In mesopotamia, what role could a women play in medicine?

Any women who could read or write would be able to be trained as a physician.

the answer to your question is:

strong-mayor system

herodotus taught this. herodotus was an ancient greek historian who was born in halicarnassus in the persian empire. he is known for having written the book the histories, a detailed record of his "inquiry" on the origins of the greco-persian wars.