Hypatia
Hypatia (born 350–370; died 415 AD) was a Hellenistic Neoplatonist philosopher, astronomer, and mathematician, who lived in Alexandria, Egypt, then part of the Eastern Roman Empire. She was a prominent thinker of the Neoplatonic school in Alexandria, where she taught philosophy and astronomy. She is the first female mathematician whose life is reasonably well recorded. Hypatia was renowned in her own lifetime as a great teacher and a wise counselor. She is known to have written a commentary on Diophantus's thirteen-volume "Arithmetica", which may survive in part, having been interpolated into Diophantus's original text, and another commentary on Apollonius of Perga's treatise on conic sections, which has not survived. Many modern scholars also believe that Hypatia may have edited the surviving text of Ptolemy's "Almagest", based on the title of her father Theon's commentary on Book III of the "Almagest".
Thales of Miletus
Thales (who died around 30 years before the time of Pythagoras and 300 years before Euclid, Eudoxus of Cnidus, and Eudemus of Rhodes) is often hailed as "the first Greek mathematician". While some historians, such as Colin R. Fletcher, point out that there could have been a predecessor to Thales who would've been named in Eudemus' lost book "History of Geometry", it is admitted that without the work "the question becomes mere speculation." Fletcher holds that as there is no viable predecessor to the title of first Greek mathematician, the only question is whether Thales qualifies as a practitioner in that field; he holds that "Thales had at his command the techniques of observation, experimentation, superposition and deduction…he has proved himself mathematician."