How much should Western complacency be blamed for this stunning revival? Quite a bit. Mr Obama was too eager to cut and run from Iraq. He is at risk of repeating the mistake in Afghanistan. America has been over-reliant on drone strikes to “decapitate” al-Qaeda groups: the previous defence secretary, Leon Panetta, even foolishly talked of defeating the network by killing just 10-20 leaders in Pakistan, Yemen and Somalia. The general perception of America’s waning appetite for engagement in the Middle East, underlined by Mr Obama’s reluctance to support the moderate Syrian opposition in any useful way has been damaging as well.

A second question is how much of a threat a resurgent al-Qaeda now poses to the West. The recently popular notion that, give or take the odd home-grown “lone wolf”, today’s violent jihadists are really interested only in fighting local battles now looks mistaken. Some of the foreign fighters in Syria will be killed. Others will be happy to return to a quieter life in Europe or America. But a significant proportion will take their training, experience and contacts home, keen to use all three when the call comes, as it surely will. There is little doubt too that Westerners working or living in regions where jihadism is strong will be doing so at greater risk than ever.

The final question is whether anything can be done to reverse the tide once again. The answer is surely yes. When Mr Bush declared his “war on terror”, his aim was the removal of regimes that sponsored terrorism. Today, the emphasis should be supporting weak (and sometimes unsavoury) governments in Yemen, Somalia, Iraq, Libya, Mali, Niger and elsewhere that are trying to fight al-Qaeda. Even Kenya and Nigeria could do with more help. That does not mean a heavy bootprint on the ground, but assistance in intelligence, logistics and even special forces and air support. Most of all, it means more help to train local security forces, to modernise administrations and to stabilise often frail economies.

The most dismaying aspect of al-Qaeda’s revival is the extent to which its pernicious ideology, now aided by the failures of the Arab spring, continues to spread through madrassas and mosques and jihadist websites and television channels.