希帕蒂娅Hypatia

希帕蒂娅是第一位对数学发展做出重大贡献的女性。

希帕蒂娅是数学家和哲学家亚历山大的席恩希帕蒂娅的女儿，相当确定她在父亲的指导和教导下学习数学。相当引人注目的是，希帕蒂娅约在公元400年成为希帕蒂娅柏拉图学派的负责人。她在那里讲授数学和哲学，尤其教授Neoplatonism的哲学。希帕蒂娅的教学基于普罗提诺（新柏拉图主义的创始人）和扬布利科斯（约公元300年新柏拉图主义的发展者）的学说。

普罗提诺教导说，存在一种终极实在，它超出思想和语言所能触及的范围。生活的目标就是朝向这种永远无法被精确描述的终极实在。普罗提诺强调，人们没有足够的心智能力去充分理解终极实在本身或其存在的后果。扬布利科斯在终极实在之下按层级进一步区分了不同层次的实在。人类心智所能进行的每一种不同思想，都对应着一个实在层次。希帕蒂娅以比早期新柏拉图主义追随者更强的科学侧重讲授这些哲学思想。所有评论者都把她描述为一位有魅力的教师。

希帕蒂娅逐渐成为学问与科学的象征，而早期基督徒将其与异教联系在一起。然而，在她于希帕蒂娅所教的学生中，有许多显赫的基督徒。其中最著名的一位是西奥多罗斯的叙内修斯，他后来成为托勒密的主教。叙内修斯写给希帕蒂娅的许多书信被保存下来，我们从中看到一个人对希帕蒂娅的学识和科学才能充满钦佩与敬仰。

412年，西里尔（后来的圣西里尔）成为希帕蒂娅牧首。然而罗马行政长官是希帕蒂娅奥雷斯特斯，随着教会与国家争夺控制权，西里尔和奥雷斯特斯成为激烈的政治对手。希帕蒂娅是奥雷斯特斯的朋友，加之她的哲学观点被基督徒视为异教而受到偏见，这导致希帕蒂娅成为基督徒与非基督徒之间骚乱的焦点。希帕蒂娅，托马斯·利特尔·希思写道，[4]：-

……凭借她的雄辩和权威……获得了如此大的影响力，以至于基督教认为自身受到了威胁……

几年后，根据一份报告，希帕蒂娅被尼特里亚的修士残忍杀害，这些修士是一个狂热的基督教派别，支持西里尔。根据另一种说法（由苏格拉底·斯考拉斯蒂库斯所述），她是在读者彼得的领导下被亚历山大暴民杀害的。似乎无可争议的是，她被基督徒杀害，这些基督徒感到受到她的学术、学识和科学知识深度的威胁。这一事件似乎是一个转折点，正如[2]中所描述的：-

无论谋杀的精确动机是什么，许多学者不久后的离开标志着希帕蒂娅作为古代学术主要中心的衰落的开始。

没有证据表明希帕蒂娅进行了原创数学研究。然而，她协助她的父亲亚历山大的席恩希帕蒂娅撰写了关于克劳狄乌斯·托勒密的AlmagestⓉ的十一部分评注（主要论题：来自阿拉伯语“al-majisti”——希腊语“Mathematike Syntaxis”的阿拉伯语翻译，后来翻译成拉丁语为“Magna Syntaxis”）。人们还认为，她还协助她的父亲制作了欧几里得的Elements的新版本，该版本已成为欧几里得所有后续版本的基础。托马斯·利特尔·希思写到亚历山大的席恩和希帕蒂娅的Elements版本[4]：-

……虽然对《几何原本》的内容只做了微不足道的增补，但他努力消除学习者在研读此书时可能感到的困难，就像现代编辑为学校使用而编辑经典教科书时所做的那样；毫无疑问，他的版本得到了他在希帕蒂娅的学生们的认可，因为这是为他们而写的，也得到了后来几乎完全使用该版本的希腊人的认可……

除了与父亲的合作工作外，苏伊达斯告诉我们，希帕蒂娅撰写了关于丢番图的Arithmetica、关于阿波罗尼奥斯的圆锥曲线以及关于克劳狄乌斯·托勒密的天文学著作的评注。苏伊达斯中的段落远不清楚，大多数历史学家怀疑希帕蒂娅除了与父亲共同创作的作品外，还撰写了任何关于克劳狄乌斯·托勒密的评注。

希帕蒂娅的著作除标题和一些引用外已经失传。然而，没有已知的纯哲学著作，只有数学和天文学方面的著作。基于这一少量证据，迪金在[8]和[9]中论证说，希帕蒂娅是一位出色的早期数学著作的编纂者、编辑者和保存者。

如上所述，叙内修斯写给希帕蒂娅的一些书信存世。这些书信向她请教关于建造星盘和水准仪的问题。

查尔斯·金斯利（最著名的是The Water Babies的作者）使她成为他的一部小说Hypatia, or New Foes with an Old Face的女主角。正如克莱默在[1]中所写：-

这类作品使一个传说流传下来：她不仅才智过人，而且美丽、雄辩、谦逊。

Hypatia of Alexandria was the first woman to make a substantial contribution to the development of mathematics.

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

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

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

In 412 Cyril (later St Cyril) became patriarch of Alexandria. However the Roman prefect of Alexandria was Orestes and Cyril and Orestes became bitter political rivals as church and state fought for control. Hypatia was a friend of Orestes and this, together with prejudice against her philosophical views which were seen by Christians to be pagan, led to Hypatia becoming the focal point of riots between Christians and non-Christians. Hypatia, Heath writes, [4]:-

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

A few years later, according to one report, Hypatia was brutally murdered by the Nitrian monks who were a fanatical sect of Christians who were supporters of Cyril. According to another account (by Socrates Scholasticus) she was killed by an Alexandrian mob under the leadership of the reader Peter. What certainly seems indisputable is that she was murdered by Christians who felt threatened by her scholarship, learning, and depth of scientific knowledge. This event seems to be a turning point as described in [2]:-

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

There is no evidence that Hypatia undertook original mathematical research. However she assisted her father Theon of Alexandria in writing his eleven part commentary on Ptolemy's Almagest Ⓣ. It is also thought that she also assisted her father in producing a new version of Euclid's Elements which has become the basis for all later editions of Euclid. Heath writes of Theon and Hypatia's edition of the Elements [4]:-

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

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

All Hypatia's work is lost except for its titles and some references to it. However no purely philosophical work is known, only work in mathematics and astronomy. Based on this small amount of evidence Deakin, in [8] and [9], argues that Hypatia was an excellent compiler, editor, and preserver of earlier mathematical works.

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

Charles Kingsley (best known as the author of The Water Babies) made her the heroine of one of his novels Hypatia, or New Foes with an Old Face. As Kramer writes in [1]:-

Such works have perpetuated the legend that she was not only intellectual but also beautiful, eloquent, and modest.