数学家传记
勒内·笛卡儿 是一位法国哲学家，其著作《几何学》包含了他将代数应用于几何的研究，由此产生了我们现在所称的笛卡尔几何学。他的工作对数学家和哲学家都产生了很大影响。
勒内·笛卡儿是一位哲学家，他的著作La GéométrieⓉ（几何学）包括他将代数应用于几何，由此我们如今有了笛卡尔几何。
笛卡儿的父母是Joachim Descartes（1563-1640）和让娜·布罗沙尔（1566-1597）。若阿基姆是医生Pierre Descartes（1515-1566）的儿子，学习法律，并成为驻扎在雷恩的布列塔尼议会的参事。让娜是军人笛卡儿·布罗沙尔的女儿，后者是驻扎在普瓦捷的驻军的一部分。让娜的一个兄弟，也叫笛卡儿·布罗沙尔，成为笛卡儿的两个教父之一；笛卡儿是以他的教父笛卡儿·布罗沙尔命名的。让娜寡居的母亲让娜·桑·布罗沙尔住在图尔附近的拉海，笛卡儿就是在她的家中出生的。若阿基姆和让娜·笛卡儿于1589年1月15日结婚，住在沙泰勒罗。他们有两个比笛卡儿年长的存活子女，一个叫让娜的女孩（生于1590年）和一个叫皮埃尔的男孩（生于1591年）。笛卡儿在四天大时在拉海的圣乔治罗马天主教堂受洗。他的母亲在他出生一年后死于分娩，在她去世时出生的男孩也死了。此时，笛卡儿被送回拉海他祖母的家中，由让娜·桑·布罗沙尔照顾。Joachim Descartes于1600年与安妮·莫兰再婚，他们有一个叫若阿基姆的男孩（生于1602年）和一个叫安妮的女孩（生于1611年）。因此笛卡儿有一个哥哥和一个姐姐，以及一个同父异母的弟弟和同父异母的妹妹。然而，他没有回到父亲和继母那里生活，而是继续和祖母住在拉海。现在笛卡儿小时候健康状况不佳。在整个童年时期，直到二十多岁，他都面色苍白，并持续咳嗽，这可能是由于肺结核。他很可能从母亲那里继承了这些健康问题。
笛卡儿在安茹的拉弗莱什耶稣会学院接受教育。他于1607年复活节时十一岁进入该学院，成为寄宿生。[这里有些不确定，一些传记作者声称他两年前就进入了学院。]该学院于1604年1月开办，因此是一所相对较新的学校。他在那里学习古典文学、逻辑学和传统亚里士多德哲学课程。他还从克里斯托佛·克拉乌的书籍中学习数学，同时学习数学的所有分支，即算术、几何、天文学和音乐。在学校期间，他的健康状况不佳，不像其他男孩那样早上5点起床，而是被允许在床上待到上午11点，这一习惯他一直保持到去世那年。在学校的最后几年，他学习了自然哲学、形而上学和伦理学。他于1614年离开拉弗莱什学院。学校让笛卡儿明白自己所知甚少，在他看来唯一令人满意的科目是数学。这一想法成为他思维方式的基础，并构成他所有著作的基础。
笛卡儿自己描述他在THIS LINK的求学经历。
关于笛卡儿在1614年至1618年间的生平，人们所知相对较少。他在巴黎待了一段时间，显然深居简出，有人推测他此时可能经历过某种精神崩溃。之后他在普瓦捷大学学习，于1616年在普瓦捷获得法学学位。他攻读法学学位是为了遵从父亲的意愿，但他很快认定这不是他想走的路。他在Discourse on the Method中写道：-
我完全放弃了文学研究，决心除了能在自身中或在世界这本大书中找到的知识之外，不再寻求任何知识。我把余下的青春用于旅行，访问宫廷和军队，与各种性情和阶层的人交往，积累各种经验，在命运提供给我的境遇中考验自己，并始终反思遇到的一切，以便从中获得一些益处。
他可能在1618年入伍布雷达的军事学校之前已回到巴黎，成为杰森·约翰·拿骚的莫里斯军队中的志愿者。在布雷达期间，他正式学习的是军事工程，但他开始在荷兰科学家艾萨克·贝克曼指导下学习数学和力学，并开始寻求一种统一的自然科学。在贝克曼的建议下，他开始考虑力学问题。在荷兰期间，他于1619年3月写信给贝克曼，谈及他的新想法：-
[我想推进]一门全新的科学，借助它，关于任何种类量——连续的以及离散的——所能提出的一切问题一般都可以得到解决。但每个问题都按其自身性质来处理。……例如，在算术中，有些问题可以用有理的数解决，有些可以用无理数解决，还有一些可以想象但无法解决。对于连续量，我希望证明，类似地，某些问题可以仅用直线或圆线解决，有些问题需要其他曲线才能解决，但这些曲线仍由单一运动产生，因而可以用新的圆规画出，我认为这种圆规并不比用来画圆的通常圆规更不确定或更不几何；最后，还有其他问题可以用由彼此不从属的分离运动产生的曲线解决。
在荷兰的这段时间之后，他离开了拿骚的莫里斯的服役，游历欧洲，计划加入巴伐利亚的马克西米利安的军队。1619年，他加入巴伐利亚军队，驻扎在乌尔姆。他一生中的一个重要事件是他在1619年11月做的三个梦。他相信这些梦是由一种神圣精神送来的，意图向他揭示一种新的哲学方法。从那时起，这些梦中的想法将主导他大部分工作。
笛卡儿自己描述他此时发展的想法，见THIS LINK。
在服务于巴伐利亚的马克西米利安期间，笛卡儿作为官方观察员随天主教联盟出席了1620年11月在布拉格附近的白山战役。此后他离开了军队，但由于瘟疫在巴黎肆虐，他无法返回那里，而是开始了一段旅行时期。
从1620年到1628年，笛卡儿游历欧洲，在波希米亚（1620年）、匈牙利（1621年）、德国、荷兰和法国（1622-23年）度过时光。1623年他在巴黎逗留，与马兰·梅森建立了联系，这是一个重要的联系，使他多年来与科学界保持接触，并与Claude Mydorge联系。从巴黎他穿越瑞士到意大利，在威尼斯和罗马逗留了一段时间，然后再次返回法国（1625年）。他重新结识了马兰·梅森和Mydorge，并会见了吉拉尔·笛沙格。他在巴黎的家成为哲学家和数学家的聚会场所，并逐渐变得越来越繁忙。到1628年，笛卡儿厌倦了巴黎的喧嚣、满屋的人和以前旅行的生活，决定在一个可以独自工作的地方定居下来。他深思熟虑地选择一个适合他本性的国家，他选择了荷兰。他渴望的是一个安静的地方，可以在那里工作，远离巴黎这样的城市的干扰，但仍然可以接触到城市的设施。这是一个好的决定，在接下来的二十年里他似乎没有后悔过。他告诉马兰·梅森他住在哪里，以便与数学界保持联系，但除此之外，他对自己的居住地保密。
他在荷兰定居后不久，笛卡儿开始撰写他的第一部重要物理学论著Le Monde, ou Traité de la LumièreⓉ（《世界或论光》）。1629年10月，他写信给马兰·梅森：——
［物理学的基础］是我研究得最多的主题，感谢上帝，我在这上面并没有完全浪费时间。至少我认为我已经找到了如何以比几何证明更明显的方式来证明形而上学真理——在我看来是这样：我不知道我能否说服其他人。在这个国家的头九个月里，我没有做其他任何事情。
这项工作接近完成时，伽利略被软禁的消息传到了他那里。他或许明智地决定不冒险出版，这部作品只在他去世后部分出版。他后来解释自己方向的改变说：——
……为了更自由地表达我的判断，而不必被迫同意或反驳博学之士的意见，我决定把这一切世界留给他们，只谈论如果上帝现在创造……并允许她按照他所建立的法则行动，在一个新世界中会发生什么。
笛卡儿自己对Le Monde, ou Traité de la LumièreⓉ（《世界或论光》）内容的描述见THIS LINK。
笛卡儿有许多科学界的朋友，并与马兰·梅森保持联系。他与Beeckman的友谊继续，他还与Mydorge、Hortensius、克里斯蒂安·惠更斯和弗兰斯·范斯霍滕（老）有联系。Langer［112］描述了笛卡儿在荷兰的生活：——
他一生中，早晨都继续在床上工作。晚上他通常用来处理信件，这些信件主要是科学方面的，很少涉及私人事务，而他对此极为细心；白天中间的那段时间他则用来放松。在金钱方面，他既不奢侈也不吝啬，在这方面表现出一个真正的哲学家。他总是会做一些娱乐活动，时多时少，自称在交谈中找到相当大的乐趣，尽管他自己相当沉默寡言。
笛卡儿被朋友们催促发表他的想法，尽管他坚决不出版Le Monde Ⓣ（论世界或论光），他还是写了一篇科学论文，题为Discours de la méthode pour bien conduire sa raison et chercher la vérité dans les sciences Ⓣ（谈谈正确运用自己的理性在各门学问里寻求真理的方法）。这部著作有三个附录，分别是La Dioptrique Ⓣ（屈光学）、Les Météores Ⓣ（气象学）和La Géométrie Ⓣ（几何学）。该论文于1637年在莱顿出版，笛卡儿写信给马兰·梅森说：-
我在我的“屈光学”和“气象学”中试图表明我的方法优于庸俗的方法，并在我的“几何学”中证明了这一点。
这部著作描述了笛卡儿认为比亚里士多德的逻辑学所提出的更为令人满意的获取知识的方法。笛卡儿觉得只有数学是确定的，所以一切都必须建立在数学的基础上。
La Dioptrique Ⓣ（屈光学）是一部关于光学的作品，尽管笛卡儿没有为他提出的想法引用以前的科学家，但实际上几乎没有新内容。然而，他通过实验的方法是一个重要的贡献。
Les Météores Ⓣ（气象学）是一部关于气象学的著作，其重要性在于它是第一部试图将天气研究置于科学基础之上的著作。然而，笛卡儿的许多主张不仅是错误的，而且如果他做过一些简单的实验，就很容易看出这些主张是错误的。例如，罗吉尔·培根已经证明了人们普遍认为煮沸过的水冻结得更快这一错误观念。然而笛卡儿声称：-
……我们从经验中看到，在火上放置了一段时间的水比在其他情况下冻结得更快，原因是其中那些最容易折叠和弯曲的部分在加热过程中被驱散，只留下那些刚性的部分。
尽管有许多缺陷，气象学这门学科在Les MétéoresⓉ（气象学）出版后走上了正轨，特别是通过罗伯特·波义耳、罗伯特·胡克和爱德蒙·哈雷的工作。
La GéométrieⓉ（几何学）是这部著作中迄今为止最重要的部分。在[22]中，Scott将这部著作的重要性总结为四点：-
笛卡儿的La GéométrieⓉ（几何学）的一些摘录在THIS LINK。
La GéométrieⓉ（几何学）中的一些思想可能来自尼克尔·奥里斯姆的早期工作，但在尼克尔·奥里斯姆的工作中没有证据表明将代数与几何联系起来。约翰·沃利斯在Algebra（1685年）中强烈主张La GéométrieⓉ（几何学）的思想是从托马斯·哈里奥特抄袭来的。约翰·沃利斯写道：-
……笛卡儿读过《实践》，而笛卡儿分析的每一行都带有这种印象的痕迹。
似乎没有什么能证明约翰·沃利斯的说法，这可能是部分出于爱国主义，但也出于他公正地希望给予托马斯·哈里奥特更多工作认可的愿望。然而，托马斯·哈里奥特关于方程的工作可能确实影响了笛卡儿，后者总是声称——显然是虚假地——他的工作中没有任何东西受到他人工作的影响。
笛卡儿的Meditations on First Philosophy于1641年出版，是为哲学家和神学家而写的。它由六个沉思组成：我们可以怀疑的事物、人的心灵的本性、上帝：他存在、真理与错误、物质事物的本质、物质事物的存在以及人的心灵与身体之间的真正区别。然而许多科学家反对笛卡儿的思想，包括安托尼·阿尔诺、托马斯·霍布斯和皮埃尔·伽桑狄。
笛卡儿最全面的著作，Principia PhilosophiaeⓉ（哲学原理）于1644年在阿姆斯特丹出版。它分为四部分，The Principles of Human Knowledge、The Principles of Material Things、Of the Visible World 和 The Earth，试图将整个宇宙置于数学基础之上，将研究简化为力学。这是一个重要的观点，并指明了前进的方向。笛卡儿不相信超距作用。因此，鉴于此，地球周围不可能有真空，否则力就无法传递。在许多方面，笛卡儿的理论，即力通过接触起作用，比超距作用的引力的神秘效应更令人满意。然而，笛卡儿的力学还有很多不足之处。他假设宇宙充满了物质，由于某种初始运动，这些物质已稳定成一个涡旋系统，携带着太阳、恒星、行星和彗星沿其轨道运行。尽管涡旋理论存在问题，但它在法国被拥护了近一百年，甚至在艾萨克·牛顿表明它作为动力系统不可能之后仍然如此。正如艾萨克·牛顿19世纪的传记作者之一布鲁斯特所说：-
因此，正如笛卡尔体系那样根深蒂固……难怪《原理》的纯粹而崇高的学说被不信任地接受……未受教育的头脑无法轻易接受这样的观念：行星的巨大质量悬浮在虚空中，并通过一种看不见的影响保持其轨道……
尽管笛卡儿的理论令人满意，但即使是他的自然哲学的支持者，如剑桥的形而上学神学家亨利·莫尔，也提出了反对意见。莫尔当然钦佩笛卡儿，他写道：-
我应该把笛卡尔看作是一个在自然知识方面最真正受到启发的人，比过去一千六百年中任何自称如此的人都要强……
然而在1648年至1649年间，他们交换了许多信件，其中莫尔提出了一些有力的反对意见。然而笛卡儿在回复中对莫尔的观点没有做出任何让步。莫尔接着问道：-
为什么你的漩涡不是柱状或圆柱形，而是椭圆形，因为漩涡轴上的任何一点都好像是一个中心，天体物质从中退去，据我所见，具有完全恒定的冲力？……是谁使所有行星不在一个平面（黄道面）上旋转？……而月球本身，既不在地球赤道面上，也不在与此平行的平面上？
1644年，即他的Meditations出版的那一年，笛卡儿访问了法国。他于1647年再次返回，当时他会见了帕斯卡，并与他争论真空不可能存在，然后又在1648年再次访问。
1649年，瑞典女王Christina说服笛卡儿前往斯德哥尔摩。然而女王想在凌晨5点画切线，而笛卡儿打破了他一生中11点起床的习惯。在寒冷的北方气候中只待了几个月，每天早上5点步行去王宫，他就死于肺炎。
在他去世后，他的文件中发现了一份未完成的手稿，题为Regulae ad directionem ingenii Ⓣ（指导智力的规则）。只呈现了前21条规则，最后三条只给出了其预定的标题。遗憾的是，原始手稿已丢失，只剩下副本。以下是手稿的一段简短摘录：-
如果这些规则只适用于解决那些算术学家和几何学家倾向于用来消磨时间的无意义问题，我就不会如此看重它们，因为那样的话，我能夸耀的成就只不过是以比他们更精妙的方式涉猎琐事而已。下面我将大量谈论图形和数字，因为没有其他学科能像它们一样提供如此明显和确定的例证。但如果有人仔细注意我的意思，就会很容易看出，我在这里远非考虑普通数学，我所阐述的是完全另一门学科，而这些例证更像是它的外衣而非其内在部分。这门学科应包含人类理性的基本要素，并扩展到在任何领域中发现的真理。坦率地说，我确信它是人类所拥有的比任何其他知识工具都更强大的工具，因为它是所有其他知识的源泉。
我们应以再多谈一点笛卡儿作为一个人来结束这本传记。在[112]中，Langer描述了笛卡儿的外貌和个性：-
在外貌上，笛卡儿是一个身材矮小、体型相当瘦弱的人，头很大。他的鼻子突出，下唇有些前凸，胡须和髭呈半军事风格，头发向下长到额头上几乎到眉毛。他戴着一顶自然颜色的假发，总是对它极为讲究，对他的衣服也是如此，现在总是穿黑色布料。在举止上，他通常愉快，很少欢快。他的风度总是优雅、温和、礼貌，脾气平静而随和。作为一个人，他骄傲，有些贵族式的矜持，敏感，有点棱角分明，虽然有点专横，但极为乐于助人。
他总是穿着得体，佩带一把剑。他不勤奋；工作时间短，读书少。当他去荷兰时，他带了几本书，但其中有《圣经》和Thomas Aquinas。他的工作似乎是在短时间内高度集中完成的；但也许，为了保持绅士业余爱好者的形象，他可能假装工作得比实际少，因为否则他的成就似乎几乎不可信。
René Descartes was a philosopher whose work, La Géométrie Ⓣ, includes his application of algebra to geometry from which we now have Cartesian geometry.
René Descartes' parents were Joachim Descartes (1563-1640) and Jeanne Brochard (1566-1597). Joachim, the son of the medical doctor Pierre Descartes (1515-1566), studied law and was a counsellor in the Parliament of Brittany which sat at Rennes. Jeanne was the daughter of the military man René Brochard who formed part of the garrison stationed at Poitiers. One of Jeanne's brothers, also named René Brochard, became one of René Descartes' two godfathers; René Descartes was named after his godfather René Brochard. Jeanne's widowed mother, Jeanne Sain Brochard, lived at La Haye, near Tours, and it was in her home that René was born. Joachim and Jeanne Descartes were married on 15 January 1589 and lived at Châtellerault. They had two surviving children older than René, a girl named Jeanne (born 1590) and a boy named Pierre (born 1591). René was baptised in the Roman Catholic Church of Saint George in La Haye when he was four days old. His mother died in childbirth a year after he was born and the boy, born at the time of her death, also died. At this time, René was sent back to his grandmother's home in La Haye where he was cared for by Jeanne Sain Brochard. Joachim Descartes remarried in 1600 to Anne Morin and they had a boy named Joachim (born 1602) and a girl named Anne (born 1611). René therefore had a older brother and an older sister, as well as a younger half-brother and younger half-sister. He did not return to live with his father and step-mother, however, but continued living with his grandmother at La Haye. Now René's health was poor when he was a child. Throughout his childhood, up to his twenties, he was pale and had a persistent cough which was probably due to tuberculosis. It seems likely that he inherited these health problems from his mother.
Descartes was educated at the Jesuit college of La Flèche in Anjou. He entered the college at Easter 1607 at the age of eleven years where he became a boarder. [There is some uncertainty here, with some biographers claiming that he entered the College two years earlier.] The college had opened in January 1604 so was a comparatively new school. He studied there taking courses in classics, logic and traditional Aristotelian philosophy. He also learnt mathematics from the books of Clavius, while studying all the branches of mathematics, namely arithmetic, geometry, astronomy and music. While in the school his health was poor and, instead of rising at 5 a.m. like the other boys, he was granted permission to remain in bed until 11 o'clock in the morning, a custom he maintained until the year of his death. In his final years at the school he studied natural philosophy, metaphysics and ethics. He left the La Flèche College in 1614. School had made Descartes understand how little he knew, the only subject which was satisfactory in his eyes was mathematics. This idea became the foundation for his way of thinking, and was to form the basis for all his works.
See Descartes' own words describing his schooling at THIS LINK.
Comparatively little is known of Descartes' life between 1614 and 1618. He spent a while in Paris, apparently keeping very much to himself, and some have speculated that he might have suffered some sort of a breakdown at this time. Then he studied at the University of Poitiers, receiving a law degree from Poitiers in 1616. He took the law degree to comply with his father's wishes but he quickly decided that this was not the path he wanted to follow. He wrote in Discourse on the Method:-
I entirely abandoned the study of letters, resolving to seek no knowledge other than that which could be found in myself or else in the great book of the world. I spent the rest of my youth travelling, visiting courts and armies, mixing with people of diverse temperaments and ranks, gathering various experiences, testing myself in the situations which fortune offered me, and at all times reflecting on whatever came my way so as to derive some profit from it.
He may have returned to Paris before he enlisted in the military school at Breda in 1618, becoming a volunteer in the army of Maurice of Nassau. While in Breda his formal study was of military engineering but he started studying mathematics and mechanics under the Dutch scientist Isaac Beeckman, and began to seek a unified science of nature. Advised by Beeckman, he began considering mechanical problems. While in Holland, he wrote to Beeckman in March 1619 about his new ideas:-
[I want to promote a] completely new science by which all questions in general may be solved that can be proposed about any kind of quantity, continuous as well as discrete. But each according to its own nature. ... In arithmetic, for instance, some questions can be solved by rational numbers, some by surd numbers, and others can be imagined but not solved. For continuous quantity I hope to prove that, similarly, certain problems can be solved by using only straight or circular lines, that some problems require other curves for their solution, but still curves which arise from one single motion and which therefore can be traced by the new compasses, which I consider to be no less certain and geometrical than the usual compasses by which circles are traced; and, finally, that other problems can be solved by curved lines generated by separate motions not subordinate to one another.
After this time in Holland he left the service of Maurice of Nassau and travelled through Europe with the plan to join the army of Maximilian of Bavaria. In 1619 he joined the Bavarian army and was stationed in Ulm. An important event in his life was three dreams he had in November 1619. These he believed were sent by a divine spirit with the intention of revealing to him a new approach to philosophy. The ideas from these dreams would dominate much of his work from that time on.
For Descartes' own description of the ideas that he developed at this time see THIS LINK.
While serving Maximilian of Bavaria, Descartes was present as an official observer with the Catholic League at the Battle of the White Mountain near Prague in November 1620. After this he left the army but since the plague was ravaging in Paris he could not return there but instead began a period of travel.
From 1620 to 1628 Descartes travelled through Europe, spending time in Bohemia (1620), Hungary (1621), Germany, Holland and France (1622-23). He spent time in 1623 in Paris where he made contact with Marin Mersenne, an important contact which kept him in touch with the scientific world for many years, and with Claude Mydorge. From Paris he travelled through Switzerland to Italy where he spent some time in Venice and in Rome, then he returned to France again (1625). He renewed his acquaintance with Mersenne and Mydorge, and met Girard Desargues. His Paris home became a meeting place for philosophers and mathematicians and steadily became more and more busy. By 1628 Descartes, tired of the bustle of Paris, the house full of people, and of the life of travelling he had before, decided to settle down where he could work in solitude. He gave much thought to choosing a country suited to his nature and he chose Holland. What he longed for was somewhere peaceful where he could work away from the distractions of a city such as Paris yet still have access to the facilities of a city. It was a good decision which he did not seem to regret over the next twenty years. He told Mersenne where he was living so that he might keep in touch with the mathematical world, but otherwise he kept his place of residence a secret.
Soon after he settled in Holland, Descartes began work on his first major treatise on physics, Le Monde, ou Traité de la Lumière Ⓣ. He wrote to Mersenne in October 1629:-
[The foundations of physics] is the topic which I have studied more than any other and in which, thank God, I have not altogether wasted my time. At least I think that I have found how to prove metaphysical truths in a manner which is more evident than the proofs of geometry - in my opinion, that is: I do not know if I shall be able to convince others of it. During my first nine months in this country I worked on nothing else.
This work was near completion when news that Galileo was condemned to house arrest reached him. He, perhaps wisely, decided not to risk publication and the work was published, only in part, after his death. He explained later his change of direction saying:-
... in order to express my judgement more freely, without being called upon to assent to, or to refute the opinions of the learned, I resolved to leave all this world to them and to speak solely of what would happen in a new world, if God were now to create ... and allow her to act in accordance with the laws He had established.
For Descartes' own description of the contents of Le Monde, ou Traité de la Lumière Ⓣ see THIS LINK.
In Holland, Descartes had a number of scientific friends as well as continued contact with Mersenne. His friendship with Beeckman continued and he also had contact with Mydorge, Hortensius, Huygens and Frans van Schooten (the elder). Langer [112] describes Descartes' life in Holland:-
As throughout his life he continued to do his work abed in the mornings. His evenings he generally devoted to the consideration of his correspondence, which was mainly scientific, rarely personal, and of which he was painstakingly careful, while the intermediate part of the day he gave to relaxation. In matters of money he was neither extravagant nor parsimonious, showing himself in this respect a true philosopher. He always did some entertaining, now more, now less, professing to find considerable enjoyment in conversation, though he was himself rather taciturn.
Descartes was pressed by his friends to publish his ideas and, although he was adamant in not publishing Le Monde Ⓣ, he wrote a treatise on science under the title Discours de la méthode pour bien conduire sa raison et chercher la vérité dans les sciences Ⓣ. Three appendices to this work were La Dioptrique Ⓣ, Les Météores Ⓣ, and La Géométrie Ⓣ. The treatise was published at Leiden in 1637 and Descartes wrote to Mersenne saying:-
I have tried in my "Dioptrique" and my "Météores" to show that my Méthode is better than the vulgar, and in my "Géométrie" to have demonstrated it.
The work describes what Descartes considers is a more satisfactory means of acquiring knowledge than that presented by Aristotle's logic. Only mathematics, Descartes feels, is certain, so all must be based on mathematics.
La Dioptrique Ⓣ is a work on optics and, although Descartes does not cite previous scientists for the ideas he puts forward, in fact there is little new. However his approach through experiment was an important contribution.
Les Météores Ⓣ is a work on meteorology and is important in being the first work which attempts to put the study of weather on a scientific basis. However many of Descartes' claims are not only wrong but could have easily been seen to be wrong if he had done some easy experiments. For example Roger Bacon had demonstrated the error in the commonly held belief that water which has been boiled freezes more quickly. However Descartes claims:-
... and we see by experience that water which has been kept on a fire for some time freezes more quickly than otherwise, the reason being that those of its parts which can be most easily folded and bent are driven off during the heating, leaving only those which are rigid.
Despite its many faults, the subject of meteorology was set on course after publication of Les Météores Ⓣ particularly through the work of Boyle, Hooke and Halley.
La Géométrie Ⓣ is by far the most important part of this work. In [22] Scott summarises the importance of this work in four points:-
Some extracts from Descartes' La Géométrie Ⓣ are at THIS LINK.
Some ideas in La Géométrie Ⓣ may have come from earlier work of Oresme but in Oresme's work there is no evidence of linking algebra and geometry. Wallis in Algebra (1685) strongly argues that the ideas of La Géométrie Ⓣ were copied from Harriot. Wallis writes:-
... the Praxis was read by Descartes, and every line of Descartes' analysis bears token of the impression.
There seems little to justify Wallis's claim, which was probably made partly through patriotism but also through his just desires to give Harriot more credit for his work. Harriot's work on equations, however, may indeed have influenced Descartes who always claimed, clearly falsely, that nothing in his work was influenced by the work of others.
Descartes' Meditations on First Philosophy, was published in 1641, designed for the philosopher and for the theologian. It consists of six meditations, Of the Things that we may doubt, Of the Nature of the Human Mind, Of God: that He exists, Of Truth and Error, Of the Essence of Material Things, Of the Existence of Material Things and of the Real Distinction between the Mind and the Body of Man. However many scientists were opposed to Descartes' ideas including Arnauld, Hobbes and Gassendi.
The most comprehensive of Descartes' works, Principia Philosophiae Ⓣ was published in Amsterdam in 1644. In four parts, The Principles of Human Knowledge, The Principles of Material Things, Of the Visible World and The Earth, it attempts to put the whole universe on a mathematical foundation reducing the study to one of mechanics. This is an important point of view and was to point the way forward. Descartes did not believe in action at a distance. Therefore, given this, there could be no vacuum around the Earth otherwise there was no way that forces could be transferred. In many ways Descartes' theory, where forces work through contact, is more satisfactory than the mysterious effect of gravity acting at a distance. However Descartes' mechanics leaves much to be desired. He assumes that the universe is filled with matter which, due to some initial motion, has settled down into a system of vortices which carry the sun, the stars, the planets and comets in their paths. Despite the problems with the vortex theory it was championed in France for nearly one hundred years even after Newton showed it was impossible as a dynamical system. As Brewster, one of Newton's 19th century biographers, puts it:-
Thus entrenched as the Cartesian system was ... it was not to be wondered at that the pure and sublime doctrines of the 'Principia' were distrustfully received ... The uninstructed mind could not readily admit the idea that the great masses of the planets were suspended in empty space, and retained their orbits by an invisible influence ...
Pleasing as Descartes' theory was, even the supporters of his natural philosophy such as the Cambridge metaphysical theologian Henry More, found objections. Certainly More admired Descartes, writing:-
I should look upon Des-Cartes as a man most truly inspired in the knowledge of Nature, than any that have professed themselves so these sixteen hundred years...
However between 1648 and 1649 they exchanged a number of letters in which More made some telling objections. Descartes however in his replies makes no concessions to More's points. More went on to ask:-
Why are not your vortices in the form of columns or cylinders rather than ellipses, since any point of the axis of a vortex is as it were a centre from which the celestial matter recedes with, as far as I can see, a wholly constant impetus? ... Who causes all the planets not to revolve in one plane (the plane of the ecliptic)? ... And the Moon itself, neither in the plane of the Earth's equator nor in a plane parallel to this?
In 1644, the year his Meditations were published, Descartes visited France. He returned again in 1647, when he met Pascal and argued with him that a vacuum could not exist, and then again in 1648.
In 1649 Queen Christina of Sweden persuaded Descartes to go to Stockholm. However the Queen wanted to draw tangents at 5 a.m. and Descartes broke the habit of his lifetime of getting up at 11 o'clock. After only a few months in the cold northern climate, walking to the palace for 5 o'clock every morning, he died of pneumonia.
After his death an unfinished manuscript entitled Regulae ad directionem ingenii Ⓣ was found in his papers. Only the first 21 of the Rules were presented, the last three being only given by their intended titles. Sadly, the original manuscript has been lost and only copies remain. Here is a short extract from the manuscript:-
I would not value these Rules so highly if they were good only for solving those pointless problems with which arithmeticians and geometers are inclined to while away their time, for in that case all I could credit myself with achieving would be to dabble in trifles with greater subtlety than they. I shall have much to say below about figures and numbers, for no other disciplines can yield illustrations as evident and certain as these. But if one attends closely to my meaning, one will readily see that ordinary mathematics is far from my mind here, that it is quite another discipline I am expounding, and that these illustrations are more its outer garments than its inner parts. This discipline should contain the primary rudiments of human reason and extend to the discovery of truths in any field whatever. Frankly speaking, I am convinced that it is a more powerful instrument of knowledge than any other with which human beings are endowed, as it is the source of all the rest.
We should end this biography by saying a little more about Descartes as a person. In [112] Langer describes Descartes' appearance and personality:-
In appearance Descartes was a small man of rather slight figure with a large head. His nose was prominent, his lower lip somewhat protruding, his beard and moustache of a semi-military type, and his hair growing down upon his forehead almost to his eyebrows. He wore a wig of natural colour to which he always gave fastidious attention, as he did also to his clothes which were now invariably of black cloth. In demeanour he was generally cheerful, rarely gay. His manners were always refined, gentle, and polite, and his temper tranquil and easy. As a personality he was proud, somewhat aristocratically reserved, sensitive, a bit angular, and, though a shade domineering, was pre-eminently obliging.
Bertrand Russell writes [150]:-
He always was well dressed, and wore a sword. He was not industrious; he worked short hours, and read little. When he went to Holland he took few books with him, but among them were the Bible and Thomas Aquinas. His work seems to have been done with great concentration during short periods; but perhaps, to keep up the appearance of a gentlemanly amateur, he may have pretended to work less than in fact he did, for otherwise his achievements seem scarcely credible.
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