" For example: without free will how to you come to a new idea? how do you work out a math problem you have never done before?
I think the vast majority of what re do an say are rote and lack free will; but I think it's free will that allows us to change what we do.
I think that if you really look at ideas and thought processes, you don't really come up with them. They occur and you then perceive them. They certainly aren't conscious. I think it was in a Sam Harris book or lecture where he references brain imaging studies that show that the decision is made _before_ the person is consciously aware of it. The researchers can point to when the idea/decision occurs before the subject is aware of it himself. Where is the free will here?