Nerve cells can’t divide, but sensory nerve fibers (not the whole cell) can be regenerated in the process of healing of injured nerves; also in very limited places, whole neurons can be produced anew from stem cells. read more
If you will read the next part, where I have discussed division of nerve cells, I have written in detail, as to, there have been continuous efforts by the neuroscientists to somehow make the nerve cells divide. read more