before vowels neur-, word-forming element meaning "pertaining to a nerve or nerves or the nervous system," from Greek neura "nerve" (Galen), originally "sinew, bowstring," also neuron "sinew, string (of a bow or musical instrument); cord; penis;" in plural "strength, vigor," from PIE *(s)neuro- "tendon, sinew" (see nerve (n.)). In Greek, puppets were neurospastos, literally "drawn by strings."
c. 1300, sorgien, cirurgian "person who heals by manual operation on the patient," from Anglo-French surgien (13c.), from Old French surgien, cirurgien (13c.), from cirurgie "surgery," from Latin chirurgia "surgery," from Greek kheirourgia, from kheirourgos "working or done by hand," from kheir "hand" (from PIE root *ghes- "the hand") + ergon "work" (from PIE root *werg- "to do").
<a href="https://www.etymonline.com/word/neurosurgeon">Etymology of neurosurgeon by etymonline</a>
Harper, D. (n.d.). Etymology of neurosurgeon. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/neurosurgeon