"...a terrible problem for the rest of the world....."
Ever so correct, but don't leave us out of that thought.
Jihad is occurring in many places in the world. What is also frightening (to me) is the rapid growth of Islam in the world, and the vast amount of emigration of middle east Muslims to Western countries. Canada is full of Muslims, peaceful so far.
Virtually no westerners emigrate to Muslim countries.
It is logical to conclude, given the spreading I mentioned, that Islam will, indeed, take over the world.
Unless it is stopped. (That's one reason they're fighting so savagely in Iraq to prevent Democracy. If Iraq becomes a solid democracy, the world jihadist movement will be severely weakened, as Iraq will stand as the antithesis to Islamic jihad.)
Hugoball said it well. An Islamist cannot be changed. Muhamed wrote that "infidels" (everybody else) should be shunned and killed, until only Muslims remain. That is a very clear statement. These words are engraved in the minds of every Muslim in the world, whether he's a jihadist or not. (Which may explain why apparently "good" Muslims suddenly blow up trains!)
To say that Islam is on a collision course with the West, and Christianity, is not true. The collision is occurring now.