She learned Mathematics from her father, Theon of Alexandria, the last "president" (possibly) of the famous Alexandrian Musuem. She soon surpassed him and went on to pen at least 3 texts which are known today within the fields of geometry, (?), and astronomy.
She speaks Greek, Latin, Arabic (she is a mathematician, so I assume), and (possibly the language indigenous to the region, however she is of a 'privileged' and learned class so perhaps not). I also assume she can write in all of these languages.
Hypatia has been described as a charismatic and effective teacher as well as a great beauty. There are even reports that in pursuit of her work, she lead a life of chastity (slight elaboration re: pursuit of her work, no reason for the rumor of chastity is given). By all accounts she was well-respected by her colleagues and in one instance speculation is made that certain works of the mathematician Diophantus are lost to us today because she did not include a mention of them in one of her publications.
I imagine Hypatia was a woman driven by an intense love of mathematics, religion, and teaching. Her passions were not so much of the flesh, but of the mind. Her father played a significant role in the development of at least her interest in mathematics and I would suspect the burning of his Alexandrian Museum and the other libraries and institutions of learning in the late 300s had a large impact upon her. Perhaps she is zealous when it comes to learning?
Hypatia was a Neo-Platonist (a school of philosophy I am not currently familiar with which is classed as a religion/philosopy in one of my references). This, in part, is what led to her death at the hands of Christians. (This event is a something of a continuation of the uneasiness which lead to the burnings of the 390s.)
Teaching -- Philosophy, Mathematics
Reading and Writing - (see languages above)
Public Speaking -- I didn't got into this above, but Ms. Hypatia was also a public speaker.