Dorothea von Rodde-Schlözer

Thanks to STEM-ma Luise-Charlotte Kappe, who pointed out:

Just for the record: The first female Ph.D. recipient in Germany was Dorothea Schlözer (1770-1825), who recieved her Ph.D. in Philosophy in Goettingen in 1787! Others we are familiar with received their Ph.D. in mathematics much later, e.g. Sonya Kovalevki in 1874 also in Goettingen, and Emmy Noether in 1907 in Erlangen.

You can read about her here.  Apparently she was one of a group of five daughters of academics who studied at the university.  As the story goes, her father made a bet with another professor that his teaching methods were superior.  They agreed to test their methods on their first-born children (are the statisticians cringing?), both of whom were female.  Not sure who won … probably the students, who received terrific and broad educations.