When we talk about doubts about the historical Jesus, we must realize that this conversation takes place within a larger context. There are those who doubt whether there was a historical Moses, a historical Buddha and yes, even a historical Muhammad.
So was there a historical Muhammad? I think so. I don’t take the hyper-critical stance that some do toward all religious founders.
People like Sven Kalisch doubt that there was a historical Muhammad and believes the same thing about Jesus.
I am not a scholar of Islam, nor have I studied Kalisch’s work. But I seriously doubt that a movement like Islam could start without a founder. I know that there are some Christian apologists that question the existence of Muhammad, but I don’t think that is very helpful.
What some people (unfortunately including some scholars) don’t realize is that history is not like a court of law. Lawyers do not have to prove that the defendant is innocent, only that there is room for doubt. If we tried to apply this standard to history, then we could say very little about anything that took place in the past.
So yes, I think that there was a historical Muhammad. And Buddha and Moses. And yes, Jesus as well.
Check out Similarities and Differences Between Christianity and Islam.