Hypatia likely assisted her father, Theon, in his commentary on Euclid's "Elements". Theon's revised edition of the "Elements" became the standard version for centuries, and it is believed that Hypatia contributed significantly to its accuracy and clarity. While the exact nature of her contributions is debated, her mathematical acumen is evident.

Hypatia is known to have written a commentary on Apollonius of Perga's "Conics", which deals with the properties of conic sections (ellipses, parabolas, and hyperbolas). Although the commentary itself is lost, its existence is confirmed by other historical sources. This demonstrates her deep understanding of advanced geometry.

Hypatia wrote a commentary on Diophantus' "Arithmetica", a groundbreaking work on algebra and number theory. A fragment of this commentary survives, providing insight into her mathematical expertise and her ability to explain complex algebraic concepts. She is credited with developing new methods for solving Diophantine equations.

Hypatia is credited with designing and improving astronomical instruments, such as the astrolabe and the hydroscope. While no instruments directly attributed to her survive, descriptions from her students suggest her practical skills in applying mathematical principles to astronomical observation and measurement.