ANCIENT GREEK WOMEN MATHEMATICIANS
The president of Harvard University, Lawrence H. Summers, sparked an uproar at an academic conference Friday when he said that innate differences between men and women might be one reason fewer women succeed in science and math careers. However, after a research in the ancient Greek years, we have realized the successful participation of women in various fields including science, regardless of the above view and the hardship of that time‌
Geometric period (11th-8th century BC)
AETHRA (Αίθρα) According to Vitruvius and to the Roman historian Titus Livy (1st century BC) Theseus’ mother, Aethra (10th-9th century BC) taught the children of Triziana accounting (practical arithmetic) that was based on the use of the abacus and some symbols, where there was no zero, making the symbolism of numbers very difficult.
Ionia’s School (6th-5th century BC)
Polygnotos (Πολυγνώτη) Polygnotos was student and lover of Thales. According to the author Boethius (5th century AD) Polygnotos knew many geometric theorems and also she introduced the principle of acrophonic at the symbolism of arithmetic characters. These symbols are called “Herodianus”. According to Vitruvius, Polygnotos was the first person who wrote and proved that “each registered angle going in a semicircle is right”.
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School of Pythagoras (6 -5 century BC)
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Themistoclean (Θεμιστόκλεια) Themistoclean was a priestess of Delphi and teacher of Pythagoras. She managed to instill him moral principles and values as well as introduced him to the authorities of numbers’ wisdom and geometry.
Deino (Δεινώ) Deino was Pythagoras' mother in law. According to Dasypodius, she studied the insufficient numbers (ελλειπείς αριθμοί).
Theano the Thouria (Θεανώ η Θουρία) Theano was student as well as Pythagoras’ wife. She is considered as the most famous ancient woman astronomer and cosmologist. She worked on the theory of numbers and taught mathematics and astronomy at the Pythagorean school of Samos and Krotona. She is assigned with the concept of the “Golden Ratio”.
Damo (Δαμώ) She was Pythagoras' daughter. According to Geminus of Rhodes (1st century BC) the construction of a regular tetrahedron as well as the method of inscribing a regular dodecahedron in a sphere is a work of Damo. Furthermore she is attributed to the words “The sphere is the finest of all the solid shapes, whereas among the flat shapes the finest one is the circle”.
Mus or Myria (Μυία ή Μυρία) Myria was the wife of Milon of Croton. She taught at his school, she also worked on geometric fields as well as the invention of the third analogue between two segments was attributed to her. Arignoti (Αριγνώτη) Arignoti, the daughter of Pythagoras, was a philosopher, a writer and a mathematician. She wrote a mathematical book entitled “On Numbers”, which is unfortunately lost.
Fintis or Filtis ( Φιντύς ή Φίλτυς) Fintis was Theofori’s daughter and taught at the School of Crotona. The following equality relation that is associated with the Pythagorean triples is attributed to her. 2
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Type: a + (a +1/2) = (a +1/2)
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Melissa (Μελίσσα) She worked on the construction of regular polygons which are inscribable in a circle. The following relation is attributed to Melissa. Type: 12+22+…+ν2= [ν(ν+1)/2]2
Tymicha (Τυμίχα) Tymicha was born in Croton and wrote about the “Friend Numbers”. The tyrant Dionysius asked her to reveal the content of the Pythagorean teaching which she absolutely denied.
Ptolemais (Πτολεμαΐς) Ptolemais was a new-Pythagorean philosopher, physicist, musician and mathematician who approved the commutative property of numbers.
Diotima (Διοτίμα) Diotima was a priestess of Mantinea, an expert in the Pythagorean numbers’ wisdom and geometry. She was the only woman who participated in the male-dominated Plato’s Symposium.
Vitali or Vistala (Βιτάλη ή Βιστάλα) Vitali, the daughter of Damo, was expert in the Pythagorean maths and as Nafkratios said, she taught geometry in Athens. Damo trusted to Vitali the memos-the philosophical texts of her father.
Periktioni (Περικτιόνη) Periktioni was Plato’s mother, a Pythagorean philosopher, writer and mathematician. Stovaios states that Periktioni “is an expert in geometry and arithmetic”
Academy of Plato (4th century BC)
Many women studied at the Academy of Plato
Lastheneia (Λασθένεια) She was coming from Mantinea. It is said that she entered the Plato’s Academy to study mathematics and philosophy, dressed like a man, as the entrance was not allowed to women. Lastheneia is mentioned to the following definition of the sphere: “a sphere is a solid figure bounded by a surface to which all segments from a point inside the sphere are equal’’.
Axiotheas the Fliasia (Αξιοθέα η Φλιασία) She focused particularly on mathematics and natural philosophy and taught in Corinth and in Athens.
The Cyrenaica School (4th-3rd century BC) Areti the Cyrenean (Αρετή η Κυρηνεία) Areti the Cyrenean was Aristippos' daughter. Her father was the founder of the Cyrenaica School which Areti inherited after his death. She wrote forty books. Two of them contained and treatised on mathematics. She also taught mathematics, physics and moral philosophy in Athens.
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Epikorou School (4 to 3 century BC)
Themisi (Θέμιση) and Leondis the Corinthean (Λεοντία η Κορινθία) expertised in mathematics. Leondis wrote many works, but unfortunately nothing is saved.
Other women mathematicians in the 4th Century BC) Nicareti the Corinthean (Νικαρέτη η Κορινθία) Nikareti the Corinthen expertised in mathematics and wrote many essays which unfortunately are lost. The following theorems are attributed to her. “Each exterior angle of a triangle is larger than each interior one on the opposite side of the triangle” and “In each triangle the sum of two angles is less than two right angles in each way we get them”.
Aglaoniki (Αγλαονίκη) The mathematician and astronomer Aglaoniki was accused of witchcraft, having predicted the eclipses of the sun and the moon. Her name is given to a crater in the southern hemisphere of Venus. Many other women mathematician of that period are mentioned by the philosopher Athinaios . These women are: Caliki, Archediki, Telessina, Pythioniki, Labito, Danai, Theokleia, Antheia, Chloe (Καλύκη, Αρχεδίκη, Τελέσσινα, Πυθιονίκη, Λαμπιτό, Δανάη, Θεόκλεια, Άνθεια, Χλόη)
Hellenistic Period (2nd BC-1st AD century ) Pythais (Πυθαΐς) Pythais worked with her father mostly on calculating the area of the flat shapes. It is said that she proved the theorem: “of all isoperimetric shapes that have the same number of sides the largest one is the regular one”.
From the 2nd century BC till to the rd 3 century AD, none woman mathematician is mentioned.
Alexandrian School (3rd-6th century AD) Pandrosion (Πανδροσίων) 4th century AD Pandrosion is also called Pandrosus (Πάνδροσος). She was an Alexandrian geometer probably Pappu’s student who had dedicated her his third book of “Synagogue” (Συναγωγή). Pandrosion separated the geometrical problems in three categories: “There are three genders of geometrical problems, some of them are called plane and some others linear”
Hypatia (Υπατία) Hypatia was Theona's daughter. Theonas was a mathematician, a philosopher and an astronomer at the Museum of Alexandria that was a foremost institute. Her father wished that his daughter would become “the perfect human being” at a time when women were considered to be inferiors. Hypatia originally studied at the School of Alexandria, at the New-Platon school of Plutarch in Athens and after that in Rome. Hypatia was the first woman “collegiate” in the East. She taught “le quadrivium” which means
she taught arithmetic, geometry, astronomy and music. Her similarity to the modern collegiates is impressive. Her project research Hypatia mostly collected, organized, simplified and taught all previous knowledge. Some of her important writings are: Comments on the first six books of Diophantus' “Arithmetics” which is considered the first book of Algebra Number theory. Thesis on the conic sections of Apollonius of Pergama. A dissertation on Euclid's work and she helped her father to review and reissuance the Elements of Euclid. Hypatia edited the “Great Syntaxis” or “Mathematical treatise of Ptolemy” (Almagest), which was an encyclopaedia consisted of thirteen books that featured whatever was known about the astronomy in ancient times. Teaching method Hypatia was a gifted teacher and an orator. Although she was paganist, she was teaching Christian children as well as foreigners.
Practice – Experimental Ideas. He made some tools for refining water and some others for measuring the water level, a classified hydrometer for measuring the specific gravity, a tool which was used to measure and predict the positions of the planets and one more tool to estimate the time. The Painful End She died violently, sliding through the streets by fanatical Christian mob. Her body was dismembered and then its members were burned. Her death marked the end of the ancient Greek science. In her memory.. In her honor, a crater and a crack 180 km on the moon were named Hypatia.
In conclusion:
From the ancient years until nowadays it has been necessary for all the women to fight every single day to implement the rights of equality in work and in life. From the ancient years until nowadays, women scientists -mathematicians managed to succeed in various male-dominated sectors prevailing racism and prejudice and finally they are able to illustrate that nothing in life is donated, so, fight for everything!
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The text was written, edited, translated in English by the students: Stefania Tsouri Evaggelia Margaritaki Georgia Papaevangelou Aneta Mpariotaki Antonia Mouzouraki Anggela Mpekiri
Sources: Greek Mathematical magazine “ΕΥΚΛΕΙΔΗΣ” issue nr 77 Wikipedia Photos from the web