Behind the martyr stands a working mathematician, and parts of her work can be recovered with reasonable confidence. The Suda credits Hypatia with commentaries on the Arithmetica of Diophantus, on the Conics of Apollonius of Perga, and on the astronomical canon. None survives under her name, but a note in the manuscripts of her father Theon's commentary on the Almagest describes Book III as prepared in the edition of my daughter, which makes her the reviser of the standard late antique text on Ptolemaic astronomy, and scholars have argued that portions of the surviving Diophantus tradition pass through her classroom. The other window is her student Synesius of Cyrene, later a bishop, whose surviving letters address her as mother, sister and teacher. He asks her advice before publishing, describes in his essay on the gift of an astrolabe an instrument built after her teaching, and in one letter asks her to have a hydroscope, an instrument for measuring the density of liquids, made for him.
Teacher of astronomy and its instruments, editor of Ptolemy, commentator on the hardest Greek arithmetic: that is a career, not a legend. It corrects the persistent habit of making her either a martyr of science or a mere symbol; the documented Hypatia is a Neoplatonist school head whose mathematics was the ordinary, serious work of keeping an exact tradition alive.