布丰Georges-Louis Leclerc, Comte de Buffon

布丰的母亲是安妮-克里斯蒂娜·马林，父亲是本杰明-弗朗索瓦·勒克莱尔。布丰-路易·勒克莱尔，这是他在1725年之前的名字，是他父母五个孩子中的长子。他出生在一个富裕家庭，他的母亲是一位受过良好教育的人，他说他从她那里继承了智慧，她与一位富有的银行家有亲戚关系。当布丰十岁时，他的母亲继承了一大笔钱，这使得本杰明·勒克莱尔成为布丰和蒙巴尔的领主。布丰这个名字是他母亲安妮此时继承的一处地产的名称。

1717年他的母亲继承财富后，全家搬进了第戎的一栋精美房屋，本杰明·勒克莱尔成为勃艮第议会的顾问。雅克·罗杰写道，在第戎，勒克莱尔家族[1]：-

……在社会中占有重要地位。那个省会的知识生活很活跃，但在那个特定时期并不以科学为导向。

此时布丰进入第戎的戈德朗耶稣会学院，并在那里接受教育直到1723年。他的三个弟弟后来加入了教会，但布丰的父亲希望他的长子学习法律。看起来布丰不会成为法律界的明星，因为他的学业表现并不高于平均水平。他确实表现出天赋的一门学科是数学，但他遵从父亲的意愿，于1723年开始学习法律。然而，他对数学的兴趣超过了对法律的兴趣，并在20岁时布丰（他现在自称布丰 Leclerc 布丰）发现了二项式定理。他与加布里尔·克拉默通信讨论力学、几何学、probability、数论以及微分和积分。

1728年，布丰前往昂热学习数学，但他也学习了医学和植物学等其他科目。1730年，在昂热求学期间，他卷入了一场决斗，因此不得不逃离该镇。他去了南特，在那里与一位年轻的英国贵族金斯顿公爵同住。布丰、金斯顿公爵及其导师纳撒尼尔·希克曼访问了法国南部和意大利，于1732年初抵达罗马。当消息传到布丰那里，说他的母亲去世了，他返回了法国。他的母亲将她的财产留给了布丰，尽管他的父亲强烈反对，他还是继承了这笔财产。布丰决定在他现在位于蒙巴尔的庄园定居。

这位富有的年轻人现在能够在巴黎政治和科学界的最高层留下印象。海军大臣让-弗雷德里克·菲利波布丰·德·莫尔帕正在承担重组严重士气低落的法国海军的艰巨任务。他想改进战舰的建造，并请布丰研究木材的抗拉强度以协助这项任务。他接下来发表了Mémoire sur le jeu de franc-carreauⓉ（关于‘法兰西方块’游戏的回忆录），将微分和积分引入概率论。由于这篇出色的回忆录，布丰于1734年1月9日在巴黎被选入Royal Academy of Sciences。

一个精通金融事务并以大量资金起步的人通常能够为自己创造相当可观的财富，这正是布丰在1734年至1740年间所做的。然而，除了花时间处理金融事务外，他还能够从事数学、植物学（特别是植物生理学）和林业方面的工作，在林业方面他考察了勃艮第自己森林中木材的改良特性。这一时期他的主要数学贡献是于1740年出版了他翻译的艾萨克·牛顿的Method of Fluxions and infinite series。

布丰生命中的一个新阶段始于1739年7月，当时他被任命为皇家植物园，即Jardin du Roi的管理者。正是我们上面提到的布丰 de Maurepas是这一显赫任命背后的主要影响者。Roger在[1]中描述了布丰在此任命后的生活：-

从1740年起，每年春天布丰离开巴黎前往蒙巴尔，管理他的庄园，继续他的研究，并编辑他的著作。他强健的体质使他能够遵循一个安排良好的日程：他黎明起床，上午工作，下午处理事务。五十年来，布丰在庄园度过夏天，秋天返回巴黎。在这段时间结束时，他将国王花园的面积扩大了一倍，丰富了其收藏，并大大扩建了其建筑；此外，他本人也变得富有，获得了大量养老金并增加了他的土地持有量。

布丰于1752年与Françoise de Saint-Belin-Malain结婚。此时布丰已经四十五岁，但他的妻子二十岁。他们在1764年有一个儿子，但布丰的妻子五年后去世。看起来布丰的儿子有着光明的未来，人们期望他至少能取得与他父亲同等的名声。当布丰的儿子十七岁时，他的父亲安排博物学家J-B Lamarck带他一起进行穿越欧洲的植物学研究。然而才华并不总是导致学习的愿望，他变成了一个不稳定的挥霍者。在法国大革命的恐怖时期，他于1794年被送上断头台。

布丰写作的广泛主题包括数学、概率论、天文学和物理学，尤其是光学。然而，他最著名的是他在自然历史方面的著作，特别是Discours sur la manière d'étudier et de traiter l'histoire naturelle, Théorie de la terre Ⓣ（关于如何研究和处理自然历史的论述；地球理论）和Histoire des animaux Ⓣ（动物史），这三部著作均于1749年出版。他的目标是出版50卷Histoire naturelle, générale et particulière Ⓣ（自然历史，一般和具体），但到他去世时只出版了36卷。这是一项重大成就，雄心勃勃地试图在一部著作中以系统的方式呈现自然历史、地质学和人类学的所有知识及其相互联系。

与艾萨克·牛顿不同，布丰相信一切通过自然现象发展。他强烈支持艾萨克·牛顿的Principia，但拒绝行星及其运动是上帝干预的直接结果这一观念。布丰提出了一种行星形成的方法，涉及彗星与太阳的碰撞。尽管我们现在知道这样的模型行不通，但它在提出一个遵循力学定律的模型方面很重要。他对地质学和地球结构的看法同样基于自然事件。他写道：-

为了判断已经发生的事情，甚至将要发生的事情，只需考察正在发生的事情。……每天发生的事件，接连出现并不断重复的运动，持续且不断重复的操作，这些就是我们的原因和理由。

布丰认为地球上的生命是通过有机物质的出现而产生的，而有机物质是热量作用于含水的油性物质的结果。他努力试图理解生殖，这是当时的一个主要话题，尽管他的理论是错误的，但它们再次基于科学原理。他主张物种存在，但科不存在，科只是那些试图对动物界进行分类的人的发明。然而，在他后来的著作中，他确实承认了科的概念，尽管他更愿意使用属这个名称，并对其处理方式与当时其他人看待动物分类的方式略有不同。布丰将人类物种作为他研究的动物物种之一，并应用了相同的方法和途径

Roger在[1]中写道：-

布丰的工作因其多样性、丰富性、独创性和影响力而异常重要。布丰是最早创建一门自主科学的人之一，这门科学不受任何神学影响。他强调了自然史的重要性和地质时间的漫长。他构想了科学的本质，并理解了古生物学、动物地理学和动物心理学的作用。

尽管取得了这些成就，布丰在他有生之年并未受到极大的赞赏，正如[2]所指出的：-

布丰在他同时代人中的地位绝非稳固。尽管公众几乎一致钦佩他，但他在学者中遇到了众多诋毁者。神学家们被他的地质史概念所激怒；其他人批评他在生物分类上的观点；哲学家Étienne de Condillac质疑他关于动物心理能力的观点；许多人从他的工作中只提取了一些关于自然的一般哲学观念，而这些观念并不忠实于他所写的内容。Voltaire不欣赏他的风格，让·勒朗·达朗贝尔称他为“伟大的空话家”。据作家J-F Marmontel说，布丰不得不忍受数学家、化学家和天文学家的冷落，而博物学家们自己也几乎不支持他，有些人甚至责备他在一个需要简单自然风格的学科中卖弄文笔。

布丰本人以极大的尊严回应了对他的攻击，没有像这一时期的许多科学家那样陷入恶语相向的争执。他写信给一位朋友说：-

我将保持绝对的沉默……让他们的攻击落到他们自己身上。

他对数学最显著的贡献是一个概率实验，他通过将棍棒从肩后扔到铺有瓷砖的地板上，并计算棍棒落在瓷砖之间线条上的次数来进行计算。他指出（见[10]），有利情况对应于：-

……对应于摆线一部分的面积，该摆线的生成圆直径等于针的长度。

这个实验在数学家中引起了大量讨论，有助于增进对概率的理解。1980年的论文[6]对布丰的针实验给出了新的分析，作者进行了2000次投掷的实验，得到π = 3.1430……。

1777年描述的针实验并不是布丰研究过的唯一概率问题。同样在1777年，他试图计算太阳在连续观察$n$天升起后继续升起的概率；详情见[13]。

Georges Buffon's mother was Anne-Cristine Marlin and his father was Benjamin-François Leclerc. Georges-louis Leclerc, as was his name until 1725, was the eldest of his parents five children. He was born into a wealthy family and his mother, who was a well educated person from whom he said he inherited his intelligence, was related to a wealthy banker. When Georges was ten years old his mother inherited a large sum of money which allowed Benjamin Leclerc to become lord of Buffon and Montbard. The name Buffon was that of an estate that his mother Anne inherited at this time.

After his mother inherited the fortune in 1717 the family moved into a fine house in Dijon and Benjamin Leclerc became a counsellor in the Burgundian parliament. Jacques Roger writes that in Dijon the Leclerc family [1]:-

... occupied an important place in society. The intellectual life of that provincial capital was active but not oriented towards science at that particular time.

At this time Georges entered the Jesuit College of Godrans in Dijon and he was educated there until 1723. Three of his younger brothers went on to join the Church but Georges' father wanted his eldest son to study law. It did not look that Georges would become a star in legal circles for his school performance was not above average. The one subject that he did show a talent for was mathematics but he followed his father's wishes and began to study law in 1723. However, he was more interested in mathematics than he was in the law and at the age of 20 Buffon (he was now calling himself Georges-Louis Leclerc De Buffon) discovered the binomial theorem. He corresponded with Gabriel Cramer on mechanics, geometry, probability, number theory and the differential and integral calculus.

In 1728 Buffon went to Angers to study mathematics, but he also studied other topics such as medicine and botany. In 1730, while a student in Angers, he became involved in a duel and as a result had to flee the town. He went to Nantes, where he lived with a young English nobleman, the Duke of Kingston. Buffon, the Duke of Kingston and his tutor Nathaniel Hickman, visited southern France and Italy, arriving in Rome early in 1732. When news reached Buffon that his mother had died, he returned to France. His mother had left Buffon her fortune which he inherited despite his father objecting strongly. Buffon decided to settle on what was now his estate at Montbard.

The rich young man was now able to make an impression in the highest ranks of the political and scientific circles in Paris. Jean-Frédéric Phélypeaux Comte de Maurepas, the minister to the navy, was undertaking the huge task of reorganizing the severely demoralized French navy. He wanted to improve the construction of ships of war, and he asked Buffon to study the tensile strength of timber to assist in this task. He next published Mémoire sur le jeu de franc-carreau Ⓣ which introduced differential and integral calculus into probability theory. As a result of this fine memoir Buffon was elected to the Royal Academy of Sciences in Paris on 9 January 1734.

Someone who is skilled in financial affairs and who starts with a large amount of money is usually able to make a considerably larger fortune for themselves, and this is precisely what Buffon did over the years from 1734 to 1740. However, in addition to time spent on his financial affairs he was also able to work on mathematics, on botany (in particular plant physiology) and on forestry where he examined improving properties of timber in his own forests in Burgundy. His main mathematical contribution of this period was the publication of his translation of Newton's Method of Fluxions and infinite series in 1740.

A new phase in Buffon's life began in July 1739 when he was appointed as keeper of the royal botanical garden, the Jardin du Roi. It was the Comte de Maurepas, whom we mentioned above, who was the main influence behind this prestigious appointment. Roger in [1] describes Buffon's life following this appointment:-

Each spring, from 1740 on, Buffon left Paris for Montbard, to administer his estates, continue his research, and edit his writings. His robust constitution allowed him to adhere to a well-organised schedule: he arose at dawn and spent the morning at work, and the afternoon on business affairs. For fifty years, Buffon spent the summer on his estate, returning to Paris in the autumn. At the end of this time, he had doubled the area of the Jardin du Roi, enriched its collections, and enlarged its buildings considerably; moreover, he himself had become rich, having been showered with pensions and having increased his landholding.

Buffon married Françoise de Saint-Belin-Malain in 1752. By this time Buffon was forty-five years of age but his wife was twenty. They had one son in 1764 but Buffon's wife died five years later. It looked as though Buffon's son had a brilliant future and he was expected to achieve fame at least equal to that of his father. When Buffon's son was seventeen years old his father arranged for the naturalist J-B Lamarck to take him with him on his botanical studies through Europe. However brilliance does not always lead to a desire to study and he turned into an unstable spendthrift. During the Terror of the French Revolution he was sent to the guillotine in 1794.

The wide range of topics which Buffon wrote on include mathematics, the theory of probability, astronomy and physics, especially optics. He is best known, however, for his work on natural history especially Discours sur la manière d'étudier et de traiter l'histoire naturelle, Théorie de la terre Ⓣ and Histoire des animaux Ⓣ all three of which were published in 1749. His aim was to publish 50 volumes of Histoire naturelle, générale et particulière Ⓣ but only 36 had appeared by the time of his death. It is a major achievement which ambitiously attempts to present all knowledge of natural history, geology, and anthropology and their interconnections in a systematic way in a single work.

Unlike Newton, Buffon believed that everything developed through natural phenomena. He what a strong supporter of Newton's Principia but rejected the notion that the planets and their motions were a direct consequence of God's intervention. Buffon proposed a method of creation of the planets which involved the collision of a comet with the sun. Although we now know that such a model will not work, it was important in proposing a model which followed the laws of mechanics. His views of geology and the structure of the earth was similarly based on natural events. He wrote:-

In order to judge what has happened, or even what will happen, one need only examine what is happening. ... Events which occur every day, movements which succeed each other and repeat themselves without interruption, constant and constantly reiterated operations, these are our causes and our reasons.

Similarly Buffon argued that life came about on earth through the appearance of organic matter which was the result of heat on aqueous, oily substances. He worked hard trying to understand reproduction, a major topic of the day, and although his theories are in error they are again based on scientific principles. He argued that species existed but that families did not, being merely an invention of those attempting classification of the animal world. Later in his writings, however, he does admit the idea of a family although he prefers to use the name genus an treat it a little differently from the way others viewed animal classification at this time. Buffon included the human species as one of the species of animals which he studied and applied the same approach and methods

Roger writes in [1]:-

Buffon's work is of exceptional importance because of its diversity, richness, originality, and influence. Buffon was among the first to create an autonomous science, free of any theological influence. He emphasised the importance of natural history and the great length of geological time. He envisioned the nature of science and understood the roles of palaeontology, zoological geography, and animal psychology.

Despite these achievements Buffon was not greatly admired during his lifetime as is pointed out in [2]:-

Buffon's position among his contemporaries was by no means assured. Though the public was nearly unanimous in its admiration of him, he met with numerous detractors among the learned. The theologians were aroused by his conceptions of geological history; others criticized his views on biological classification; the philosopher Étienne de Condillac disputed his views on the mental faculties of animals; and many took from his work only some general philosophical ideas about nature that were not faithful to what he had written. Voltaire did not appreciate his style, and d'Alembert called him "the great phrasemonger." According to the writer J-F Marmontel, Buffon had to put up with snubs from the mathematicians, chemists, and astronomers, while the naturalists themselves gave him little support and some even reproached him for writing ostentatiously in a subject that required a simple and natural style.

Buffon himself reacted to the attacks on him with great dignity and did not get into bad tempered disputes as many scientists of this period did. He wrote to a friend:-

I shall keep absolute silence ... and let their attacks fall upon themselves.

His most notable contribution to mathematics was a probability experiment which he carried out calculating by throwing sticks over his shoulder onto a tiled floor and counting the number of times the sticks fell across the lines between the tiles. He stated (see [10]) that the favourable cases correspond:-

... to the area of part of the cycloid whose generating circle has diameter equal to the length of the needle.

This experiment caused much discussion among mathematicians which helped towards an understanding of probability. The 1980 paper [6] gives a new analysis of Buffon's needle experiment, and the author conducts an experiment with 2000 throws which gives π = 3.1430 ....

The needle experiment, described in 1777, was not the only problem in probability that Buffon examined. Also in 1777 he attempted to calculate the probability that the sun would continue to rise after having been observed to rise $n$ days in a row; see [13] for details.