120-528: Gauss was a ship built in Germany specially for polar exploration, named after the mathematician and physical scientist Carl Friedrich Gauss . Purchased by Canada in 1904, the vessel was renamed CGS Arctic . As Arctic , the vessel made annual trips to the Canadian Arctic until 1925. The ship's fate is disputed among the sources, but all claim that by the mid-1920s, the vessel was out of service. The ship
240-441: A close reading in comparison with her supposed contributions to the work of Diophantus, Knorr suggests that Hypatia may also have edited Archimedes ' Measurement of a Circle , an anonymous text on isometric figures, and a text later used by John of Tynemouth in his work on Archimedes' measurement of the sphere. A high degree of mathematical accomplishment would have been needed to comment on Apollonius's advanced mathematics or
360-446: A forged anti-Christian letter appeared under her name. Damascius was "anxious to exploit the scandal of Hypatia's death", and attributed responsibility for her murder to Bishop Cyril and his Christian followers. A passage from Damascius's Life of Isidore , preserved in the Suda , concludes that Hypatia's murder was due to Cyril's envy over "her wisdom exceeding all bounds and especially in
480-480: A universal genius , but she was probably more of a teacher and commentator than an innovator. No evidence has been found that Hypatia ever published any independent works on philosophy and she does not appear to have made any groundbreaking mathematical discoveries. During Hypatia's time period, scholars preserved classical mathematical works and commented on them to develop their arguments, rather than publishing original works. It has also been suggested that
600-532: A "hydroscope", a device now known as a hydrometer , to determine the density or specific gravity of liquids. Based on this request, it has been claimed that Hypatia invented the hydrometer. The minute detail in which Synesius describes the instrument, however, indicates that he assumes she has never heard of the device, but trusts she will be able to replicate it based on a verbal description. Hydrometers were based on Archimedes ' 3rd century BC principles, may have been invented by him, and were being described by
720-514: A "martyr for philosophy", and her murder led philosophers to adopt attitudes that increasingly emphasized the pagan aspects of their beliefs system and helped create a sense of identity for philosophers as pagan traditionalists set apart from the Christian masses. Thus, while Hypatia's death did not bring an end to Neoplatonist philosophy as a whole, Watts argues that it did bring an end to her particular variety of it. Shortly after Hypatia's murder,
840-431: A "treacherous" priest. In his 1852 Hypatie and 1857 Hypathie et Cyrille , French poet Charles Leconte de Lisle portrayed Hypatia as the epitome of "vulnerable truth and beauty". Leconte de Lisle's first poem portrayed Hypatia as a woman born after her time, a victim of the laws of history. His second poem reverted to the eighteenth-century Deistic portrayal of Hypatia as the victim of Christian brutality, but with
960-414: A Christian church. There, the mob stripped Hypatia naked and murdered her using ostraka , which can either be translated as " roof tiles ", " oyster shells " or simply "shards". Damascius adds that they also cut out her eyeballs. They tore her body into pieces and dragged her limbs through the town to a place called Cinarion, where they set them on fire. According to Watts, this was in line with
1080-565: A Jewish-led massacre, Cyril closed all the synagogues in Alexandria, confiscated all the property belonging to the Jews, and expelled a number of Jews from the city ; Scholasticus suggests all the Jews were expelled, while John of Nikiu notes it was only those involved in the massacre. Orestes , the Roman prefect of Alexandria, who was also a close friend of Hypatia and a recent convert to Christianity,
1200-575: A backlash against her entire ideology. Hypatia, with her tolerance toward Christian students and her willingness to cooperate with Christian leaders, had hoped to establish a precedent that Neoplatonism and Christianity could coexist peacefully and cooperatively. Instead, her death and the subsequent failure by the Christian government to impose justice on her killers destroyed that notion entirely and led future Neoplatonists such as Damascius to consider Christian bishops as "dangerous, jealous figures who were also utterly unphilosophical." Hypatia became seen as
1320-432: A believer in "the laws of rational Nature" and "the capacities of the human mind free of dogmas " and described her death as "a bestial murder perpetrated by Cyril's tonsured hounds, with a fanatical gang at their heels". Later, in an entry for his Dictionnaire philosophique (1772), Voltaire again portrayed Hypatia as a freethinking deistic genius brutally murdered by ignorant and misunderstanding Christians. Most of
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#17330860462201440-404: A contemporary of Hypatia, describes her in his 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
1560-479: A controversy over the date of the Christian holiday of Easter 417 and that she was killed on the vernal equinox while making astronomical observations. Classical scholars Alan Cameron and Edward J. Watts both dismiss this hypothesis, noting that there is absolutely no evidence in any ancient text to support any part of the hypothesis. Hypatia's death sent shockwaves throughout the empire; for centuries, philosophers had been seen as effectively untouchable during
1680-436: 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. Philostorgius , another Christian historian, who
1800-692: A female intellectual, Hypatia became a role model for modern intelligent women and two feminist journals were named after her: the Greek journal Hypatia: Feminist Studies was launched in Athens in 1984, and Hypatia: A Journal of Feminist Philosophy in the United States in 1986. In the United Kingdom , the Hypatia Trust maintains a library and archive of feminine literary, artistic and scientific work; and, sponsors
1920-471: A financial economist might study the structural reasons why a company may have a certain share price , a financial mathematician may take the share price as a given, and attempt to use stochastic calculus to obtain the corresponding value of derivatives of the stock ( see: Valuation of options ; Financial modeling ). According to the Dictionary of Occupational Titles occupations in mathematics include
2040-495: A letter written in around 395 to his friend Herculianus, Synesius describes Hypatia as "... a person so renowned, her reputation seemed literally incredible. We have seen and heard for ourselves she who honorably presides over the mysteries of philosophy." Synesius preserves the legacy of Hypatia's opinions and teachings, such as the pursuit of "the philosophical state of apatheia —complete liberation from emotions and affections". The Christian historian Socrates of Constantinople ,
2160-517: A letter written to Hypatia in 413, Synesius requests her to intercede on behalf of two individuals impacted by the ongoing civil strife in Alexandria, insisting, "You always have power, and you can bring about good by using that power." He also reminds her that she had taught him that a Neoplatonic philosopher must introduce the highest moral standards to political life and act for the benefit of their fellow citizens. According to Socrates Scholasticus , in 414, following an exchange of hostilities and
2280-412: A lifelong virgin and that, when one of the men who came to her lectures tried to court her, she tried to soothe his lust by playing the lyre. When he refused to abandon his pursuit, she rejected him outright, displaying her bloody menstrual rags and declaring "This is what you really love, my young man, but you do not love beauty for its own sake." Damascius further relates that the young man
2400-575: A living truth–often more so, since a superstition is so intangible you can not get at it to refute it, but truth is a point of view, and so is changeable. Falsehoods and misconceptions about Hypatia continued to proliferate throughout the late twentieth century. Though Hubbard's fictional biography may have been intended for children, Lynn M. Osen relied on it as her main source in her influential 1974 article on Hypatia in her 1974 book Women in Mathematics . Fordham University used Hubbard's biography as
2520-550: A man does over a woman, but in the way a genuine philosopher will over a mere geometer." Hypatia's death was similar to those of Christian martyrs in Alexandria, who had been dragged through the streets during the Decian persecution in 250. Other aspects of Hypatia's life also fit the mold for a Christian martyr, especially her lifelong virginity. In the Early Middle Ages , Christians conflated Hypatia's death with stories of
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#17330860462202640-400: A manner which will help ensure that the plans are maintained on a sound financial basis. As another example, mathematical finance will derive and extend the mathematical or numerical models without necessarily establishing a link to financial theory, taking observed market prices as input. Mathematical consistency is required, not compatibility with economic theory. Thus, for example, while
2760-661: A political dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked and scraping off her skin with clamshells (some say roofing tiles). Science and mathematics in the Islamic world during the Middle Ages followed various models and modes of funding varied based primarily on scholars. It was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. Funding for translation of scientific texts in other languages
2880-423: A riot and attempting to murder the governor, not for his faith. Prominent Alexandrian Christians intervened and forced Cyril to drop the matter. Nonetheless, Cyril's feud with Orestes continued. Orestes frequently consulted Hypatia for advice because she was well-liked among both pagans and Christians alike, she had not been involved in any previous stages of the conflict, and she had an impeccable reputation as
3000-503: A saint." In response to these accusations, Catholic authors, as well as some French Protestants, insisted with increased vehemence that Cyril had absolutely no involvement in Hypatia's murder and that Peter the Lector was solely responsible. In the course of these heated debates, Hypatia tended to be cast aside and ignored, while the debates focused far more intently on the question of whether Peter
3120-468: A scholar, but does not mention her death, perhaps indicating that he saw her scholarly work as more significant. The intellectual Eudokia Makrembolitissa (1021–1096), the second wife of Byzantine emperor Constantine X Doukas , was described by the historian Nicephorus Gregoras as a "second Hypatia". Early eighteenth-century Deist scholar John Toland used the murder of Hypatia as the basis for an anti-Catholic tract, portraying Hypatia's death in
3240-547: A school edition, designed for the use of students rather than professional mathematicians." Hypatia also wrote a commentary on Apollonius of Perga 's work on conic sections , but this commentary is not extant. She also created an " Astronomical Canon "; this is believed to have been either a new edition of the Handy Tables by the Alexandrian Ptolemy or the aforementioned commentary on his Almagest . Based on
3360-532: A student of Athanasius of Alexandria . In the Laodikeia of Asia Minor (today Denizli in Turkey) until late 19th century Hypatia was venerated as identical to St. Catherine. The Byzantine Suda encyclopedia contains a very long entry about Hypatia, which summarizes two different accounts of her life. The first eleven lines come from one source and the rest of the entry comes from Damascius's Life of Isidore . Most of
3480-435: A tenth-century Byzantine encyclopedia, Hypatia flourished during the reign of Arcadius . Hoche reasoned that Damascius's description of her physical beauty would imply that she was at most 30 at that time, and the year 370 was 30 years prior to the midpoint of Arcadius's reign. In contrast, theories that she was born as early as 350 are based on the wording of the chronicler John Malalas (c. 491 – 578), who calls her old at
3600-560: A victim to the political jealousy which at that time prevailed. For as she had frequent interviews with Orestes, it was calumniously reported among the Christian populace that it was she who prevented Orestes from being reconciled to the bishop." Socrates Scholasticus unequivocally condemns the actions of the mob, declaring, "Surely nothing can be farther from the spirit of Christianity than the allowance of massacres, fights, and transactions of that sort." The Canadian mathematician Ari Belenkiy has argued that Hypatia may have been involved in
3720-522: A wise counselor. Despite Hypatia's popularity, Cyril and his allies attempted to discredit her and undermine her reputation. Socrates Scholasticus mentions rumors accusing Hypatia of preventing Orestes from reconciling with Cyril. Traces of other rumors that spread among the Christian populace of Alexandria may be found in the writings of the seventh-century Egyptian Coptic bishop John of Nikiû , who alleges in his Chronicle that Hypatia had engaged in satanic practices and had intentionally hampered
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3840-436: A young woman by the early photographer Julia Margaret Cameron and an 1885 painting by Charles William Mitchell showing a nude Hypatia standing before an altar in a church. At the same time, European philosophers and scientists described Hypatia as the last representative of science and free inquiry before a "long medieval decline". In 1843, German authors Soldan and Heppe argued in their highly influential History of
3960-420: Is mathematics that studies entirely abstract concepts . From the eighteenth century onwards, this was a recognized category of mathematical activity, sometimes characterized as speculative mathematics , and at variance with the trend towards meeting the needs of navigation , astronomy , physics , economics , engineering , and other applications. Another insightful view put forth is that pure mathematics
4080-451: Is a mathematical science with specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on problems, often concrete but sometimes abstract. As professionals focused on problem solving, applied mathematicians look into the formulation, study, and use of mathematical models in science , engineering , business , and other areas of mathematical practice. Pure mathematics
4200-426: Is better than to never think at all." Hubbard claims that, as a young woman, Hypatia traveled to Athens, where she studied under Plutarch of Athens . All of this supposed biographical information, however, is completely fictional and is not found in any ancient source. Hubbard even attributes to Hypatia numerous completely fabricated quotations in which she presents modern, rationalist views. The cover illustration for
4320-447: Is either built on myth or hearsay as opposed to evidence. Either that or we are missing all of the evidence that would support it." Neoplatonism and paganism both survived for centuries after Hypatia's death, and new academic lecture halls continued to be built in Alexandria after her death. Over the next 200 years, Neoplatonist philosophers such as Hierocles of Alexandria , John Philoponus , Simplicius of Cilicia , and Olympiodorus
4440-573: Is known, but also because it contradicts Damascius's own statement quoted in the same entry about Hypatia being a lifelong virgin. Watts suggests that someone probably misunderstood the meaning of the word gynē used by Damascius to describe Hypatia in his Life of Isidore , since the same word can mean either "woman" or "wife". The Byzantine and Christian intellectual Photios ( c. 810/820–893) includes both Damascius's account of Hypatia and Socrates Scholasticus's in his Bibliotheke . In his own comments, Photios remarks on Hypatia's great fame as
4560-590: Is not agreed upon. According to schiffe-und-mehr.com , Arctic was abandoned in 1925 and left to rot at her moorings. Maginley and Collin claim the vessel was broken up in 1926 while the Miramar Ship Index say the ship was abandoned in 1927. Mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems . Mathematicians are concerned with numbers , data , quantity , structure , space , models , and change . One of
4680-400: Is not necessarily applied mathematics : it is possible to study abstract entities with respect to their intrinsic nature, and not be concerned with how they manifest in the real world. Even though the pure and applied viewpoints are distinct philosophical positions, in practice there is much overlap in the activity of pure and applied mathematicians. To develop accurate models for describing
4800-473: The Almagest , based on the title of Theon's commentary on the third book of Almagest , which reads "Commentary by Theon of Alexandria on Book III of Ptolemy's Almagest , edition revised by my daughter Hypatia, the philosopher", but, based on analysis of the titles of Theon's other commentaries and similar titles from the time period, scholars have concluded that Hypatia corrected, not her father's commentary, but
4920-564: The Almagest . Hypatia wrote a commentary on Diophantus 's thirteen-volume Arithmetica , which had been written sometime around the year 250 AD. It set out more than 100 mathematical problems, for which solutions are proposed using algebra . For centuries, scholars believed that this commentary had been lost. Only volumes one through six of the Arithmetica have survived in the original Greek, but at least four additional volumes have been preserved in an Arabic translation produced around
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5040-746: The Eastern Roman Empire . She was a prominent thinker in Alexandria where she taught philosophy and astronomy . Although preceded by Pandrosion , another Alexandrian female mathematician , she is the first female mathematician whose life is reasonably well recorded. Hypatia was renowned in her own lifetime as a great teacher and a wise counselor. She wrote a commentary on Diophantus 's thirteen-volume Arithmetica , which may survive in part, having been interpolated into Diophantus's original text, and another commentary on Apollonius of Perga 's treatise on conic sections , which has not survived. Many modern scholars also believe that Hypatia may have edited
5160-634: The Pythagorean school , whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypatia of Alexandria ( c. AD 350 – 415). She succeeded her father as librarian at the Great Library and wrote many works on applied mathematics. Because of
5280-602: The Schock Prize , and the Nevanlinna Prize . The American Mathematical Society , Association for Women in Mathematics , and other mathematical societies offer several prizes aimed at increasing the representation of women and minorities in the future of mathematics. Several well known mathematicians have written autobiographies in part to explain to a general audience what it is about mathematics that has made them want to devote their lives to its study. These provide some of
5400-411: The beam , with a draught of 4.8 m (15 ft 9 in). With a 325 hp (242 kW) triple expansion steam engine driving one screw to augment the sails, she was capable of 7 knots (13 km/h; 8.1 mph). Classed "A1" by Germanischer Lloyds , she was designed to carry 700 tons of stores, enough to make her self-sufficient for up to three years with a crew of 30 aboard. The hull
5520-477: The feminist movement . Since the late twentieth century, some portrayals have associated Hypatia's death with the destruction of the Library of Alexandria , despite the historical fact that the library no longer existed during Hypatia's lifetime. Hypatia was the daughter of the mathematician Theon of Alexandria ( c. 335 – c. 405 AD ). According to classical historian Edward J. Watts , Theon
5640-478: The graduate level . In some universities, a qualifying exam serves to test both the breadth and depth of a student's understanding of mathematics; the students who pass are permitted to work on a doctoral dissertation . Mathematicians involved with solving problems with applications in real life are called applied mathematicians . Applied mathematicians are mathematical scientists who, with their specialized knowledge and professional methodology, approach many of
5760-566: The "spirit of Plato and the body of Aphrodite ." Kingsley's novel was tremendously popular; it was translated into several European languages and remained continuously in print for the rest of the century. It promoted the romantic vision of Hypatia as "the last of the Hellenes" and was quickly adapted into a broad variety of stage productions, the first of which was a play written by Elizabeth Bowers, performed in Philadelphia in 1859, starring
5880-446: The 2nd century AD in a poem by the Roman author Remnius. Although modern authors frequently credit Hypatia with having developed a variety of other inventions, these other attributions may all be discounted as spurious. Booth concludes, "The modern day reputation held by Hypatia as a philosopher, mathematician, astronomer, and mechanical inventor, is disproportionate to the amount of surviving evidence of her life's work. This reputation
6000-418: The 5th and 6th centuries, and perhaps until the age of Justinian I . Fables should be taught as fables, myths as myths, and miracles as poetic fantasies. To teach superstitions as truths is a most terrible thing. The child mind accepts and believes them, and only through great pain and perhaps tragedy can he be in after years relieved of them. In fact, men will fight for a superstition quite as quickly as for
6120-600: The Decian martyrs and she became part of the basis for the legend of Saint Catherine of Alexandria , a virgin martyr said to have been exceedingly wise and well-educated. The earliest attestation for the cult of Saint Catherine comes from the eighth century, around three hundred years after Hypatia's death. One story tells of Saint Catherine being confronted by fifty pagan philosophers seeking to convert her, but instead converting all of them to Christianity through her eloquence. Another legend claimed that Saint Catherine had been
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#17330860462206240-448: The Earth. In his early commentary, Theon had tried to improve upon Ptolemy's division calculation. In the text edited by Hypatia, a tabular method is detailed. This tabular method might be the "astronomical table" which historic sources attribute to Hypatia. Classicist Alan Cameron additionally states that it is possible Hypatia may have edited, not only Book III, but all nine extant books of
6360-548: The Hypatia-in-the-Woods women's retreat in Washington , United States. Judy Chicago 's large-scale art piece The Dinner Party awards Hypatia a table setting . The table runner depicts Hellenistic goddesses weeping over her death. Chicago states that the social unrest leading to Hypatia's murder resulted from Roman patriarchy and mistreatment of women and that this ongoing unrest can only be brought to an end through
6480-578: The Italian and German universities, but as they already enjoyed substantial freedoms and autonomy the changes there had begun with the Age of Enlightenment , the same influences that inspired Humboldt. The Universities of Oxford and Cambridge emphasized the importance of research , arguably more authentically implementing Humboldt's idea of a university than even German universities, which were subject to state authority. Overall, science (including mathematics) became
6600-451: The Lector had acted alone or under Cyril's orders. In the nineteenth century European literary authors spun the legend of Hypatia as part of neo-Hellenism , a movement that romanticised ancient Greeks and their values. Interest in the "literary legend of Hypatia" began to rise. Diodata Saluzzo Roero 's 1827 Ipazia ovvero delle Filosofie suggested that Cyril had actually converted Hypatia to Christianity, and that she had been killed by
6720-478: The Roman prefects and other prominent political leaders. Partly as a result of Theophilus's tolerance, Hypatia became extremely popular with the people of Alexandria and exerted profound political influence. Theophilus died unexpectedly in 412. He had been training his nephew Cyril , but had not officially named him as his successor. A violent power struggle over the diocese broke out between Cyril and his rival Timothy . Cyril won and immediately began to punish
6840-528: The Syrian bishop Severus Sebokht (575–667), who describes its contents in his own treatise on astrolabes. Hypatia and Theon may have also studied Ptolemy's Planisphaerium , which describes the calculations necessary in order to construct an astrolabe. Synesius's wording indicates that Hypatia did not design or construct the astrolabe, but acted as a guide and mentor during the process of constructing it. In another letter, Synesius requests Hypatia to construct him
6960-484: The Witchcraft Trials that Hypatia may have been, in effect, the first famous " witch " punished under Christian authority (see witch-hunt ). Hypatia was honored as an astronomer when 238 Hypatia , a main belt asteroid discovered in 1884, was named for her. The lunar crater Hypatia was also named for her, in addition to craters named for her father Theon. The 180 km Rimae Hypatia are located north of
7080-489: The Younger made astronomical observations, taught mathematics, and wrote lengthy commentaries on the works of Plato and Aristotle. Hypatia was not the last female Neoplatonist philosopher; later ones include Aedesia , Asclepigenia , and Theodora of Emesa . According to Watts, however, Hypatia had no appointed successor, no spouse, and no offspring and her sudden death not only left her legacy unprotected, but also triggered
7200-492: The additional material in the Arabic manuscripts came from Hypatia was the nineteenth-century scholar Paul Tannery . In 1885, Sir Thomas Heath published the first English translation of the surviving portion of the Arithmetica . Heath argued that surviving text of Arithmetica is actually a school edition produced by Hypatia to aid her students. According to Mary Ellen Waithe, Hypatia used an unusual algorithm for division (in
7320-429: The astronomical Canon. Because of this, most scholars today recognize that Hypatia must have been among the leading mathematicians of her day. One of Synesius's letters describes Hypatia as having taught him how to construct a silver plane astrolabe as a gift for an official. An astrolabe is a device used to calculate date and time based on the positions of the stars and planets. It can also be used to predict where
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#17330860462207440-423: The author of the interpolations can only have been "an essentially trivial mind... in direct conflict with ancient testimonies of Hypatia's high caliber as a philosopher and mathematician." Cameron rejects this argument, noting that "Theon too enjoyed a high reputation, yet his surviving work has been judged 'completely unoriginal.'" Cameron also insists that "Hypatia's work on Diophantus was what we today might call
7560-455: The best glimpses into what it means to be a mathematician. The following list contains some works that are not autobiographies, but rather essays on mathematics and mathematicians with strong autobiographical elements. Hypatia Hypatia (born c. 350–370 - March 415 AD) was a Neoplatonist philosopher, astronomer, and mathematician who lived in Alexandria , Egypt , then part of
7680-445: The biological sense and was often used merely to signal strong feelings of paternal connection. Hypatia's exact year of birth is still under debate, with suggested dates ranging from 350 to 370 AD. Many scholars have followed Richard Hoche in inferring that Hypatia was born around 370. According to Damascius's lost work Life of Isidore, preserved in the entry for Hypatia in the Suda ,
7800-430: The book, a drawing of Hypatia by artist Jules Maurice Gaspard showing her as a beautiful young woman with her wavy hair tied back in the classical style, has now become the most iconic and widely reproduced image of her. Around the same time, Hypatia was adopted by feminists , and her life and death began to be viewed in the light of the women's rights movement. The author Carlo Pascal claimed in 1908 that her murder
7920-511: The church's influence over Orestes: And in those days there appeared in Alexandria a female philosopher, a pagan named Hypatia, and she was devoted at all times to magic, astrolabes and instruments of music, and she beguiled many people through her Satanic wiles. And the governor of the city honoured her exceedingly; for she had beguiled him through her magic. And he ceased attending church as had been his custom... And he not only did this, but he drew many believers to her, and he himself received
8040-578: The closure of the Mouseion and the destruction of the Serapeum may have led Hypatia and her father to focus their efforts on preserving seminal mathematical books and making them accessible to their students. The Suda mistakenly states that all of Hypatia's writings have been lost, but modern scholarship has identified several works by her as extant. This kind of authorial uncertainty is typical of female philosophers from antiquity. Hypatia wrote in Greek, which
8160-657: The crater, one degree south of the equator, along the Mare Tranquillitatis . In 1908, American writer Elbert Hubbard published a putative biography of Hypatia in his series Little Journeys to the Homes of Great Teachers . The book is almost entirely a work of fiction. In it, Hubbard relates a completely made-up physical exercise program which he claims Theon established for his daughter, involving "fishing, horseback-riding, and rowing". He claims that Theon taught Hypatia to "Reserve your right to think, for even to think wrongly
8280-468: The displays of public violence that sometimes occurred in Roman cities and the murder of a female philosopher at the hand of a mob was seen as "profoundly dangerous and destabilizing". Although no concrete evidence was ever discovered definitively linking Cyril to the murder of Hypatia, it was widely believed that he had ordered it. Even if Cyril had not directly ordered the murder, his smear campaign against Hypatia had inspired it. The Alexandrian council
8400-500: The earliest known mathematicians was Thales of Miletus ( c. 624 – c. 546 BC ); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry , by deriving four corollaries to Thales's theorem . The number of known mathematicians grew when Pythagoras of Samos ( c. 582 – c. 507 BC ) established
8520-607: The entry ignores Hypatia altogether and instead deals with the controversy over whether or not Cyril was responsible for her death. Voltaire concludes with the snide remark that "When one strips beautiful women naked, it is not to massacre them." In his monumental work The History of the Decline and Fall of the Roman Empire , the English historian Edward Gibbon expanded on Toland and Voltaire's misleading portrayals by declaring Cyril as
8640-401: The fate of this book." Hypatia's death became symbolic for some historians. For example, Kathleen Wider proposes that the murder of Hypatia marked the end of Classical antiquity , and Stephen Greenblatt writes that her murder "effectively marked the downfall of Alexandrian intellectual life". On the other hand, Christian Wildberg notes that Hellenistic philosophy continued to flourish in
8760-484: The first eleven lines of the entry probably come from Hesychius 's Onomatologos , but some parts are of unknown origin, including a claim that she was "the wife of Isidore the Philosopher" (apparently Isidore of Alexandria ). Watts describes this as a very puzzling claim, not only because Isidore of Alexandria was not born until long after Hypatia's death, and no other philosopher of that name contemporary with Hypatia
8880-494: The focus of universities in the 19th and 20th centuries. Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content. According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge. The German university system fostered professional, bureaucratically regulated scientific research performed in well-equipped laboratories, instead of
9000-992: The following. There is no Nobel Prize in mathematics, though sometimes mathematicians have won the Nobel Prize in a different field, such as economics or physics. Prominent prizes in mathematics include the Abel Prize , the Chern Medal , the Fields Medal , the Gauss Prize , the Nemmers Prize , the Balzan Prize , the Crafoord Prize , the Shaw Prize , the Steele Prize , the Wolf Prize ,
9120-629: The imposing problems presented in related scientific fields. With professional focus on a wide variety of problems, theoretical systems, and localized constructs, applied mathematicians work regularly in the study and formulation of mathematical models . Mathematicians and applied mathematicians are considered to be two of the STEM (science, technology, engineering, and mathematics) careers. The discipline of applied mathematics concerns itself with mathematical methods that are typically used in science, engineering, business, and industry; thus, "applied mathematics"
9240-569: The kind of research done by private and individual scholars in Great Britain and France. In fact, Rüegg asserts that the German system is responsible for the development of the modern research university because it focused on the idea of "freedom of scientific research, teaching and study." Mathematicians usually cover a breadth of topics within mathematics in their undergraduate education , and then proceed to specialize in topics of their own choice at
9360-470: The king of Prussia , Fredrick William III , to build a university in Berlin based on Friedrich Schleiermacher 's liberal ideas; the goal was to demonstrate the process of the discovery of knowledge and to teach students to "take account of fundamental laws of science in all their thinking." Thus, seminars and laboratories started to evolve. British universities of this period adopted some approaches familiar to
9480-435: The late fourth century. The first was the overtly pagan religious Neoplatonism taught at the Serapeum , which was greatly influenced by the teachings of Iamblichus . The second variety was the more moderate and less polemical variety championed by Hypatia and her father Theon, which was based on the teachings of Plotinus . Although Hypatia was a pagan, she was tolerant of Christians. In fact, every one of her known students
9600-598: The main source of information about Hypatia in a medieval history course. Carl Sagan 's 1980 PBS series Cosmos: A Personal Voyage relates a heavily fictionalized retelling of Hypatia's death, which results in the " Great Library of Alexandria " being burned by militant Christians. In actuality, though Christians led by Theophilus did destroy the Serapeum in 391 AD, the Library of Alexandria had already ceased to exist in any recognizable form centuries prior to Hypatia's birth. As
9720-457: The opposing faction; he closed the churches of the Novatianists , who had supported Timothy, and confiscated their property. Hypatia's school seems to have immediately taken a strong distrust toward the new bishop, as evidenced by the fact that, in all his vast correspondences, Synesius only ever wrote one letter to Cyril, in which he treats the younger bishop as inexperienced and misguided. In
9840-425: The parabalani from attending "any public spectacle whatever" or entering "the meeting place of a municipal council or a courtroom." It also severely restricted their recruitment by limiting the total number of parabalani to no more than five hundred. According to Damascius , Cyril allegedly only managed to escape even more serious punishment by bribing one of Theodosius's officials. Watts argues that Hypatia's murder
9960-515: The plane astrolabe, but the plane astrolabe was in use at least 500 years before Hypatia was born. Hypatia may have learned how to construct a plane astrolabe from her father Theon, who had written two treatises on astrolabes: one entitled Memoirs on the Little Astrolabe and another study on the armillary sphere in Ptolemy's Almagest . Theon's treatise is now lost, but it was well known to
10080-531: The probability and likely cost of the occurrence of an event such as death, sickness, injury, disability, or loss of property. Actuaries also address financial questions, including those involving the level of pension contributions required to produce a certain retirement income and the way in which a company should invest resources to maximize its return on investments in light of potential risk. Using their broad knowledge, actuaries help design and price insurance policies, pension plans, and other financial strategies in
10200-484: The real world, many applied mathematicians draw on tools and techniques that are often considered to be "pure" mathematics. On the other hand, many pure mathematicians draw on natural and social phenomena as inspiration for their abstract research. Many professional mathematicians also engage in the teaching of mathematics. Duties may include: Many careers in mathematics outside of universities involve consulting. For instance, actuaries assemble and analyze data to estimate
10320-484: The restoration of an original, primeval matriarchy. She (anachronistically and incorrectly) concludes that Hypatia's writings were burned in the Library of Alexandria when it was destroyed. Major works of twentieth century literature contain references to Hypatia, including Marcel Proust 's volume "Within a Budding Grove" from In Search of Lost Time , and Iain Pears 's The Dream of Scipio . Hypatia has continued to be
10440-403: The seventeenth century at Oxford with the scientists Robert Hooke and Robert Boyle , and at Cambridge where Isaac Newton was Lucasian Professor of Mathematics & Physics . Moving into the 19th century, the objective of universities all across Europe evolved from teaching the "regurgitation of knowledge" to "encourag[ing] productive thinking." In 1810, Alexander von Humboldt convinced
10560-408: The sole cause of all evil in Alexandria at the beginning of the fifth century and construing Hypatia's murder as evidence to support his thesis that the rise of Christianity hastened the decline of the Roman Empire. He remarks on Cyril's continued veneration as a Christian saint, commenting that "superstition [Christianity] perhaps would more gently expiate the blood of a virgin, than the banishment of
10680-541: The stars and planets will be on any given date. A "little astrolabe", or "plane astrolabe", is a kind of astrolabe that used stereographic projection of the celestial sphere to represent the heavens on a plane surface, as opposed to an armillary sphere , which was globe-shaped. Armillary spheres were large and normally used for display, whereas a plane astrolabe was portable and could be used for practical measurements. The statement from Synesius's letter has sometimes been wrongly interpreted to mean that Hypatia invented
10800-436: The surviving text of Ptolemy 's Almagest , based on the title of her father Theon 's commentary on Book III of the Almagest . Hypatia constructed astrolabes and hydrometers , but did not invent either of these, which were both in use long before she was born. She was tolerant toward Christians and taught many Christian students, including Synesius , the future bishop of Ptolemais . Ancient sources record that Hypatia
10920-460: The text of Almagest itself. Her contribution is thought to be an improved method for the long division algorithms needed for astronomical computation. The Ptolemaic model of the universe was geocentric , meaning it taught that the Sun revolved around the Earth. In the Almagest , Ptolemy proposed a division problem for calculating the number of degrees swept out by the Sun in a single day as it orbits
11040-438: The textbook for centuries and almost totally supplanted all other editions. Nothing is known about Hypatia's mother, who is never mentioned in any of the extant sources. Theon dedicates his commentary on Book IV of Ptolemy's Almagest to an individual named Epiphanius, addressing him as "my dear son", indicating that he may have been Hypatia's brother, but the Greek word Theon uses ( teknon ) does not always mean "son" in
11160-443: The then-standard sexagesimal numeral system), making it easy for scholars to pick out which parts of the text she had written. The consensus that Hypatia's commentary is the source of the additional material in the Arabic manuscripts of the Arithmetica has been challenged by Wilbur Knorr , a historian of mathematics, who argues that the interpolations are "of such low level as not to require any real mathematical insight" and that
11280-447: The things concerning astronomy". Damascius's account of the Christian murder of Hypatia is the sole historical source attributing direct responsibility to Bishop Cyril. At the same time, Damascius was not entirely kind to Hypatia either; he characterizes her as nothing more than a wandering Cynic , and compares her unfavorably with his own teacher Isidore of Alexandria , remarking that "Isidorus greatly outshone Hypatia, not just as
11400-399: The time of her death in 415. Robert Penella argues that both theories are weakly based, and that her birth date should be left unspecified. Hypatia was a Neoplatonist, but, like her father, she rejected the teachings of Iamblichus and instead embraced the original Neoplatonism formulated by Plotinus . The Alexandrian school was renowned at the time for its philosophy, and Alexandria
11520-410: The time, Theon's mathematical work has been deemed by modern standards as essentially "minor", "trivial", and "completely unoriginal". His primary achievement was the production of a new edition of Euclid's Elements , in which he corrected scribal errors that had been made over the course of nearly 700 years of copying. Theon's edition of Euclid's Elements became the most widely used edition of
11640-661: The traditional manner in which Alexandrians carried the bodies of the "vilest criminals" outside the city limits to cremate them as a way of symbolically purifying the city. Although Socrates Scholasticus never explicitly identifies Hypatia's murderers, they are commonly assumed to have been members of the parabalani . Christopher Haas disputes this identification, arguing that the murderers were more likely "a crowd of Alexandrian laymen". Socrates Scholasticus presents Hypatia's murder as entirely politically motivated and makes no mention of any role that Hypatia's paganism might have played in her death. Instead, he reasons that "she fell
11760-425: The twist that Hypatia tries and fails to convince Cyril that Neoplatonism and Christianity are actually fundamentally the same. Charles Kingsley 's 1853 novel Hypatia; Or, New Foes with an Old Face was originally intended as a historical treatise, but instead became a typical mid- Victorian romance with a militantly anti-Catholic message, portraying Hypatia as a "helpless, pretentious, and erotic heroine" with
11880-556: The unbelievers at his house. According to Socrates Scholasticus , during the Christian season of Lent in March 415, a mob of Christians under the leadership of a lector named Peter raided Hypatia's carriage as she was travelling home. They dragged her into a building known as the Kaisarion , a former pagan temple and center of the Roman imperial cult in Alexandria that had been converted into
12000-465: The worst possible light by changing the story and inventing elements not found in any of the ancient sources. A 1721 response by Thomas Lewis defended Cyril, rejected Damascius's account as unreliable because its author was "a heathen " and argued that Socrates Scholasticus was "a Puritan ", who was consistently biased against Cyril. Voltaire , in his Examen important de Milord Bolingbroke ou le tombeau de fanatisme (1736) interpreted Hypatia as
12120-561: The writer in the titular role. On 2 January 1893, a much higher-profile stage play adaptation Hypatia , written by G. Stuart Ogilvie and produced by Herbert Beerbohm Tree , opened at the Haymarket Theatre in London. The title role was initially played by Julia Neilson , and it featured an elaborate musical score written by the composer Hubert Parry . The novel also spawned works of visual art, including an 1867 image portraying Hypatia as
12240-458: The year 860. The Arabic text contains numerous expansions not found in the Greek text, including verifications of Diophantus's examples and additional problems. Cameron states that the most likely source of the additional material is Hypatia, since Hypatia is the only ancient writer known to have written a commentary on the Arithmetica and the additions appear to follow the same methods used by her father Theon. The first person to deduce that
12360-938: Was Al-Khawarizmi . A notable feature of many scholars working under Muslim rule in medieval times is that they were often polymaths. Examples include the work on optics , maths and astronomy of Ibn al-Haytham . The Renaissance brought an increased emphasis on mathematics and science to Europe. During this period of transition from a mainly feudal and ecclesiastical culture to a predominantly secular one, many notable mathematicians had other occupations: Luca Pacioli (founder of accounting ); Niccolò Fontana Tartaglia (notable engineer and bookkeeper); Gerolamo Cardano (earliest founder of probability and binomial expansion); Robert Recorde (physician) and François Viète (lawyer). As time passed, many mathematicians gravitated towards universities. An emphasis on free thinking and experimentation had begun in Britain's oldest universities beginning in
12480-406: Was Christian. One of her most prominent pupils was Synesius of Cyrene , who went on to become a bishop of Ptolemais (now in eastern Libya ) in 410. Afterward, he continued to exchange letters with Hypatia and his extant letters are the main sources of information about her career. Seven letters by Synesius to Hypatia have survived, but none from her addressed to him are extant. In
12600-421: Was alarmed at Cyril's conduct and sent an embassy to Constantinople. The advisors of Theodosius II launched an investigation to determine Cyril's role in the murder. The investigation resulted in the emperors Honorius and Theodosius II issuing an edict in autumn of 416, which attempted to remove the parabalani from Cyril's power and instead place them under the authority of Orestes. The edict restricted
12720-448: Was also a contemporary of Hypatia, states that she excelled her father in mathematics and the lexicographer Hesychius of Alexandria records that, like her father, she was also an extraordinarily talented astronomer. Damascius writes that Hypatia was "exceedingly beautiful and fair of form", but nothing else is known regarding her physical appearance and no ancient depictions of her have survived. Damascius states that Hypatia remained
12840-518: Was an anti-feminist act and brought about a change in the treatment of women, as well as the decline of the Mediterranean civilization in general. Dora Russell published a book on the inadequate education of women and inequality with the title Hypatia or Woman and Knowledge in 1925. The prologue explains why she chose the title: "Hypatia was a university lecturer denounced by Church dignitaries and torn to pieces by Christians. Such will probably be
12960-484: Was built by the Howaldtswerke-Deutsche Werft shipyard at Kiel at a cost of 500,000 marks . Launched on 2 April 1901 she was modelled on Fridtjof Nansen 's ship Fram , and rigged as a barquentine . Displacing 1,442 long tons (1,465 t), Gauss had a tonnage of 762 gross register tons (GRT). The ship was 46 m (150 ft 11 in) long, 11 m (36 ft 1 in) in
13080-565: Was exceptionally strong, and the rudder and propeller were designed to be hoisted aboard for inspection or repairs. Between 1901 and 1903 Gauss explored the Antarctic in the Gauss expedition under the leadership of Erich von Drygalski . In early 1904 the ship was purchased by the Canadian government under the advice of Joseph-Elzéar Bernier , who had surveyed the ship before the acquisition. The ship
13200-495: Was murdered by a mob of Christians led by a lector named Peter. Hypatia's murder shocked the empire and transformed her into a " martyr for philosophy", leading future Neoplatonists such as the historian Damascius ( c. 458 – c. 538 ) to become increasingly fervent in their opposition to Christianity . During the Middle Ages , Hypatia was co-opted as a symbol of Christian virtue and scholars believe she
13320-431: Was ongoing throughout the reign of certain caliphs, and it turned out that certain scholars became experts in the works they translated, and in turn received further support for continuing to develop certain sciences. As these sciences received wider attention from the elite, more scholars were invited and funded to study particular sciences. An example of a translator and mathematician who benefited from this type of support
13440-468: Was outraged by Cyril's actions and sent a scathing report to the emperor. The conflict escalated and a riot broke out in which the parabalani , a group of Christian clerics under Cyril's authority, nearly killed Orestes. As punishment, Orestes had Ammonius, the monk who had started the riot, publicly tortured to death. Cyril tried to proclaim Ammonius a martyr, but Christians in Alexandria were disgusted, since Ammonius had been killed for inciting
13560-460: Was part of the basis for the legend of Saint Catherine of Alexandria . During the Age of Enlightenment , she became a symbol of opposition to Catholicism . In the nineteenth century, European literature, especially Charles Kingsley 's 1853 novel Hypatia , romanticized her as "the last of the Hellenes ". In the twentieth century, Hypatia became seen as an icon for women's rights and a precursor to
13680-586: Was regarded as second only to Athens as the philosophical capital of the Greco-Roman world. Hypatia taught students from all over the Mediterranean. According to Damascius, she lectured on the writings of Plato and Aristotle . He also states that she walked through Alexandria in a tribon , a kind of cloak associated with philosophers, giving impromptu public lectures. According to Watts, two main varieties of Neoplatonism were taught in Alexandria during
13800-610: Was renamed Arctic and under the command of Bernier she explored the Arctic Archipelago . Bernier and Arctic made annual expeditions to Canada's north. On 1 July 1909, Bernier, without government approval, claimed the entire area between Canada's eastern and western borders all the way to the North Pole . Bernier only left the ship during the First World War , returning to command Arctic again from 1922 to 1925. The vessel's end
13920-549: Was so traumatized that he abandoned his desires for her immediately. From 382 – 412, the bishop of Alexandria was Theophilus . Theophilus was militantly opposed to Iamblichean Neoplatonism and, in 391, he demolished the Serapeum. Despite this, Theophilus tolerated Hypatia's school and seems to have regarded Hypatia as his ally. Theophilus supported the bishopric of Hypatia's pupil Synesius, who describes Theophilus in his letters with love and admiration. Theophilus also permitted Hypatia to establish close relationships with
14040-472: Was the head of a school called the "Mouseion", which was named in emulation of the Hellenistic Mouseion , whose membership had ceased in the 260s AD. Theon's school was exclusive, highly prestigious, and doctrinally conservative. Theon rejected the teachings of Iamblichus and may have taken pride in teaching a pure, Plotinian Neoplatonism . Although he was widely seen as a great mathematician at
14160-527: Was the language spoken by most educated people in the Eastern Mediterranean at the time. In classical antiquity, astronomy was seen as being essentially mathematical in character. Furthermore, no distinction was made between mathematics and numerology or astronomy and astrology . Hypatia is now known to have edited the existing text of Book III of Ptolemy 's Almagest . It was once thought that Hypatia had merely revised Theon's commentary on
14280-520: Was the turning point in Cyril's fight to gain political control of Alexandria. Hypatia had been the linchpin holding Orestes's opposition against Cyril together, and, without her, the opposition quickly collapsed. Two years later, Cyril overturned the law placing the parabalani under Orestes's control and, by the early 420s, Cyril had come to dominate the Alexandrian council. Hypatia has been described as
14400-406: Was widely beloved by pagans and Christians alike and that she established great influence with the political elite in Alexandria. Toward the end of her life, Hypatia advised Orestes , the Roman prefect of Alexandria , who was in the midst of a political feud with Cyril , the bishop of Alexandria . Rumors spread accusing her of preventing Orestes from reconciling with Cyril and, in March 415 AD, she
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