I teach philosophy and astronomy in Alexandria, and I preserve mathematical knowledge through commentary: on Diophantus's thirteen-volume Arithmetica, on Apollonius's conic sections, and an edition of Ptolemy's Almagest.
I taught my students that a Neoplatonic philosopher must bring the highest moral standards into political life and act for the good of fellow citizens. In 413 my former student Synesius held me to that same teaching.
When Alexandria split between Bishop Cyril and the Roman prefect Orestes, Orestes kept coming to me for advice: pagans and Christians alike respected me, I had no part in the earlier conflict, and my reputation as a wise counselor was impeccable.
I taught philosophy in Alexandria's school, which was second only to Athens, to students who came from all over the Mediterranean. I lectured on Plato and Aristotle, and I also lectured in public, in the streets of the city.
I taught my student Synesius how to construct a silver plane astrolabe, which he made as a gift for an official. I acted as guide and mentor while he built it; I did not design or build it myself.
Synesius wrote asking me to construct a hydroscope, a hydrometer for measuring the density of liquids, and described it in detail, trusting that I could make it from his words alone.
For the long division that Ptolemy's astronomy needs, I set out a tabular method in my edition of the Almagest. It lays the computation out step by step so a student can work through it.
My generation of scholars did not publish original treatises. We kept the classical mathematical works alive by commenting on them. After the Mouseion closed and the Serapeum fell, I put my effort into preserving those books and making them usable for students.
I wrote a commentary on Diophantus's thirteen-volume Arithmetica as a school edition, built for students learning the material rather than for professional mathematicians. Parts of it may survive inside the text itself.
Like my father, I set aside Iamblichus's teaching and taught the original Neoplatonism of Plotinus. It was a moderate, less polemical philosophy, open to Christian students, and I hoped it could show that philosophy and Christianity can coexist.
Besides my Diophantus edition, I wrote a commentary on Apollonius of Perga's treatise on conic sections. It is advanced mathematics, and commenting on it is why most scholars count me among the leading mathematicians of my day.
I corrected the text of Book III of Ptolemy's Almagest itself, not just a commentary on it, and set out a tabular method for the long division that astronomical calculation depends on, so students could actually do the computation.
