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Hypatia: The Last Academic – Part Two

by May 8, 2022

By Mary Naples, Contributing Writer, Classical Wisdom
Under Christian rule, Alexandria, once the definitive center of learning throughout the empire, was fast becoming anti-intellectual and inhospitable to Hypatia and the academic circle in which she traveled. In fact, this burgeoning new religion was oftentimes suspicious of learning, equating it to the work of the devil. Faith in Christ replaced scholarship in this brave new world.
An example of this hatred for scholarship was demonstrated in 392 when Theophilus (384 CE-412 CE) Bishop of Alexandria, led a braying mob of Christian zealots in the pummeling of the Serapeum, the city’s premier temple and library complex. Elevated by one-hundred steps on the acropolis of Alexandria, the Serepeum was made of luminous marble and rose above all other structures commanding the city skyscape. Equally impressive, the library within the Serapeum was considered the daughter to the defunct Library of Alexandria housing hundreds of thousands of scrolls. After the extremists razed the Serapeum complex and set fire to the scrolls, the swarm went on a holy mission tearing down other temples, statuary and religious sites, when all was said and done destroying over twenty-five hundred structures in total.
Serapeum of Alexandria
Papyrus drawing of Pope Theophilus of Alexandria, gospel in hand, standing triumphantly atop the Serapeum in 391 (from the Alexandrian World Chronicle)
In 414 CE Theophilus died and was succeeded by his nephew, Cyril (378 CE- 444 CE) who made his uncle look conciliatory in comparison. Ruling with an iron-fist from the get-go, he made his wrath known against another enemy of the Christians—the Jews. When some Christians were killed in a skirmish that had broken out between Christians and Jews, Cyril organized an army of thousands called the parabalani. Typically, from the lower rungs of society and oftentimes illiterate, the parabalani were at his call to serve their god, or in this case god’s representative, Cyril. In addition, some in his army were Nitrian monks who traveled to Alexandria from the desert fired up in righteous religious indignation against non-Christians. Both groups had a flagrant reputation for violence.
At Cyril’s behest, they seized the synagogues converting them into churches. But defacing their places of worship was not enough for the iron-fisted bishop, he also exiled the Jews from Alexandria and encouraged his Christian disciples to occupy their now abandoned homes and to seize their possessions.
Cyril of Alexandria
St Cyril of Alexandria, Patriarch, Confessor, and Doctor of the Catholic Church
It is emblematic of the staggering influence wielded by religious authority that Orestes—the governor of Alexandria—could do little but stand by the sidelines in horror and despair at this gross injustice. Though a Christian himself, Orestes was a nonsectarian and like his good friend Hypatia appalled by Cyril’s barbaric actions against the Jews.
Though it did no good, Orestes reported the atrocious events to the emperor in Constantinople, which put him squarely in the crosshairs of Cyril’s band of thugs. One night while out in his chariot, Orestes was confronted by an angry mob of parabalani and Nitrian monks—which soon turned into a physical altercation when one of the monks gashed Orestes’ head open with a stone. If not for the help of nonsectarian bystanders, Orestes would have died.
Illustration of Constantinople
Ancient Constantinople reconstructed from 4th-13th century
When the stone-hurling monk was apprehended, Orestes had him publicly tortured and the monk ultimately died. In true form, Cyril used the monk’s death in a propaganda campaign against the governor further fueling the fire between the disparate factions.
Attempts at reconciliation between the two leaders ended in failure. Through it all, the governor sought counsel from the wisest person in the land who stood resolutely by his side. But Cyril’s supporters saw Hypatia’s advocacy on Orestes’ behalf not as uniting but as dividing. Alexandria’s most acclaimed pagan was an easy target who they blamed for the continuing rift between the two men.
Then the rumors began. She has an undue influence on Orestes, they blustered. She’s bewitched him with her sorcery, others moaned. She is teaching idolatry, they shrieked. Calling her a witch, they even used her famed astrolabe against her saying it was an instrument of Satan. The cacophony of outcries against her became deafening. Then it happened. Demonstrating once again how easy it is to harm those who have been dehumanized.
Orestes and Hypatia
Oscar Isaac and Rachel Weisz play Orestes and Hypatia – Agora (2009)
On her daily ride through the city on that bright and sunny day in March of 415, Hypatia had set off for school in her chariot. As was usual for her, her mind was a million miles away. Perhaps she was thinking about her next seminar; about some philosophical dictate or mathematical law she would discuss in class. Being an exemplary teacher, her fortunate students were never far from mind.
But her introspection was savagely broken when she found herself physically confronted by a howling mob under the leadership of Peter, a church magistrate. Because she was not a civil authority, she lacked the security detail that Orestes enjoyed. But up until then, no academic had needed such protection in Alexandria.
From the beginning, it was violent. They ordered her off her chariot, then dragged her through the streets and into a church. She must have tried to reason with them, but her reasoning fell on the deafened ears of the righteous. After all, theirs is the will of god. They tore the clothes off of the “luminous child of reason” and in God’s house they flayed her with the jagged edges of roofing tiles.
As if that were not enough, while still alive and breathing, they gouged out her eyes. Once dead, they further violated her by cutting her body into pieces and parading the pieces throughout the streets of Alexandria. Finding rest, at long last, on a pyre. Violent criminals were treated with more forbearance than Alexandria’s most prominent intellectual.
Illustration of Hypatia's murder
Illustration by Louis Figuier in Vies des savants illustres, depuis l’antiquité jusqu’au dix-neuvième siècle from 1866, representing the author’s imagining of what the assault against Hypatia might have looked like.
From the farthest reaches of the empire to close by, both Christian and non-Christian alike were in an uproar about the abhorrent slaying of the greatest mathematician of the day. It was an outrage. Academics were considered inviolable because they enhanced the community with their scholarship and wisdom. But if being an academic was not enough to protect her, Hypatia was also an elite woman. A rank by itself deemed sacrosanct.
How could something of this magnitude happen to one as beloved as she? But the truth is that Hypatia was part of a dying breed, the last champion of a seven-hundred-year academic tradition vanishing under a tidal wave of anti-intellectual religious dogma. After Hypatia’s death, many pagan academics fled Alexandria in search of more tolerant cities. But eventually the tidal wave could be felt throughout the empire with religion replacing philosophy and clergy replacing academics.
Devastated, Orestes soon left public life. But Cyril’s star was still rising. Although never formally charged in Hypatia’s violent end, if not for the anti-pagan fervor he stirred up amongst his minions, such a horror would never have taken place. Following her death, Cyril was given the honorary moniker “the new Theophilus” by his jubilant followers for quashing the “last remnants of idolatry.” Under his continued leadership, Alexandria became an important Christian hub with Cyril eventually canonized as a saint. He is venerated in the Roman Catholic and Eastern Orthodox Churches to this day.

Hypatia: The Last Academic – Part One

by May 3, 2022

By Mary Naples, Contributing Writer, Classical Wisdom
They came to her by land. They came to her by sea. They came to her from the farthest reaches of the Roman Empire and they came to her from close by. Amongst the literati, Hypatia (355-415 CE), acclaimed philosopher and leading mathematician, was a rock star.
She was bold, she was beautiful, but most of all, she was brilliant. Her students, many of them adherents in the burgeoning new religion, Christianity, adored her and flocked to hear her every word. Congregating not only in the classroom but in the public square and even at her home—just to hear her speak. Hers was the school all serious students throughout the empire wished to attend. But students weren’t the only ones who were captivated by her brilliance. Amongst academics from near and from far, she was the one with whom they sought council.
But how did Hypatia, a woman in a deeply misogynist society, earn such high acclaim? By the tender age of thirty, Hypatia had become a legend within academic circles for fusing the two apparently disparate disciples of mathematics and philosophy together in the classroom. Although well-versed in both disciplines, academics tended to be trained as either philosophers or mathematicians and had schools in one discipline or the other but not in both. Hypatia’s school was the exception.
Weaned on mathematics by her father, Theon (335 CE-405 CE), the foremost mathematician in Alexandria, Hypatia would become his best pupil even assisting him in the seminal writings of Euclid and Ptolemy. In fact, Hypatia was so gifted, that her father ceded his school to her—retiring at only fifty-five years of age—when it became apparent that she surpassed him in ability. But for all her mathematical acumen, Hypatia had a strong affinity for philosophy which she believed led to the highest truth. Her robust background in mathematics and philosophy made her school a perfect venue for students who wanted to learn how the two disciplines were unified.
Ptolemaic System
Hypatia is known to have edited at least Book III of Ptolemy’s Almagest, which supported the geocentric model of the universe shown in this diagram.
But it’s important to have an understanding of what was meant by mathematics and philosophy in ancient times. Today, what two disciplines are more at odds than mathematics and philosophy? Though one is considered practical and useful, the other is considered metaphysical and without merit in our highly technical world. While both were thought to be sacrosanct by the ancients, a debate ensued between scholars over which of the two disciplines led to the highest truth.
Mathematics, which encompassed arithmetic, geometry, algebra, as well as astronomy, was irrefutable and as such was considered sacred and a path to a higher being or what the ancients termed “the One.” Meanwhile philosophy, a less demonstrable field, was a study employed to instill honor, wisdom and integrity within an individual. The philosophical goal being that this moral code could impart a oneness with the divine. Thus, the goal of both mathematics and philosophy was a transcendent affinity with the sacred, making them both more akin to our notion of religion.
Conic Sections
Hypatia wrote a commentary on Apollonius of Perga’s treatise on conic sections, but this commentary is no longer extant.
Neoplatonism, the type of speculative philosophy that Hypatia taught, espoused a renunciation of the material world in favor of spirituality. Neoplatonists believed that the materiality of the body and the world in general are things to be overcome. Hypatia herself was exemplar of this creed, choosing to remain celibate so she could focus her energies on scholarship and the satisfaction of the incorporeal world. One famous vignette has her thwarting the unwelcome advances of a student by showing him one of her menstruation rags, quipping “Is this what you love, young man?” Unsurprisingly, his desire for her was quelled.
Hypatia’s severe rejection of his advances illustrates how fundamental repudiation of the material world was to Neoplatonism. In this way, it was a philosophy not inconsistent with the essential tenets of Christianity. On account of this compatibility, many of Hypatia’s students were both Neoplatonists and Christian. Although a pagan, Hypatia was nonpartisan and endowed all her students to honor and respect one another and others in the world, regardless of religious affiliation.
Hypatia illustration
The play Hypatia, performed at the Haymarket Theatre in January 1893, was based on the novel by Charles Kingsley.
For as much as peaceful coexistence was the order of the day in Hypatia’s school, Alexandria was a tinderbox with disparate factions in conflict with one another; Christian against pagan and Jew, orthodox against heterodox, sectarian against non-sectarian and finally religious authority against civil authority.
To Be Continued….

Archimedes’ Awesome Inventions That Will Blow Your Mind

by November 4, 2021

We are just too inspired. Your editor and her small family are exploring the island of Sicily… and our surroundings have forced us to pen/type a few thoughts on our recent locale.
In fact, we have a pretty spectacular object in our sights… though it’s not exactly ancient… but straight out our window is one of the world’s largest megayachts… really. 
Sporting two helicopters, a whirlpool, a glass bottomed pool and a ten person submarine, the 126 meter Octopus, owned by Microsoft co-founder Paul Allen, is an impressive sight to behold. It also boasts a cinema, a juice bar and a music recording studio… and is protected by Navy Seals.
I spy with my little eye…. a super yacht!
It’s seriously money. 
Now, this ultra modern ship may seem out of place in an ancient seaside town, indeed in these pages as well. But actually, it’s quite fitting… because this isn’t the first impressive vessel to wade these waters.
In fact, this Sicilian port was once home to classical antiquity’s largest boat, one that was only 16 meters shorter than the Octopus.
Built around 240 BC, the Syracusia could hold almost 2,000 passengers and reputedly bore more than 200 soldiers. Features included a garden, an indoor bath room with hot water, a library, a gymnasium, as well as a small temple dedicated to Aphrodite.
There were eight towers on the top deck which was supported by beautifully crafted wooden Atlases. All public spaces were decorated with ivory and marble and floored with mosaics depicting the entire story of the Iliad.
Oh, and there was a catapult.
Not much is known about the outside appearance of the ship, but Athenaeus describes that the top deck, which was wider than the rest of the ship, was supported by beautifully crafted wooden Atlases instead of simply wooden columns. Additionally, the top deck featured eight towers, equipped with two archers and four fully armed men. On the bow of the ship was a raised platform for fighting, on top of which was a giant catapult. 20 rows of oars would also have been visible from the outside, and possibly a promenade lined with flowers and tents for use by the passengers.
Makes our modern equivalents look pretty puny, eh?
But amazingly enough, the man behind the Syracusia was even more impressive.
The designer of Syracuse’s magnificent ship was the city’s most famous native. A polymath and a verifiable genius, he is generally considered the leading scientist and greatest mathematician of antiquity, indeed one of the greatest of all time.
We are talking about Archimedes.
Ah… the “Eureka!” man, you may be thinking… and you would be right.
The most famous anecdote of the mathematician comes from his days in service of King Hiero II. According to Vitruvius, a votive crown for a temple had been made for the king of Syracuse, who had supplied the gold for such a purpose. However, the royal was a bit suspicious that the crown was wholly gold, thinking that the greedy goldsmith had kept some for himself and used silver to make up the weight.
Archimedes was set on the task of finding out…without damaging the crown. It was a tricky problem, as the answer lie in finding out the density, not just the weight of the piece in question.
But then Archimedes took a bath (or so the story goes), and as he sunk into the tub he noticed the water rising… ah displacement!
It was at this moment that our hero figured out that by dividing the mass of the crown by the volume of water displaced, the density of the crown could be obtained… cheaper materials (aka not gold) would have a lesser density.
Incredibly pleased with this realization, Archimedes jumped out the bath, still naked, crying, “Eureka!” (I’ve found it!)
Of course, this could be a slightly fanciful version, as the story does not actually appear in any of the known works by Archimedes.
Moreover, on a scale of wow to super Archimedes cool, the crown yarn hardly ranks on the list.
His warfare inventions, however, are truly something to talk about. In fact, our own Van Bryan has done an excellent job covering some of his stranger/more villainous inventions. (If you haven’t had a chance to read it, we highly suggest giving it a lookover here: https://classicalwisdom.com/archimedes-super-villain/.)
Other notable (less violent) contributions from the Sicilian are the odometer, the compound pulley and the Archimedes pump screw, a still popular tool for bringing water upwards (out of the bottom of the hull of a giant ship, for example).
But it was in Mathematics where Archimedes truly shone… where his insights have had the greatest impact. He anticipated modern calculus and analysis by applying concepts of infinitesimals and the method of exhaustion to derive and rigorously prove a range of geometrical theorems, including the area of a circle, the surface area and volume of a sphere, and the fun area under a parabola.
Pretty important stuff really…
Archimedes’ other mathematical achievements include deriving an accurate approximation of pi (he was really very close), defining and investigating the spiral bearing his name, and creating a system using exponentiation for expressing very large numbers. He basically made his own numbers, not being fully satisfied with those already in existence.
He was also one of the first to apply mathematics to physical phenomena, founding hydrostatics and statics, as well as an explanation of the principle of the lever.
You can’t help but be impressed by Archimedes.
In fact, even his enemies were… when Archimedes was killed at the end of the siege of Syracuse, the Roman General Marcus Claudius Marcellus, the man heading the attack, was very upset. He had requested that the great mind be spared… and when he hadn’t, the General ensured that Archimedes was properly buried. His tomb illustrated the mathematician’s favorite proof, consisting of a sphere and a cylinder of the same height and diameter.
Death of Archimedes (1815) by Thomas Degeorge
137 years after Archimedes’ death, the famous Roman Orator, Cicero, found himself dispatched to Sicily. He wanted to find the mathematicians’ tomb, but the locals were not able to tell him the location. Eventually Cicero discovered it, unkept and overgrown, near the Agrigentine gate in Syracuse. After cleaning it up, Cicero saw the carving and read some of the verses that had been added as an inscription.
Sadly, the tomb’s location has once again been lost… neglected or hidden somewhere on this island.
While Archimedes’ other contributions have not been forgotten, not all have maintained their once esteemed statuses. His beautiful ship, the Syracusia, only sailed once to Alexandria before she was outdone.
Ptolemy’s son won the prize of having the largest vessel when he ordered the construction of a huge warship, the Tessarakonteres. It was 128 meters long, and bore more than 4,000 oarsmen and 2,850 soldiers… though according to Plutarch, it was almost immobile.
Our modern counterpart, the Octopus, still moored outside our window, suffered the same fate. While it held the honor of largest megayacht in the world after its completion in 2003, it now stands in the 11th position. The Azzam, a full 54 meters longer, is now the winner…but we suspect it can move.

Hypatia: The Last Academic – Part Two

by February 4, 2019

By Mary Naples, Contributing Writer, Classical Wisdom
Under Christian rule, Alexandria, once the definitive center of learning throughout the empire, was fast becoming anti-intellectual and inhospitable to Hypatia and the academic circle in which she traveled. In fact, this burgeoning new religion was oftentimes suspicious of learning, equating it to the work of the devil. Faith in Christ replaced scholarship in this brave new world.
An example of this hatred for scholarship was demonstrated in 392 when Theophilus (384 CE-412 CE) Bishop of Alexandria, led a braying mob of Christian zealots in the pummeling of the Serapeum, the city’s premier temple and library complex. Elevated by one-hundred steps on the acropolis of Alexandria, the Serepeum was made of luminous marble and rose above all other structures commanding the city skyscape. Equally impressive, the library within the Serapeum was considered the daughter to the defunct Library of Alexandria housing hundreds of thousands of scrolls. After the extremists razed the Serapeum complex and set fire to the scrolls, the swarm went on a holy mission tearing down other temples, statuary and religious sites, when all was said and done destroying over twenty-five hundred structures in total.
Serapeum of Alexandria
Papyrus drawing of Pope Theophilus of Alexandria, gospel in hand, standing triumphantly atop the Serapeum in 391 (from the Alexandrian World Chronicle)
In 414 CE Theophilus died and was succeeded by his nephew, Cyril (378 CE- 444 CE) who made his uncle look conciliatory in comparison. Ruling with an iron-fist from the get-go, he made his wrath known against another enemy of the Christians—the Jews. When some Christians were killed in a skirmish that had broken out between Christians and Jews, Cyril organized an army of thousands called the parabalani. Typically, from the lower rungs of society and oftentimes illiterate, the parabalani were at his call to serve their god, or in this case god’s representative, Cyril. In addition, some in his army were Nitrian monks who traveled to Alexandria from the desert fired up in righteous religious indignation against non-Christians. Both groups had a flagrant reputation for violence.
At Cyril’s behest, they seized the synagogues converting them into churches. But defacing their places of worship was not enough for the iron-fisted bishop, he also exiled the Jews from Alexandria and encouraged his Christian disciples to occupy their now abandoned homes and to seize their possessions.
Cyril of Alexandria
St Cyril of Alexandria, Patriarch, Confessor, and Doctor of the Catholic Church
It is emblematic of the staggering influence wielded by religious authority that Orestes—the governor of Alexandria—could do little but stand by the sidelines in horror and despair at this gross injustice. Though a Christian himself, Orestes was a nonsectarian and like his good friend Hypatia appalled by Cyril’s barbaric actions against the Jews.
Though it did no good, Orestes reported the atrocious events to the emperor in Constantinople, which put him squarely in the crosshairs of Cyril’s band of thugs. One night while out in his chariot, Orestes was confronted by an angry mob of parabalani and Nitrian monks—which soon turned into a physical altercation when one of the monks gashed Orestes’ head open with a stone. If not for the help of nonsectarian bystanders, Orestes would have died.
Illustration of Constantinople
Ancient Constantinople reconstructed from 4th-13th century
When the stone-hurling monk was apprehended, Orestes had him publicly tortured and the monk ultimately died. In true form, Cyril used the monk’s death in a propaganda campaign against the governor further fueling the fire between the disparate factions.
Attempts at reconciliation between the two leaders ended in failure. Through it all, the governor sought counsel from the wisest person in the land who stood resolutely by his side. But Cyril’s supporters saw Hypatia’s advocacy on Orestes’ behalf not as uniting but as dividing. Alexandria’s most acclaimed pagan was an easy target who they blamed for the continuing rift between the two men.
Then the rumors began. She has an undue influence on Orestes, they blustered. She’s bewitched him with her sorcery, others moaned. She is teaching idolatry, they shrieked. Calling her a witch, they even used her famed astrolabe against her saying it was an instrument of Satan. The cacophony of outcries against her became deafening. Then it happened. Demonstrating once again how easy it is to harm those who have been dehumanized.
Orestes and Hypatia
Oscar Isaac and Rachel Weisz play Orestes and Hypatia – Agora (2009)
On her daily ride through the city on that bright and sunny day in March of 415, Hypatia had set off for school in her chariot. As was usual for her, her mind was a million miles away. Perhaps she was thinking about her next seminar; about some philosophical dictate or mathematical law she would discuss in class. Being an exemplary teacher, her fortunate students were never far from mind.
But her introspection was savagely broken when she found herself physically confronted by a howling mob under the leadership of Peter, a church magistrate. Because she was not a civil authority, she lacked the security detail that Orestes enjoyed. But up until then, no academic had needed such protection in Alexandria.
From the beginning, it was violent. They ordered her off her chariot, then dragged her through the streets and into a church. She must have tried to reason with them, but her reasoning fell on the deafened ears of the righteous. After all, theirs is the will of god. They tore the clothes off of the “luminous child of reason” and in God’s house they flayed her with the jagged edges of roofing tiles.
As if that were not enough, while still alive and breathing, they gouged out her eyes. Once dead, they further violated her by cutting her body into pieces and parading the pieces throughout the streets of Alexandria. Finding rest, at long last, on a pyre. Violent criminals were treated with more forbearance than Alexandria’s most prominent intellectual.
Illustration of Hypatia's murder
Illustration by Louis Figuier in Vies des savants illustres, depuis l’antiquité jusqu’au dix-neuvième siècle from 1866, representing the author’s imagining of what the assault against Hypatia might have looked like.
From the farthest reaches of the empire to close by, both Christian and non-Christian alike were in an uproar about the abhorrent slaying of the greatest mathematician of the day. It was an outrage. Academics were considered inviolable because they enhanced the community with their scholarship and wisdom. But if being an academic was not enough to protect her, Hypatia was also an elite woman. A rank by itself deemed sacrosanct.
How could something of this magnitude happen to one as beloved as she? But the truth is that Hypatia was part of a dying breed, the last champion of a seven-hundred-year academic tradition vanishing under a tidal wave of anti-intellectual religious dogma. After Hypatia’s death, many pagan academics fled Alexandria in search of more tolerant cities. But eventually the tidal wave could be felt throughout the empire with religion replacing philosophy and clergy replacing academics.
Devastated, Orestes soon left public life. But Cyril’s star was still rising. Although never formally charged in Hypatia’s violent end, if not for the anti-pagan fervor he stirred up amongst his minions, such a horror would never have taken place. Following her death, Cyril was given the honorary moniker “the new Theophilus” by his jubilant followers for quashing the “last remnants of idolatry.” Under his continued leadership, Alexandria became an important Christian hub with Cyril eventually canonized as a saint. He is venerated in the Roman Catholic and Eastern Orthodox Churches to this day.

Hypatia: The Last Academic – Part One

by February 1, 2019

By Mary Naples, Contributing Writer, Classical Wisdom
They came to her by land. They came to her by sea. They came to her from the farthest reaches of the Roman Empire and they came to her from close by. Amongst the literati, Hypatia (355-415 CE), acclaimed philosopher and leading mathematician, was a rock star.
She was bold, she was beautiful, but most of all, she was brilliant. Her students, many of them adherents in the burgeoning new religion, Christianity, adored her and flocked to hear her every word. Congregating not only in the classroom but in the public square and even at her home—just to hear her speak. Hers was the school all serious students throughout the empire wished to attend. But students weren’t the only ones who were captivated by her brilliance. Amongst academics from near and from far, she was the one with whom they sought council.
But how did Hypatia, a woman in a deeply misogynist society, earn such high acclaim? By the tender age of thirty, Hypatia had become a legend within academic circles for fusing the two apparently disparate disciples of mathematics and philosophy together in the classroom. Although well-versed in both disciplines, academics tended to be trained as either philosophers or mathematicians and had schools in one discipline or the other but not in both. Hypatia’s school was the exception.
Weaned on mathematics by her father, Theon (335 CE-405 CE), the foremost mathematician in Alexandria, Hypatia would become his best pupil even assisting him in the seminal writings of Euclid and Ptolemy. In fact, Hypatia was so gifted, that her father ceded his school to her—retiring at only fifty-five years of age—when it became apparent that she surpassed him in ability. But for all her mathematical acumen, Hypatia had a strong affinity for philosophy which she believed led to the highest truth. Her robust background in mathematics and philosophy made her school a perfect venue for students who wanted to learn how the two disciplines were unified.
Ptolemaic System
Hypatia is known to have edited at least Book III of Ptolemy’s Almagest, which supported the geocentric model of the universe shown in this diagram.
But it’s important to have an understanding of what was meant by mathematics and philosophy in ancient times. Today, what two disciplines are more at odds than mathematics and philosophy? Though one is considered practical and useful, the other is considered metaphysical and without merit in our highly technical world. While both were thought to be sacrosanct by the ancients, a debate ensued between scholars over which of the two disciplines led to the highest truth.
Mathematics, which encompassed arithmetic, geometry, algebra, as well as astronomy, was irrefutable and as such was considered sacred and a path to a higher being or what the ancients termed “the One.” Meanwhile philosophy, a less demonstrable field, was a study employed to instill honor, wisdom and integrity within an individual. The philosophical goal being that this moral code could impart a oneness with the divine. Thus, the goal of both mathematics and philosophy was a transcendent affinity with the sacred, making them both more akin to our notion of religion.
Conic Sections
Hypatia wrote a commentary on Apollonius of Perga’s treatise on conic sections, but this commentary is no longer extant.
Neoplatonism, the type of speculative philosophy that Hypatia taught, espoused a renunciation of the material world in favor of spirituality. Neoplatonists believed that the materiality of the body and the world in general are things to be overcome. Hypatia herself was exemplar of this creed, choosing to remain celibate so she could focus her energies on scholarship and the satisfaction of the incorporeal world. One famous vignette has her thwarting the unwelcome advances of a student by showing him one of her menstruation rags, quipping “Is this what you love, young man?” Unsurprisingly, his desire for her was quelled.
Hypatia’s severe rejection of his advances illustrates how fundamental repudiation of the material world was to Neoplatonism. In this way, it was a philosophy not inconsistent with the essential tenets of Christianity. On account of this compatibility, many of Hypatia’s students were both Neoplatonists and Christian. Although a pagan, Hypatia was nonpartisan and endowed all her students to honor and respect one another and others in the world, regardless of religious affiliation.
Hypatia illustration
The play Hypatia, performed at the Haymarket Theatre in January 1893, was based on the novel by Charles Kingsley.
For as much as peaceful coexistence was the order of the day in Hypatia’s school, Alexandria was a tinderbox with disparate factions in conflict with one another; Christian against pagan and Jew, orthodox against heterodox, sectarian against non-sectarian and finally religious authority against civil authority.
To Be Continued….

Euclid: The Father of Geometry

by December 12, 2018

By Jocelyn Hitchcock, Contributing Writer, Classical Wisdom

We all know the varsity team: Einstein, Newton, Pythagoras, Descartes. These names are drilled into our heads all through grade school math and history classes, and possibly accompanied by an under-the-breath curse from a disgruntled calculus or physics student. However, another mathematician should receive our attention: Euclid of Alexandria.

It is difficult to underscore enough the importance and significance of Euclid and his impact on mathematics for the subsequent 2000 years. Nonetheless, we will try.

Portrait of the Mathematician Euclid

Euclid of Alexandria

Euclid’s Early Life

The documentation of Euclid’s life is scant, at best. While we have a great deal of his work in extant, facts about Euclid as a person come down to us mainly through little snippets by Proclus and Apollonius (among others). Proclus, a Greek philosopher living in the 5th century CE, writes retrospectively and so his information must be taken with a grain of salt. He writes that Euclid taught in Alexandria, Egypt during the time of Ptolemy I Soter (4th-3rd century BCE). This places him as younger than Plato, but slightly older than Archimedes. Euclid was likely born around 300 BCE and resided in Alexandria, Egypt for most, if not all, of his life. Some historians think that he might have studied for a bit at Plato’s Academy in Athens, but this is conjecture based on his style of teaching. Past this, nothing is known of Euclid.

Map of Alexandria, Egypt, birthplace of Euclid

Map Showing Alexandria, Egypt, birthplace of Euclid

Euclid’s Career

Often called the “Father of Geometry,” Euclid was a teacher of mathematics, cultivating a school of pupils not unlike the style of the Academy. Proclus writes that Ptolemy once asked Euclid if there was a “shortened way to study geometry than the Elements, to which Euclid replied that there was no royal road to geometry.” This would suggest that not only was Euclid noteworthy among mathematicians and scientists in Alexandria, but was prominent enough to have an audience with the ruler of Egypt. As with details of his early life, we don’t know specifics regarding his career, save for his extant works and the fact that he was a prominent teacher in Alexandria.

Euclid’s Works and Achievements

Euclid likely wouldn’t have reached his level of renown if his works didn’t survive to such an incredible extent. His main work, The Elements, is a proto-textbook of 13 sections pulling together definitions, theories, and constructions of mathematics at the time. He covers geometry, number theory, and incommensurate lines- all subjects that have proved to be invaluable over the development of mathematics.

Book cover of Euclid's work

The cover of Euclid’s Elements

The Elements consisted of five general axioms and five geometrical postulates. Euclid provided the basic model for mathematical argument that follows logical deductions from initial assumptions. For those of us (including myself) who are not so mathematically inclined to understand the nitty-gritty details of Euclid’s Elements, Sir Thomas Heath sums them up in his 1908 publication The Elements of Euclid:

The 5 Axioms of Euclid:

1. Things which are equal to the same thing are also equal to one another
2. If equals are added to equals, the whole (sums) are equal
3. If equals are subtracted from equals, the remainders (differences) are equal
4. Things that coincide with one another are equal to one another
5. The whole is greater than the part

The 5 Geometric Postulates:

1. It is possible to draw a straight line from any point to any point
2. It is possible to extend a finite straight line continuously in a straight line
3. It is possible to create a circle with any center and distance
4. All right angles are equal to one another
5. If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the straight lines, if produced indefinitely, will meet on that side on which the angles are less than two right angles.

Other important contributions from Euclid is his proof of Pythagoras‘ Theorem, providing us with formulas that calculate the volumes of solids like cones, pyramids, and cylinders, as well as identifying the first four ‘perfect numbers,’ among a dozen or so other theories and proofs.

Euclid's Proposition 1.47

The most famous proposition from The Elements, Proposition 1.47. Also known as the Pythagorean Theorem.

In addition to the Elements, five other works of Euclid have come down to us and have been able to be interpreted: Data, dealing with the nature and implications of “given” information in geometry; On Divisions of Figures, dealing with the division of geometrical figures into two or more equal parts or into parts in given ratios; Catoptrics, dealing with the theory of mirrors and the images formed in plane and spherical concave mirrors; Phaenomena, a treatise on spherical astronomy; and Optics the earliest surviving Greek treatise on perspective.

Euclid’s Death and Legacy

Portrait of Euclid

Euclid of Alexandria

We can assume that Euclid died in the mid-3rd century BCE in Alexandria, but that is all we know. However, he left behind a legacy that has survived almost two and a half millennia. His work on geometry and theory is still in use today, governing even advanced models of dimension mathematics. He is considered one of the greatest mathematicians to have ever lived, and a European Space Agency’s spacecraft was even named in his honor, the Euclid Spacecraft.