伊萨克·巴罗Isaac Barrow

伊萨克·巴罗的父亲Thomas Barrow以亚麻布商为业。托马斯于1624年与安结婚，安是肯特郡北克雷的威廉·巴金的女儿，他们的儿子巴罗生于1630年。安于1634年去世，托马斯把巴罗送到祖父那里生活。也许经常被引用的那句话是有道理的，即巴罗的父亲：-

……有人听见他祈祷说，如果上帝决定带走他的一个孩子，他最舍得的是巴罗。

托马斯在两年内再婚，[5]中暗示这可能是为了从父亲那里要回儿子，据说父亲正在宠坏年幼的巴罗。

托马斯在巴罗还是个孩子时就计划让他成为学者。他把巴罗送到查特豪斯公学，并支付双倍学费为巴罗争取特别关注。然而巴罗没有得到这种关注，在学业受损的同时还落得个恃强凌弱的名声。托马斯听说此事后，于1640年把巴罗转到埃塞克斯郡的费尔斯特德，那里的校长以纪律严格著称。在这里，巴罗在性格培养和学业上都进步很快。在费尔斯特德，巴罗学习了希腊语、拉丁语、希伯来语和逻辑学，为上大学做准备。在费尔斯特德待了两年后，巴罗的父亲因爱尔兰叛乱损失了1000英镑，无力支付巴罗的学费。然而，校长意识到巴罗的潜力，收留了他，后来还任命他为托马斯·费尔法克斯的导师。

1643年，巴罗被剑桥大学彼得豪斯学院录取为基金会学者。他的叔叔当时是彼得豪斯学院的会士，当他的叔叔因保皇党观点而失去职位时，巴罗去了牛津，他的兄弟在那里成为了国王的亚麻布商。然而，发生了反对王室的起义，牛津被围困。

1644年，巴罗去了伦敦，由托马斯·费尔法克斯资助。然而，费尔法克斯很快没钱了，巴罗陷入贫困。巴罗陪同一位承诺资助他的前校友去了剑桥大学三一学院。巴罗于1646年入学，以做杂役换取教学，食宿很差。他的朋友资助了他六个月后离开，但此时牛津之围已经结束，巴罗与父亲取得了联系，父亲帮助资助了他。

剑桥大学希腊语钦定教授Duport指导巴罗，不收任何费用，这既是因为巴罗的才华，也是因为两人都是保皇派。在Duport指导下，巴罗学习了希腊语、拉丁语、希伯来语、法语、西班牙语、意大利语、文学、年代学、地理学和神学。当时在剑桥，学生通常在第二或第三年学习一些数学。巴罗学习了算术、几何和光学，并且像当时所有学生一样，被鼓励在毕业前不要专攻数学等某一学科。

巴罗于1649年毕业，并在同年成功竞争到学院会士职位。他发表演讲，赞扬古典著作的教学，但批评缺乏数学和科学。毕业后他立即开始深入学习数学。他的热情和教学意愿使他能够吸引足够多的人学习这门学科，从而帮助奠定在剑桥学习数学的基础。

巴罗被认为是1648年起一群保王党人的首领。然而，在1649年，巴罗宣称自己[5]：-

……对英格兰联邦真实忠诚，如同现在所建立的那样，没有国王或上议院。

然而他很快背弃了这一声明，但被院长救下免遭开除。两年后，巴罗因在火药阴谋纪念日发表演讲而再次面临开除。院长再次救了他，对要求开除他的研究员们说[4]：-

巴罗比我们任何人都优秀。

1652年，巴罗 以文学硕士学位毕业。1654年，他在一次演讲中为大学辩护，谈到学习希腊语、拉丁语和文学对于获得坚实学习基础的重要性。他还赞扬了大学在阿拉伯语、法语、西班牙语和意大利语等现代语言、数学和科学等学科上取得的进步。他在演讲结束时请求 [5]：-

... 同学们坚持学习和实践道德哲学。

巴罗 在被录取为研究员时宣誓学习神学，在短暂学习医学后，他又开始学习神学。他对教会历史的研究使他转向天文学，进而转向几何学。他自学几何，编写了 欧几里得 的 Elements 的简化版，于1655年印刷，并成为半个世纪的标准教科书。

在此期间，巴罗被任命为学院人文学科讲师。当希腊语教授职位空缺时，人们期望巴罗会被任命接替因政治原因被迫离开讲席的Duport。然而巴罗被告知，他教学经验不足，旅行经历也不够丰富，无法获得该职位。真正的原因几乎肯定是巴罗的政治观点。

1655年，巴罗在获得大学旅行奖学金后乘船前往法国。奖学金的条件是，他每年将获得16英镑，为期三年，并且必须通过信件向剑桥报告他的学习和进展。巴罗在巴黎度过了头十个月，他在报告中说他相当失望，因为大学远没有他预期的那么令人印象深刻。除了罗贝瓦尔之外，几乎没有数学家可以向他学习。1656年2月，他前往佛罗伦萨，在那里待了八个月。这比他原先计划的要长，但由于罗马爆发瘟疫，他无法前往罗马。

在Florence Barrow期间，他大部分时间都在美第奇图书馆度过，那里收藏着大量钱币。巴罗后来利用他所获得的专业知识，为一位伦敦商人担任钱币和奖章收藏者，这位商人帮助巴罗解决了急需的资金问题。在佛罗伦萨期间，巴罗遇到了正在撰写一篇关于代数的论文的Carolo Renaldini。他还遇到了温琴佐·维维亚尼，即伽利略的最后一位学生。巴罗随后乘船前往土耳其，但他的船遭到了海盗的袭击。巴罗在士麦那的塞翁登陆，并在那里度过了七个月。在士麦那的塞翁停留之后，他前往君士坦丁堡，在那里与英国大使一起待了一年半。尽管未能按照其奖学金条件的规定与剑桥保持联系，巴罗仍获得了延期。在君士坦丁堡期间，巴罗花了很多时间研究神学，特别是当地的希腊教会。由于一些经济困难，巴罗于1658年底开始了他的归途。在回家的路上，船停靠在威尼斯，那里发生了火灾，巴罗的所有财物都丢失了。然后他经由德国和荷兰返回，于1659年9月抵达剑桥。

当他回到剑桥时，由于查理二世的复辟，发生了许多政治变化。希腊语教授自愿辞职，承认有其他人更适合这个职位——其中一人就是 巴罗 本人。Duport 被提供了六年前被迫离开的职位，但他拒绝了。这为 巴罗 开辟了道路，在没有反对的情况下，他被选为许多人认为他多年前就应该拥有的职位。作为教授，他每年获得40英镑，并且不允许在学院或大学内担任任何其他职位。他不能从学院研究员职位获得任何收入，这使得他的经济状况非常困难。巴罗 为教授们争取从他们持有的学院研究员职位中获得福利，他的运动成功了。在他第一年后的年度演讲中，他鼓励学生专注于自己的私人学习，而不是讲座 [5]：-

如果你明智的话，继续呆在家里，专注于你的私人学习。翻阅你拥有的最精选的书籍，或者躲在图书馆宜人的阴凉处。把自己裹在舒适的毯子里，或者坐在温暖的炉火旁。考虑你的健康，按自己的方便学习。

巴罗 对数学的兴趣和他微薄的收入使得伦敦格雷沙姆学院的几何学教授职位在1662年空缺时显得非常有吸引力。他还可以在继续担任剑桥希腊语教授的同时担任这个讲席。他在1662年仲夏当选，年薪50英镑。在格雷沙姆，他每周教几何两小时，一小时用英语，另一小时用拉丁语。巴罗 非常认真地对待他的职责。他打算出版这些讲座，但他把它们借给了一个朋友，后来朋友丢失了。涵盖的主题包括“球体的投影”和“透视”。

巴罗成为1663年5月20日在皇家学会最初几次会议上当选为会士的150位科学家之一。然而他对学会的贡献微乎其微，这很可能与学会和大学的关系有关。Society试图任命他进入天文与光学委员会以及负责[4]的委员会：-

……收集迄今为止观察到的自然现象以及所有已进行并记录在案的实验。

然而这并未增加他的贡献，由于他未缴纳会费，Society考虑将他除名。

1663年夏天，由于Henry Lucas留下的捐赠，剑桥设立了卢卡斯数学教授职位。巴罗是这个职位的明显人选，他放弃了希腊语讲席而转向数学，因为他解释说，他对数学比希腊语更感兴趣，因为涉及的工作更少，而且他一直打算临时担任希腊语讲席。

1664年春天，巴罗讲授了他的前六次数学讲座，内容为基础材料。秋天，他又讲授了九次讲座，并在1665年春天讲授了他的前五次几何讲座。在讲授了一门由四次讲座组成的阿基米德短期课程后，大学因瘟疫不得不关闭。当它在1666年4月重新开放时，巴罗又讲授了八次讲座，但在六月之后又爆发了瘟疫。大学在1667年复活节第二次重新开放，他在1668-9学年讲授光学讲座之前又讲授了进一步的几何讲座。艾萨克·牛顿参加了这些讲座，并与巴罗就这些工作进行了许多私人讨论。艾萨克·牛顿从与巴罗的这些课程中得到了很多鼓励，它们极大地影响了他的工作。

约翰·柯林斯出版了巴罗的大部分讲稿：Lectiones OpticaeⓉ（光学讲义）于1669年出版，Lectiones GeometricaeⓉ（几何讲义）于1670年出版，Lectiones MathematicaeⓉ（数学讲义）于1683年出版。巴罗没有为出版准备他的著作，艾萨克·牛顿和其他人承担了这项工作。巴罗的大部分数学工作是在1663年至1669年间完成的。浏览这三本书可以看出他工作的范围。Lectiones Mathematicae是为了在剑桥重新唤起对数学的兴趣而设计的讲座，同时试图通过引入现代技术将其引向一个新方向。他试图对数学的不同分支进行分类，主张代数不是真正数学的一部分，应被视为逻辑，而[5]：-

几何是基本的数学科学，因为它包含算术，而数学数字只是几何量的符号。

在后面的讲座中，他涵盖了诸如整除性、同余、相等、时间和空间等主题。最后的讲座涵盖测量、比例和比率。

Lectiones Geometricae可能代表了巴罗在格雷沙姆期间所研究的工作。它们包含了关于切线的重要工作，这将成为艾萨克·牛顿在微积分方面工作的起点。巴罗陈述了两个主要目标[15]：-

……第一，在没有计算的麻烦或疲劳的情况下研究切线；第二，通过它们的切线相当快速地确定许多量的大小……

Lectiones Opticae比实用更偏理论，这在他那个时代是不寻常的。内容主要是几何光学，他陈述了讲座旨在回答的主要问题[4]：-

定义点在平面和球面反射后的像……

1669年，巴罗辞去了卢卡斯讲席，不再从事进一步的数学工作。这使艾萨克·牛顿得以接任。巴罗于1670年被任命为查理二世在索尔兹伯里的皇家牧师，然后，在1673年2月，查理二世授予巴罗三一学院院长职位，宣布他是英格兰最优秀的学者。作为三一学院院长，巴罗忙于两个主要问题。第一个是限制皇家干预的数量，第二个是建造雷恩图书馆。在第一个问题上他取得了一些成功，而在第二个问题上他花费了大量时间和精力来激发对该项目的兴趣和必要的资金。然而他没能活着看到这项工作的结果。1677年4月，巴罗前往伦敦，在那里他感染了恶性热病。他试图通过禁食和服用鸦片来治愈它，这个配方在他之前在君士坦丁堡生病时曾对他有效。然而他去世了，几天后被埋葬在威斯敏斯特教堂。

Isaac Barrow's father, Thomas Barrow, was a linen draper by trade. Thomas married Ann, daughter of William Buggin of North Cray, Kent in 1624 and their son Isaac was born in 1630. Ann died in 1634 and Thomas sent Isaac to live with his grandfather. Perhaps there is truth in the frequently quoted saying that Isaac's father:-

... was heard to pray that should God decide to take one of his children, he could best spare Isaac.

Thomas remarried within two years and it is suggested in [5] that this may have been an attempt to get his son back from his father, who was said to be spoiling young Isaac.

Thomas planned for Isaac to become a scholar while still a child. He sent Isaac to Charterhouse and paid twice the regular fee to get special attention for Isaac. However Isaac did not receive this attention and acquired the reputation as a bully while his education suffered. When Thomas heard of this, he transferred Isaac to Felstead, Essex in 1640 where the headmaster had a reputation for strict discipline. Here Isaac made rapid progress, both in developing his character and in learning. At Felstead Barrow learnt Greek, Latin, Hebrew and logic in preparation for University. After he had been at Felstead for two years, Isaac's father incurred losses of £1000 due to the Irish rebellion and was unable to pay Isaac's fees. However, the headmaster, realising Isaac's potential, took him in and later appointed him as a tutor to Thomas Fairfax.

In 1643 Barrow was admitted as a foundation scholar at Peterhouse, Cambridge. His uncle was a Fellow of Peterhouse at the time and when his uncle lost his post due to his Royalist views, Barrow went to Oxford where his brother had become the King's Linen Draper. However there was an uprising against Royalty and Oxford came under siege.

In 1644 Barrow went to London where he was supported by Thomas Fairfax. However, Fairfax soon ran out of money and left Isaac destitute. Barrow accompanied a former school friend, who promised to support him, to Trinity College, Cambridge. Barrow enrolled in 1646 and performed menial duties in return for instruction with poor board and lodging. His friend supported him for six months before he left but, by this time, the siege of Oxford had ended and Barrow made contact with his father who helped support him.

Duport, the Regius Professor of Greek at Cambridge, tutored Barrow without taking any fees, both due to Barrow's talent and that both were royalists. Under Duport, Barrow studied Greek, Latin, Hebrew, French, Spanish, Italian, literature, chronology, geography and theology. Also at Cambridge at this time it was usual for students to learn some mathematics, either in their second or third year. Barrow studied arithmetic, geometry and optics and, like all students of the time, was encouraged not to specialise in a subject such as mathematics before graduating.

Barrow graduated in 1649 and successfully competed for a college fellowship in the same year. He gave a speech in which he praised the teaching of the classics but criticised the lack of mathematics and science. He started studying mathematics in depth immediately after his graduation. His enthusiasm and willingness to teach enabled him to attract enough people to the subject to help begin to lay the foundations for studying mathematics at Cambridge.

Barrow was considered to be the ring leader of a group of royalists from 1648. However, in 1649, Barrow declared himself to be [5]:-

... true and faithful to the Commonwealth of England as the same is now established, without a King or House of Lords.

However he soon went back on this declaration but was saved from expulsion by the Master. Two years later Barrow again faced expulsion due to a speech he made on the anniversary of the Gunpowder Plot. The Master again came to his rescue by telling the Fellows who demanded his expulsion [4]:-

Barrow is a better man than any of us.

In 1652 Barrow graduated with his M.A. In 1654 he defended the University in a speech in which he spoke of the importance of learning Greek, Latin and literature for the purpose of acquiring a firm basis for learning. He also praised the advances the University had made in subjects such as Arabic, modern languages such as French, Spanish and Italian, mathematics and science. He ended his speech requesting [5]:-

... fellow students to persevere in the study and practice of moral philosophy.

Barrow had taken an oath to study divinity when he was admitted as a fellow, and, after briefly studying medicine, he began studying divinity again. His study of church history led him to astronomy which in turn led him to study geometry. He taught himself geometry, writing a simplified edition of Euclid's Elements which was printed in 1655 and remained the standard textbook for half a century.

During this period Barrow was appointed to the college lectureship in Humanity. When the professorship in Greek became available it was expected that Barrow would be appointed to replace Duport who had been forced to leave the chair on political grounds. However Barrow was told that he did not have enough experience in teaching and was not well-travelled enough to receive the position. The real reason was almost certainly Barrow's political views.

In 1655 Barrow set sail for France, after he had received an award for travelling from the University. The conditions of the award were that he would receive £16 per year for three years, and would have to report by letter to Cambridge on his learning and progress. Barrow spent the first ten months in Paris where he reported that he was rather disappointed in that the University was not nearly as impressive as he had been expecting. Apart from Roberval there were few mathematicians from whom he could learn. In February of 1656 he went to Florence, where he remained for eight months. This was longer than he had originally planned but he was unable to visit Rome due to an outbreak of the plague there.

While in Florence Barrow spent much of his time in the Medici Library where there was a great collection of coins. Barrow later used the expertise he had acquired to act as a collector of coins and medals for a London merchant who helped Barrow with much needed finance. While in Florence, Barrow met Carolo Renaldini who was writing a paper on algebra. He also met Vincenzo Viviani, Galileo's last pupil. Barrow then set sail for Turkey but his ship came under attack from pirates. Barrow landed at Smyrna where he spent seven months. After his stay in Smyrna he went to Constantinople where he remained a year and a half with the English Ambassador. Despite failing to keep in contact with Cambridge, as set out in the conditions of his award, Barrow was granted an extension. While in Constantinople Barrow spent much time studying divinity and in particular the local Greek Church. In some financial difficulty, Barrow began his return journey at the end of 1658. On the journey home the ship docked at Venice where it caught fire and all Barrow's possessions were lost. He then headed back through Germany and Holland, arriving in Cambridge in September 1659.

When he arrived back at Cambridge there had been many political changes due to the restoration of Charles II. The Professor of Greek voluntarily resigned in recognition that there were others who were better suited to the position - one of these people being Barrow himself. Duport was offered the post that he had been forced out of six years earlier, but he declined the offer. This left the way open for Barrow who, with no opposition, was elected to the position that many felt he should have had years before. As Professor he received £40 per year and was not allowed to hold any other positions inside the College or University. He could not receive any income from his College Fellowship which made his financial position very difficult. Barrow campaigned for professors to receive benefits from their College Fellowships, if they held one, and his campaign was successful. In his annual speech after his first year he encouraged students to concentrate on their own private study and not on the lectures [5]:-

Continue to stay at home, if you are wise, and apply yourselves to your private studies. Turn over the choicest books you possess or take shelter in the pleasing shade of the library. Muffle yourselves in your snug blankets or sit by your cosy fireside. Consider your health and study at your own convenience.

Barrow's interest in mathematics and his small income made the position of Professor of Geometry at Gresham College, London appear very attractive when it became vacant in 1662. He could also hold this chair while continuing as Professor of Greek at Cambridge. He was elected in mid-summer 1662 on a salary of £50 per year. At Gresham he taught geometry for two hours a week, one hour in English and the other in Latin. Barrow took his duties very seriously. He intended publishing these lectures, but he lent them to a friend who subsequently lost them. Topics covered included 'projection of spheres' and 'perspectives'.

Barrow became one of 150 scientists who were elected a Fellow of the Royal Society on 20 May 1663 at one of the first meetings of the Society. However his contribution to the Society was minimal and this could well have been influenced by the relation of the Society to the universities. The Society tried to appoint him to the Astronomical and Optical Committee and to the committee responsible for [4]:-

... collecting the phenomena of nature hitherto observed and all experiments made and recorded.

However this did not increase his contribution and, with his dues unpaid, the Society considered expelling him.

In the summer of 1663 the position as Lucasian Professor of Mathematics was created at Cambridge thanks to an endowment left by Henry Lucas. Barrow was an obvious choice for this position and he relinquished the Greek chair for the mathematics because, he explained, of his greater interest in mathematics than Greek, because less work was involved, and that it had always been his intention to hold the Greek chair temporarily.

In the spring of 1664 Barrow delivered the first six of his mathematics lectures which consisted of basic material. In the autumn he delivered nine more lectures and, in the spring of 1665 the first five of his geometrical lectures. After giving a short course on Archimedes which consisted of four lectures the University had to close due to the plague. When it re-opened in April 1666 Barrow delivered another eight lectures but after June there was another outbreak of the plague. The university re-opened for the second time in Easter 1667 when he gave further geometry lectures before delivering his optics lectures in the 1668-9 session. Isaac Newton attended these lectures and had many private discussions with Barrow about the work. Newton took much encouragement from these sessions with Barrow and they influenced his work greatly.

John Collins published most of Barrow's lectures: Lectiones Opticae Ⓣ was published in 1669, Lectiones Geometricae Ⓣ in 1670 and Lectiones Mathematicae Ⓣ in 1683. Barrow did not prepare his work for publishing, Newton and others undertook this task. Most of Barrow's mathematics had been done over the years 1663 to 1669. A look at these three books shows the extent of his work. Lectiones Mathematicae were lectures designed to revive interest in mathematics at Cambridge while trying to point it in a new direction by introducing modern techniques. He tried to classify the different branches of mathematics arguing that algebra is not part of true mathematics and should be considered to be logic while [5]:-

Geometry is the basic mathematical science, for it includes arithmetic, and mathematical numbers are simply the signs of geometrical magnitude.

In the later lectures he covered such topics as divisibility, congruence, equality, time and space. The final lectures cover measurement, proportion and ratio.

The Lectiones Geometricae probably represent work which Barrow studied while at Gresham. They contain the important work on tangents which was to form the starting point of Newton's work on the calculus. Barrow stated the main two aims were [15]:-

... first, to investigate tangents without the trouble or wearisomeness of calculation and, second, to determine the dimensions of many magnitudes quite quickly by means of their tangents ...

The Lectiones Opticae were more theoretical than practical, which was unusual for his time. The content is mainly geometrical optics and he states the main problem which the lectures are aimed at answering [4]:-

To define the image of a point after any reflection in a plane and spherical surface ...

In 1669 Barrow resigned from the Lucasian Chair and did no further mathematical work. This allowed Newton to take over. Barrow was appointed as Royal Chaplain to Charles II at Salisbury in 1670, then, in February 1673, Charles II awarded Barrow the Mastership of Trinity declaring him to be the best scholar in England. While Master of Trinity, Barrow was occupied with two major issues. The first of these was to limit the amount of Royal interventions and secondly the building of the Wren library. On the first of these issues he had some success while on the second he spent much time and effort on generating interest in the project and the necessary funds. However he did not live to see the result of this work. In April of 1677 Barrow travelled to London where he contracted malignant fever. He tried to cure it by fasting and taking opium, a formula which had previously worked for him while ill in Constantinople. However he died and was buried a few days later at Westminster Abbey.