You need sensory information from your body if you're attempting to pilot a yacht, cook a complicated meal, breakdance or pleasure your partner.
It's not so important if you're calculating the entropy of a black hole or considering the topology of space-time. Or, I would assume, making declarative statements about revolutions or Truth-Events.
Hmmm... this is probably the most interesting thing that's been said in the entire thread.
I don't know to what extent the brain can operate optimally without the body. Do you think Hawking would have had the same career had he been born with another form of sclerosis that presented very early in life? I'm not so sure he would have developed the same "mind" had he been so disabled. Although, this is not to say that there aren't all sorts of severely disabled people with exceptional talents, because there are. Hard to say just yet. The combination of genetic factors that determine whatever it is that makes Hawking good at science might be enough to override the ones that gave him ALS.
My grandmother had MS, and in fact her body was paralyzed from the neck down, but over time, this made it nearly impossible for her to speak, then it did make it impossible. Over years and years, her brain slowly stopped working, she didn't know who was who, or where she was, and she had pneumonia all the time from aspirating food. Then she had cancer, which she survived somehow. There's a lot of study going on of people in these sorts of states, or worse, in vegetative states, to see just how much is going on and whether there's mind in there. There have been stories of people who were pronounced "brain dead" who talk about hearing everything that was going on around them and getting very angry at their families for agreeing to "pull the plug" before they woke up.