shown by yesterday's protest that greeted him at Tehran airport on his return from the United Nations in New York. There were only about 60 people throwing shoes and shouting "Death to America" and "Death to Israel", outnumbered by 200 of Mr Rouhani's supporters, but the ideology of the Islamic revolution is still strong.
Iran, which could be a rich, highly educated country and a force for good in the region, is still in the grip of a backward-looking ideology that immiserates its people and threatens its neighbours. As we report today, Iran has the world's highest rate of execution by stoning. But it also has a new generation of young people who hope for a better life.
We should welcome the shift in Iranian attitudes, which Mr Rouhani represents if the response on social media to his new approach is to be believed, away from a foreign policy based on the question: will this annoy the Americans?
But it was President Obama's hand extended in friendship that meant this shift could yield results. He took the risk of looking foolish when he sought a meeting with Mr Rouhani, which was refused. But now he has a great prize in sight. Rapprochement with Iran could be as important as Richard Nixon's with China 41 years ago.