Bornu is a very poor state, however, and his preaching gave him enough of a following among the poor and ignorant to make him a political threat to the established order. So hundreds of his followers were killed in a huge military and police attack on the movement in 2009, and Mohammed Yusuf himself was murdered while in police custody.
That was what triggered Boko Haram's terrorist campaign.
Its attacks grew rapidly: by early last year Boko Haram had killed 700 people in dozens of attacks against military, police, government and media organisations and against the Christian minorities living in northern Nigeria. So last March Nigeria's President, Goodluck Jonathan, promised that the security forces would end the insurgency by June. But the death toll just kept climbing.
In September, an official told the Guardian newspaper, "There is no sense that the Government has a real grip. The situation is not remotely under control."
Last week alone, six people died in an attack on a church on Christmas Day, seven were killed in Maiduguri, the capital of Bornu state, on December 27 and 15 Christians were abducted and murdered, mostly by slitting their throats, in a town near Maiduguri on December 28.
President Jonathan's response was to visit a Christian church on Sunday and congratulate the security forces on preventing many more attacks during Christmas week: "Although we still recorded some incidents, the extent of attacks which [Boko Haram] planned was not allowed to be executed."
If this is what success looks like, Nigeria is in very deep trouble.
Part of the reason is the "security forces", which are corrupt, incompetent, and brutal. In the murderous rampages that are their common response to Boko Haram's attacks, they have probably killed more innocent people than the terrorists, and have certainly stolen more property.
But it is the Government that raises, trains and pays these security forces, and even in a continent where many countries have problems with the professionalism of the army and police, Nigeria's are in a class by themselves. That is ultimately because its politicians are also in a class by themselves. There are some honest and serious men and women among them, but as a group they are spectacularly cynical and self-serving.
One reason is Nigeria's oil: 100 million Nigerians, two-thirds of the population, live on less than a dollar a day, but there is a lot of oil money around to steal, and politics is the best way to steal it.
Another is the country's tribal, regional and religious divisions, which are extreme even by African standards. In the mainly Muslim north, 70 per cent of the population lives below the poverty line; in the mostly Christian south, only half do.
Now add a ruthless Islamist terrorist group to the mix, and stir. Boko Haram's support does not just come from a tiny minority of religious fanatics and from grieving and angry people turned against the Government by the brutality of the security forces. It also comes from a huge pool of unemployed and demoralised young men who have no hope of doing anything meaningful with their lives.
Democracy has not transformed politics dramatically anywhere in Nigeria, but the deficit is worst in the north, where the traditional rulers protected their power by making alliances with politicians who appealed to the population's Islamic sentiments.
That's why all the northern states introduced sharia law around the turn of the century: to stave off popular demands for more far-reaching reforms.
But that solution is now failing, for the cynical politicians who became Islamist merely for tactical reasons are being outflanked by genuine fanatics who reject not only science and religious freedom but democracy itself.
Nigeria only has an Islamist terrorist problem at the moment, mostly centred in the north and with sporadic attacks in the Christian-majority parts of the country. But it may be heading down the road recently taken by Mali, in which Islamist extremists seize control of the north of the country and divide it in two. And lots of people in the south wouldn't mind a bit. Just seal the new border and forget about the north.