Hypatia, the flower of learning in Ancient Alexandria


“Superstition is cowardice in the face of the Divine” wrote Theophastrus, who lived in during the founding of the Library of Alexandria. At that time, Alexandria was the greatest city the Western World had ever seen. The last scientist who worked in the Library was a mathematician, astronomer, physicist and the head of the Neoplatonic school of philosophy. Her name was Hypatia. Hypatia of Alexandria was the first woman to make a substantial contribution to the development of mathematics. She was born in Alexandria in 370 AD. At a time when women had few options and were treated as property, Hypatia moved freely and unselfconsciously through traditional male domains. By all accounts she was a great beauty. She had many suitors but rejected all offers of marriage. The Alexandria of Hypatia’s time was a city under grave strain. Slavery had sapped classical civilization of its vitality. The growing Christian Church was consolidating its power and attempting to eradicate pagan influence and culture. Hypatia stood at the epicenter of these mighty social forces.

Hypatia was the daughter of the mathematician and philosopher Theon of Alexandria and it is fairly certain that she studied mathematics under the guidance and instruction of her father. It is rather remarkable that Hypatia became head of the Platonist school at Alexandria in about 400 AD. There she lectured on mathematics and philosophy, in particular teaching the philosophy of Neoplatonism. Hypatia based her teachings on those of Plotinus, the founder of Neoplatonism, and Iamblichus who was a developer of Neoplatonism around 300 AD.

Plotinus taught that there is an ultimate reality which is beyond the reach of thought or language. The object of life was to aim at this ultimate reality which could never be precisely described. Plotinus stressed that people did not have the mental capacity to fully understand both the ultimate reality itself or the consequences of its existence. Iamblichus distinguished further levels of reality in a hierarchy of levels beneath the ultimate reality. There was a level of reality corresponding to every distinct thought of which the human mind was capable. Hypatia taught these philosophical ideas with a greater scientific emphasis than earlier followers of Neoplatonism. She is described by all commentators as a charismatic teacher.

Hypatia came to symbolise learning and science which the early Christians identified with paganism. However, among the pupils who she taught in Alexandria there were many prominent Christians. One of the most famous is Synesius of Cyrene who was later to become the Bishop of Ptolemais. Many of the letters that Synesius wrote to Hypatia have been preserved and we see someone who was filled with admiration and reverence for Hypatia’s learning and scientific abilities.

In 412 Cyril (later St Cyril) became patriarch of Alexandria (he was the archbishop there) despised Hypatia because according to him she had close friendship with the Roman governor, and she was a symbol of learning and science, which were largely identified by the early Church with paganism. However the Roman prefect of Alexandria was Orestes and Cyril and Orestes became bitter political rivals as church and state fought for control. Hypatia was a friend of Orestes and this, together with prejudice against her philosophical views which were seen by Christians to be pagan, led to Hypatia becoming the focal point of riots between Christians and non-Christians.

… by her eloquence and authority … attained such influence that Christianity considered itself threatened …

A few years later, according to one report, Hypatia was brutally murdered by the Nitrian monks who were a fanatical sect of Christians who were supporters of Cyril. According to another account (by Socrates Scholasticus) she was killed by an Alexandrian mob under the leadership of the reader Peter. What certainly seems indisputable is that she was murdered by Christians who felt threatened by her scholarship, learning, and depth of scientific knowledge. This event seems to be a turning point:

Whatever the precise motivation for the murder, the departure soon afterward of many scholars marked the beginning of the decline of Alexandria as a major centre of ancient learning.

There is no evidence that Hypatia undertook original mathematical research. However she assisted her father Theon of Alexandria in writing his eleven part commentary on Ptolemy’s Almagest. It is also thought that she also assisted her father in producing a new version of Euclid’s Elements which has become the basis for all later editions of Euclid.

.. while making only inconsiderable additions to the content of the “Elements”, he endeavoured to remove difficulties that might be felt by learners in studying the book, as a modern editor might do in editing a classical text-book for use in schools; and there is no doubt that his edition was approved by his pupils at Alexandria for whom it was written, as well as by later Greeks who used it almost exclusively…

In addition the the joint work with her father, we are informed by Suidas that Hypatia wrote commentaries on Diophantus’s Arithmetica, on Apollonius’s Conics and on Ptolemy’s astronomical works. The passage in Suidas is far from clear and most historians doubt that Hypatia wrote any commentaries on Ptolemy other than the works which she composed jointly with her father.

All Hypatia’s work is lost except for its titles and some references to it. However no purely philosophical work is known, only work in mathematics and astronomy. Based on this small amount of evidence, Hypatia was an excellent compiler, editor, and preserver of earlier mathematical works.

As mentioned above, some letters of Synesius to Hypatia exist. These ask her advice on the construction of an astrolabe and a hydroscope.

Christiaan Huygens, mathematician


One of the greatest scientists of all time was Christiaan Huygens. He was born on  April 14th, 1629 in Den Haag, Holland. His Father was Constantijn Huygens (1596-1687), a Dutch statesman, diplomat, and artist. At his home famous poets, painter, and philosopher of his time were guests, besides others Rubens, Rembrandt, and Descartes. Raised in this worldly-open family with many childrens Christiaan Huygens studied like Pierre de Fermat (1601-1665) jurisprudence first, then mathematics and natural sciences.

He was in relationship with Antony van Leeuwenhoek (1632-1723), who was known as the best microscope builder of his time and who not only grinded his lenses out of glass, but also out of rock crystal and diamond. Huygens was involved at the examination of small life forms and microscopic objects like sperms and blood cells. He grinded his own lenses for astronomical telescopes. His biggest refractor had a length of five meter. With his theory of the wave form of light he was able to calculate the refraction within the lenses and was able to make refractors with lesser chromatic and spherical aberration. He also invented a type of ocular/eyepiece named according to him, where the image pojected by the objective is placed between two different ocular lenses on a visual plate, consisting of two planoconvex lenses.

With his advanced telescopes Huygens discovered 1655 the Saturnian moon Titan, which was thought to be the biggest moon within the solar system for a long time. Today its known that the real diameter of Titan with ca. 5200 kilometer is somewhat smaller than the diameter of the Jovian moon Ganymede with ca. 5400 kilometer. After the discovery of the Galileian moons around Jupiter Titan was the second discovery of satellites around a planet. It has a dense atmosphere of methane and ammonia, which is responsible for an apparently larger size and for the reddish color.

At that same time Huygens was examining the Saturnian rings, which were an open phenomenon out of the time of the discovery by Galilei. Huygens presented the correct explanation for the rings in 1656. They are angled by 27 degrees to the Saturnian orbit, and therefore from Earth they are seen half a Saturnian year with their North side and half a Saturnian year with their South side, while the additional angle of the Saturnian orbit to the ecliptic makes some complex transitions possible. At the time around a transition the rings seem to dissapear, because in correlation to their huge diameter of ca. 280,000 kilometer—without G- and E-ring—they are extremely thin: the thickness of the rings varies from ten to fourhundred meter.

The rings are no solid objects. This fact is a deduction of the Keplerian laws. To be stable for decades and centuries the rings had to rotate and therefore stationary gas or liquids are not the material of them. At the outer edge the rotation speed of the rings are 16 and at the inner edge 21 kilometer per second(!). A solid object would chatter because of the speed differences, calculatable with the Keplerian laws. Huygens also discovered that the rings have no connections to the Saturnian body. He recorded his observations about Saturn in 1659 in his work “Systema Saturnium.”

Like Galilei before, Huygens was pointing his telescopes to nearly anything the sky presented him. He discovered the difference of polar and equatorial diameter of Jupiter, made a first map of Mars, calculated the Martian day to ca. 24 hours because of the movement of surface marks on the red planet, he proposed that Venus is covered by clouds, and he resolved the inner region of the Orion nebula and mapped the stars within. This brightest part of the nebula therefor is called Huygens region after him. He also discovered several other interstellar nebular and many double stars.

While his mathematical studies Huygens created a complete theory about the game of dice, which was published by his mathematics teacher Frans van Schooten (1615-1660) in 1657 as “De ludo aleae.” With this Huygens is known as the founder of the theory of probabilistics. Although principially the pendulum clock was invented by Galilei and da Vinci already, Huygens was the first who worked out the practical problems of such a chronometer and let build many different clocks of that type. He also invented the clock with spiral spring or cycloid pendulum, which enables a more precise time measurement and helped to determine the longitude on sea. His inventions on chronometer he wrote down until 1673 in his book “Horologium oscillatorium”.

In 1660 Huygens travelled to England. And in 1663 he was admitted as a member of honor at the British Royal Society. Toward 1666 he travelled to Paris, where he was teaching at the university since 1681. Here he also made observations together with Giovanni Domenico Cassini at the 1672 finished observatory of Paris. After a serious illness he returned to Den Haag to the families house of Hofwijck. Briefly before his dead he wrote the book “The Discovery of Celestial Worlds: Theories about Inhabitants, Plants, and Products of Planetary Worlds” where he speculated about life not only on planets of the Sun, but also about life on worlds of other stars. Huygens died on June 8th, 1695 at the early age of 66 years-old in Den Haag. A life worth living as his was has to be known.