# What A Female Ancient Greek Mathematician Can Teach Us

Written By: Zhao Gu Gammage

Hypatia of Alexandria (360-415 BCE), whom Encyclopedia Britannica calls “the world’s leading mathematician of her time,” helped develop multiple concepts in the study of conic sections, or curves created when a plane intersects a cone. She used her knowledge to educate anyone and everyone, regardless of religion or gender, and made contributions to multiple renowned mathematical works. Her work contributions influenced some of the greatest mathematicians and philosophers, including Newton, Leibnitz, and Descartes. She also fought widespread sexism and became one of the few symbols of feminism in the ancient world.

During Hypatia’s time, the majority of women were expected to remain as caretakers of the home and therefore did not receive an education. The patriarchal society prevented women from having jobs, owning land, or saving money. Hypatia was one of the few lucky women who received an education. Normally, after a woman completed her studies, she would be married off, but Hypatia remained unmarried and continued her scholarly work. Her contributions to mathematics proved to be revolutionary since no woman had ever tried to enter the field before, much less shape it.

Hypatia grew up with a strong foundation in mathematics because her father, Theon of Alexandria, was one of the most notable Greek astronomers and mathematicians himself. He had contributed to multiple works, such as those of Euclid and Ptolemy, and Hypatia decided to continue his work by commenting on Apollonius of Perga’s *Conics* and Diophantus of Alexandria’s *Arithmetic*.

During this time period, instead of making mathematical publications of their own, mathematicians commented on publications written hundreds of years earlier. Comments were crafted to help refine and develop other scholars’ theories, arguments, and/or arithmetic in order to make them more understandable to others.

Hypatia’s comments in *Conics*, which explained divisions of conic sections by planes, helped to refine the idea of ellipses, parabolas, and hyperbolas, thus making them more understandable. The most specific example being that she created the following equations (where *a*, *b*, and *m* are all known):

*x - y = a ; * *x2 - y2 = m ( x - y ) + b*

Unfortunately, many of her contributions are unclear, either because she was never given credit or because they were destroyed.

Without Hypatia’s work, we would not have the famous quadratic equation or the cornerstones of calculus, integrals and derivatives. She shared her knowledge of mathematics and astronomy by hosting public lectures and drew crowds comparable to those of Plato and Aristotle. She taught at the Platonic School of Alexandria, similar to a modern-day university, where she discussed symbolism in Diophantus’ *Arithmetic* and held lectures hosted in public areas that attracted audiences of people from different parts of the empire. She educated the public in basic arithmetic (modern-day algebra), geometry, and, most famously, conics. She taught everyone who attended, regardless of religion, which was a rarity due to the tense religious divide at the time.

**So, what can we learn from Hypatia?**

In mathematics, she demonstrated how to share our knowledge in a male-dominated field. And in antiquity, she demonstrated how to stand up for what we believe in and to be trailblazers, groundbreakers, and STEMinists.