Hypatia, the daughter of the great mathematician and philosopher, Theon of Alexandria, was born in 350 AD. She was the only child of her parents and there is no information about her mother. She was a philosopher, mathematician, and astronomer who lived in Alexandria. She was trained under the guidance of her father and became head of the Platonist school in 400 AD. In Alexandria, she taught mathematics and philosophy, precisely the teachings of Neoplatonism (the last Greek school of philosophy founded by Platonius). She believed in the spiritual aspect of mathematics and thought that numbers are the spiritual language of the universe. She divided mathematics into four branches, geometry, arithmetic, astronomy, and music. Her teachings were based on the ideas of Plotinus and Iamblichus. According to Plotinus, humans does not possess the capability to understand the ultimate reality and the consequences of its existence. Hypatia taught these philosophical ideas of Plotinus in a way better than the earlier followers of Neoplatonism. She also taught the writings of Plato and Aristotle. It is not evident that she did any new mathematical research, she however accompanied her father in creating a new version of Euclid’s Elements. She was the first female mathematician whose life was nicely recorded. She was known to be a great teacher and counsellor. The work started by Theon was carried on by his daughter Hypatia. Her commentaries on Apollonius’s Conics and Diophantus’s Arithmetica gave us evidence of her, carrying on the program initiated by her father into new and difficult areas. She was considered a follower of paganism (religion of the peasantry), however, she didn’t worship any particular diety. Amongst the prominent Christians whom she taught, the most famous was Synesius of Cyrene who wrote letters to Hypatia, out of which seven letters had survived. Later in 412 AD, Alexandria came under the patriarchy of Cyril. Orestes (the Roman prefect of Alexandria) and Cyril (nephew of the then bishop of Alexandria) fought for state control and became rivals. Hypatia who was a friend of Orestes along with her philosophical views made her the centre point of the riots between Christians and non-Christians. As a result, she was brutally murdered by a mob of Christians in 415 AD, under the leadership of lector Peter, when she was travelling in her carriage back home. Damascius adds that they took out her eyeballs, cut her body into pieces and took her to a place known as Cinarion for cremation. They considered it to be a traditional process, in which they carry the body of vilest criminals outside the city to purify their city. Hypatia’s death was a turning point in the politics of Alexandria. After her murder, Greek and Roman philosophers fled the city, and the city’s role as the centre of learning declined. She was called a ‘martyr of philosophy’ and became a symbol of feminism.

The Christian historian, Socrates of Constantinople, a contemporary of Hypatia, describes her in hisÂ Ecclesiastical History^{}

There was a woman at Alexandria named Hypatia, daughter of the philosopher Theon, who made such attainments in literature and science, as to far surpass all the philosophers of her own time. Having succeeded to the school of Plato and Plotinus, she explained the principles of philosophy to her auditors, many of whom came from a distance to receive her instructions. On account of the self-possession and ease of manner which she had acquired in consequence of the cultivation of her mind, she not infrequently appeared in public in the presence of the magistrates. Neither did she feel abashed in going to an assembly of men. For all men on account of her extraordinary dignity and virtue admired her the more.’

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## 1. Commentary on Ptolemy’s Almagest

It was believed that Hypatia had only revised the commentary made by his father on Ptolemy’s Almagest, titled “Commentary by Theon of Alexandria on Book III of Ptolemy’s Almagest”. Some of the scholars claimed that Hypatia did not revise his father’s commentaries, instead, she corrected the text of Almagest. She contributed by providing a better method of long division that is used in astronomical computations. Also, Ptolemy in his book mentioned a division problem to calculate the number of degrees covered by the sun in a single day as it orbits the earth. In the first edition, Theon tried to improve the calculation done by Ptolemy. In Hypatia’s edition, she demonstrated a tabular method for the calculation. A classicist, Alan Cameron claimed that it might be a possibility that Hypatia not only edited book III but also the rest nine extant of book Almagest.

## 2. Commentary on Diophantus’s Arithmetica

Hypatia wrote a commentary on Diophantus’s Arithmetica that contained 100 mathematical problems solved using algebra. It was believed that only volumes I-VI of Arithmetica had survived and the rest are lost, but it is later found that four additional volumes were preserved in Arabic translation. This Arabic translation contained some additional problems and verification of Diophantus examples that were not present in the Greek text. Paul Tannery, a scholar of the 19th century was the first to deduce that the additional material in the Arabic translation of Arithmetica was added by Hypatia. Cameron also claimed the same and said that the additional work on Arithmetica followed the same pattern as used by her father, Theon. Heath after publishing the first English translation of the surviving extents of Arithmetica claimed that these texts were produced by Hypatia to help her school students. Wilbur Knorr, a historian of mathematics argued that the additions are “of such low level as not to require any real mathematical insight”, and that does not go well with Hypatia’s high abilities as a philosopher and mathematician. Cameron rejects this argument by saying that this edition of Hypatia’s work was specially designed for students rather than for professional use.

## 3. Astrolabe

One of the letters of Synesius revealed that Hypatia taught him how to construct an astrolabe. Astrolabe is an inclinometer used by past astronomers to predict local time by locating the positions of the stars, sun, and moon. Astrolabe was discovered 500 years before Hypatia was born and it was reported that Synesius’s letter was misinterpreted. Hypatia might have learnt how to construct an astrolabe from her father, as he wrote two books titled, Memoirs on the Little Astrolabe and another study on the armillary sphere in Ptolemy’s Almagest. Hypatia and her father must have studied Ptolemy’s Planisphaerium that contained necessary calculations for the construction of an astrolabe.

## 4. Hydrometer

Hypatia was credited for inventing a device known as a hydrometer as there was evidence of a letter in which Synesius asked Hypatia to construct a hydrometer for him. This device is used to determine the density of fluids. It is based on Archimedes 3rd century principle and some believed that it might be invented by him. In the letter, Synesius mentioned every minute detail of the hydrometer that shows, Hypatia hardly had any idea about this device but Synesius believed that she would be able to construct it with the help of given details.

## 5. Lost works

- A commentary on Archimedes’s Sphere and Cylinder surviving as John of Tynemouth’s De Curvis Superficibus, a text on isoperimetric figures incorporated by a later author into Introduction to the Almagest.
- A commentary on Archimedes’s Dimension of the Circle.
- A commentary edition of Apollonius Pergaeus’s Conics upon which later commentary editions were based.
- She also created an “Astronomical Canon”, which is believed to have been either a new edition of the Handy Tables by Alexandrian Ptolemy or a commentary on his book Almagest.