It takes more than two speeches to overcome decades of enmity. Yet this week President Barack Obama and Hassan Rouhani, his Iranian counterpart, offered the most hopeful signs to date that the crisis over Iran’s nuclear capability might still be resolved by diplomacy rather than force.

In his speech to the UN General Assembly, Mr Rouhani declared Iran was ready to engage “immediately in time-limited, results-oriented talks” aimed at removing mutual suspicion through “full transparency”. Mr Obama, for his part, acknowledged the Iranian right to “peaceful nuclear energy”. Mr Rouhani’s speech was in many ways a restatement of the traditional Iranian position, hostile to US influence. But the subtext suggests there is now a possibility of establishing a working relationship between the US and Iran.

Mr Rouhani’s election has been the catalyst for the thaw. Gestures are being made which were unimaginable a year ago when tensions were at their peak. Even Ali Khamenei, Iran’s supreme leader, has called for “heroic flexibility” in talks.