阿尔弗雷德·诺思·怀特海Alfred North Whitehead

阿尔弗雷德·诺思·怀特海的父亲也叫怀特海，是来自拉姆斯盖特的圣公会牧师。据说他为人正直，朋友无数，怀特海的儿子怀特海曾这样写他的祖父：-

他从不向任何人求情，也从不逃避他认为应尽的义务，但不能说他花在领会《新约》教诲上的时间超出了他职责所需。

这位数学家的父亲怀特海于1851年12月20日与来自伦敦的玛丽亚·萨拉·巴克马斯特结婚。她被描述为（见[6]）：-

……一个缺乏想象力、心胸狭窄的女人，有些小聪明但毫无幽默感。

怀特海和Maria Whitehead有四个孩子，怀特海是家中最小的。他有两个比他大七八岁的哥哥，还有一个比他大两岁的姐姐。怀特海一直被父母当作家里的小宝贝，而且相当令人意外的是，他们竟认为他是个体弱多病的孩子，而事实似乎并非如此。怀特海没有上小学，因为父母觉得他太娇弱，所以他在14岁之前一直由父亲在家教导。除了通常的儿童疾病外，尽管父母那样认为，他其实是个健康的孩子。他从父亲和哥哥们那里得到许多关爱（但遗憾的是从母亲那里得到的很少），他的童年似乎并非不快乐，尽管他常常独自一人，一定有些孤独。

怀特海的父亲从十岁起教他拉丁语，从十二岁起教他希腊语。他在这些科目上的能力当然可以算作合格，但肯定不算出众；没有任何迹象显示他后来在生活中展现出的天才。他确实从父亲那里学了一点数学，但他究竟如何对这科目产生兴趣却是个谜。1875年9月，他离开父亲的牧师住宅，进入Sherbourne独立学校。他的大哥于1876年成为该校的教师，当时怀特海正进入第二年的学习。

他在Sherbourne所学的课程在当时是相当标准的。科目选择很少，所有男孩的主修科目都是拉丁语、希腊语和英语，而数学、物理科学、历史、地理和现代语言等副修科目则受到较少关注。怀特海在数学上表现出特殊天赋，获准在最后一年将额外时间投入该科目，放弃拉丁诗歌的写作和阅读，以便腾出时间学习更多数学。

1879年，怀特海参加了剑桥大学三一学院的入学考试，并赢得了奖学金。此后，他在Sherbourne度过了最后一年，担任班长和运动队队长，然后于1880年10月进入大学。作为奖学金的持有者，怀特海住在学院里。他只参加数学讲座，由詹姆斯·惠特布雷德·李·格莱舍、H M Taylor和W D Niven授课。他还参加了乔治·加布里埃尔·斯托克斯和阿瑟·凯莱的讲座，而他的辅导老师是著名的爱德华·约翰·劳思。他在剑桥的密友中有达西・汤普森。

怀特海赢得了第二项奖学金，即学院基金会奖学金，因此到他进入第二年学习时，他已经相当宽裕。他于1883年参加了数学荣誉学位考试，名列第四数学荣誉学位考试一等及格者（Wrangler）；那一年的高级牧马人是G B Mathews（高级牧马人在获得一等学位的学生名单中排名第一，第四牧马人排名第四）。次年，他也被列入数学荣誉学位考试第三部分的一等。1884年，他在竞争研究员职位时提交了一篇关于詹姆斯·克拉克·麦克斯韦的电学和磁学理论的学位论文。开尔文和安德鲁·福赛思被任命为怀特海的考官，令他大为惊讶的是，他赢得了当年可获得的五项奖学金之一。

赢得研究员职位后，怀特海被任命为助理讲师。他主要教授应用数学，但令人惊讶的是，在他担任研究员职位的最初五年里，他没有发表任何论文。不知道他在这期间是否从事数学研究。可以肯定的是，他非常孤僻，不与其他数学家多交谈。在剑桥担任教职后的十二年里，他只发表了两篇论文，都在1889年，关于粘性流体的运动。他对这个主题感兴趣的原因几乎可以肯定是因为他听过乔治·加布里埃尔·斯托克斯关于粘性流体的讲座。

尽管发表记录不佳，怀特海还是在1888年被提升为剑桥的讲师。他接受了格顿学院的教学职位，承担了额外的教学任务。此时种种迹象都表明，他已认定自己的长处在于教学而非发表。然而，1890年12月16日他在伦敦与伊夫林·韦德结婚后，发生了相当显著的变化[6]：-

他沉静内敛，她却活跃外向。

他开始对纯数学产生兴趣，并于1891年1月开始撰写Treatise on Universal Algebra，此时距他结婚仅数周。这项工作将耗费他七年时间才完成，直到1898年才最终出版。怀特海的妻子伊芙琳·韦德是A·韦德上尉的女儿，他们育有三个孩子，两子一女。两个儿子中较年幼的埃里克·怀特海成为皇家飞行队（该队成立于1912年，后成为皇家空军的一部分）的少尉，并于1918年在法国的一次飞行巡逻中阵亡。

怀特海 生活中的其他变化发生在他结婚前后。我们已经指出，怀特海 的父亲是一位圣公会牧师，当然，怀特海 也是作为圣公会教徒抚养长大的。然而在 1889-90 年左右，他开始转向罗马天主教会。他自我辩论了七年，是继续做圣公会教徒还是加入罗马天主教会。最终他两者都没有选择，并在 1890 年代中期左右成为不可知论者。他本人表示，他成为不可知论者的最大因素是科学的迅速发展；特别是他认为 艾萨克·牛顿 的物理学是错误的。对许多人来说，艾萨克·牛顿 物理学的正确性竟能成为决定任何人宗教观点的主要因素，这似乎令人惊讶。然而，人们必须理解 怀特海 是一个复杂的人，尤其是他对哲学和 形而上学 日益增长的兴趣。

我们应当回到Treatise on Universal Algebra的故事，怀特海在19世纪90年代的大部分时间里都在从事这项工作。也许我们首先应当指出，这部著作并非关于现代意义上的泛代数主题，因为“泛代数”一词对怀特海而言有着相当不同的含义。事实上，这个名称取自詹姆斯·约瑟夫·西尔维斯特十四年前发表的一篇论文。在这部论著的序言中，他写道，他的目标是：-

……对与普通代数相关的各种符号推理系统进行彻底研究……。这类系统的主要例子有威廉·哈密顿的四元数、赫尔曼·格拉斯曼的扩展演算和乔治·布尔的符号代数。

同样在序言中，怀特海还阐述了他对数学本质和数学哲学的看法：-

数学在其最广泛的意义上，是一切形式的、必然的、演绎推理的发展。这种推理是形式的，意思是命题的含义不构成研究的一部分。数学唯一关注的是从命题推出命题。……数学的理想应当是建立一种演算，以便在思想的每一个领域或外部经验中促进推理，在这些领域中，思想或事件的序列能够被明确确定并精确陈述。这样，一切不是哲学、归纳推理或想象文学的严肃思想，都应当是通过演算发展出来的数学。

怀特海婚后变得非常多产，他从不认为自己是数学新领域的创造者，而是他人所引入思想的发展者。这并不意味着他的贡献因此应被视为不那么重要，但剑桥似乎确实低估了他的贡献。1894年，怀特海成为数学荣誉学位考试的考官。1903年，他被提升为高级讲师，这一职位在剑桥才刚刚设立。

怀特海 最为人所知的也许是他与 伯特兰·罗素 的合作。我们将在下面给出这次合作的细节，但首先我们将完成 怀特海 职业生涯的细节。他留在剑桥直到 1910 年，但在某种意义上，由于未能在数学上达到标准，并且在剑桥获得数学讲席的前景渺茫，他转到了伦敦大学。对他这一转动的解释几乎肯定是基本正确的，这确实是 怀特海 思考背后的动机；然而从表面上看，相当不同且戏剧性的事件结束了他与剑桥的联系。

1910 年，自学生时代起就是 怀特海 密友的 Andrew 安德鲁·福赛思 与 查尔斯·弗农·博伊斯 的妻子 Marion Amelia 查尔斯·弗农·博伊斯 有了一段恋情，丑闻迫使他辞去剑桥的讲席。怀特海 竭尽全力确保 安德鲁·福赛思 保留其会士职位。关于他能否保留会士职位的决定由三一学院理事会做出，作为该理事会成员的 怀特海 强烈主张允许 安德鲁·福赛思 继续担任三一学院会士。然而，怀特海 在理事会中被投票否决，此后不久他辞去了高级讲师和会士职位。

随后，委员会投票决定，怀特海已担任讲师超过25年（最长期限），因此必须离职。怀特海的高级讲师任命还有三年才到期，但他没有留下来为自己的情况辩护。1910年夏天，他搬到了伦敦，没有工作可去。1914年，在四年没有正式职位之后，他成为伦敦帝国科学与技术学院的应用数学教授。1924年，他接受了哈佛大学的哲学讲席，并在哈佛任教直到1937年退休。

伯特兰·罗素于1890年进入剑桥，怀特海作为入学考试的考官，立即在伯特兰·罗素的试卷中发现了他的才华。怀特海主张，伯特兰·罗素应该获得比他的分数所应得的更负盛名的奖学金，事实上这得到了同意。当伯特兰·罗素还是本科二年级学生时，他由怀特海授课。他们在Principia Mathematica上的合作似乎始于1900年底左右，尽管两人在晚年接受采访时都记不清合作开始的确切时间。事实上，他们参加了1900年在巴黎举行的国际数学家大会，在那里他们了解到了朱塞佩·皮亚诺关于数学基础的工作。这促使他们研究朱塞佩·皮亚诺的论文，这一定是他们开始合作的一个主要因素。

在他们开始合作时，怀特海正在撰写他的文章Memoir on the algebra of symbolic logic，而伯特兰·罗素即将完成他的Principles of mathematics初稿。怀特海正在计划Treatise on Universal Algebra的第二卷，但他们的计划在1901年都受到了某种程度的干扰，当时伯特兰·罗素发现了他的著名集合论悖论。在对悖论的最初担忧之后，他们联手致力于伯特兰·罗素著作的第二卷，因此到1903年，怀特海同时在进行两个不同的第二卷工作。意识到这对他来说不是最佳方案，他放弃了自己著作的第二卷，专注于与伯特兰·罗素的合作。他们的合作工作试图在严格的逻辑基础上构建数学基础，伯特兰·罗素作为项目中的哲学家，怀特海作为数学家。

与伯特兰·罗素合作并没有完全占据怀特海的时间，因为他继续产出自己的作品。1906年，他出版了The axioms of projective geometry，次年出版了The axioms of descriptive geometry。Principia Mathematica的第一卷于1910年出版，第二卷于1912年出版，第三卷于1913年出版。他还写了通俗数学书An introduction to mathematics，该书于1911年出版，在Principia的第一卷和第二卷之间。

随着Principia Mathematica接近完成，怀特海将注意力转向了科学哲学。这种兴趣源于试图解释物理学中形式数学理论与经验基础的关系，并由阿尔伯特·爱因斯坦的广义相对论带来的革命所激发。在The Principle of Relativity（1922年）中，怀特海提出了阿尔伯特·爱因斯坦观点的替代方案。

Science and the Modern World（1925年）是在美国进行的一系列讲座，作为他后来形而上学的导论。怀特海最重要的著作Process and Reality（1929年）将这一理论提升到了更高的普遍性水平。

怀特海在其职业生涯中获得了许多荣誉。1903年当选为皇家学会会士，1925年因在数学基础方面的工作和对物理概念的研究而荣获该学会的詹姆斯·约瑟夫·西尔维斯特奖章。Royal Society of Edinburgh于1922年授予他詹姆斯·斯科特奖（他是首位获奖者）。哥伦比亚大学于1930年授予他巴特勒奖章，次年他当选为英国科学院院士。1945年他被授予功绩勋章。许多大学授予他荣誉学位，包括曼彻斯特大学、圣安德鲁斯大学、威斯康星大学、哈佛大学、耶鲁大学和蒙特利尔大学。

Alfred North Whitehead's father, also named Alfred Whitehead, was an Anglican clergyman from Ramsgate. He is said to have been an upright man with countless friends and Alfred North Whitehead's son, North Whitehead, wrote of his grandfather:-

He never asked a favour of anyone and never shirked what he considered to be a duty, but it cannot be said that he spent more time absorbing the lessons of the New Testament than was necessitated by his calling.

Canon Alfred Whitehead, the mathematician's father, married Maria Sarah Buckmaster, who came from London, on 20 December 1851. She is described as (see [6]):-

... an unimaginative, small minded woman with some wit but no sense of humour.

Alfred and Maria Whitehead had four children, with Alfred North Whitehead as the youngest of the family. He had two brother who were seven and eight years older than he was, and a sister who was two years older. Whitehead was always treated by his parents as the baby of the family and, rather surprisingly, they considered him a sickly and frail child when it appears that this was not the case. Whitehead was not sent to primary school because his parents thought that he was too delicate, so he was taught at home by his father until he was 14. Other than the usual childhood illnesses he was, despite his parents views, a healthy child. He received much affection from his father and brothers (but sadly little from his mother) and he seems to have had a childhood which was not unhappy, even though he was on his own a great deal and must have been somewhat lonely.

Whitehead's father taught him Latin from the age of ten and Greek from the age of twelve. His ability in these subjects could certainly be classed as competent but it was certainly not outstanding; there was no sign of the genius that he showed later in life. He did learn a little mathematics from his father but quite how he developed an interest in the subject is a mystery. In September 1875 he left his father's vicarage and entered Sherbourne Independent School. His oldest brother became a teacher at the school in 1876 when Whitehead was entering his second year of study.

The course he followed at Sherbourne was a fairly standard one for the time. There was little choice of subjects and all the boys studied as their major subjects Latin, Greek and English, with the minor subjects of mathematics, physical sciences, history, geography and modern languages receiving less attention. Whitehead showed a special gift for mathematics and was allowed to devote extra time to that subject in his final school year, dropping composition and reading of Latin poetry to make way for the extra mathematics.

In 1879 Whitehead took the entrance examinations for Trinity College, Cambridge, and he won a scholarship. Following this he spent his final year at Sherbourne as Head Boy and Captain of Games before he entered university in October 1880. As the holder of a scholarship, Whitehead lived in College. He attended only mathematics lectures and was taught by J W L Glaisher, H M Taylor, and W D Niven. He also attended lectures by Stokes and Cayley while his coach was the famous E J Routh. Among his close friends at Cambridge was D'Arcy Thompson.

Whitehead won a second scholarship, a College Foundation, and so by the time he entered his second year of study he was quite well off. He took the Mathematical Tripos examinations in 1883 and was placed Fourth Wrangler; the Senior Wrangler that year was G B Mathews (the Senior Wrangler was ranked first, the Fourth Wrangler ranked fourth in the list of students awarded a First Class degree). In the following year he was also placed in the First Class of Part III of the Mathematical Tripos. He presented a dissertation on Maxwell's theory of electricity and magnetism in the competition for a Fellowship in 1884. Thomson and Forsyth were appointed to examine Whitehead and, much to his surprise, he won one of the five scholarships available that year.

After winning the Fellowship, Whitehead was appointed to an assistant lectureship. He taught mostly applied mathematics but, surprisingly, he published no papers during the first five years of his tenure of the Fellowship. It is not known if he worked on mathematical research over this period. Certainly he was very much of a loner and did not talk much with the other mathematicians. In the twelve years following taking up the teaching position at Cambridge he published only two papers, both in 1889 on the motion of viscous fluids. The reason that the topic interested him was almost certainly because he had attended lectures by Stokes on viscous fluids.

Despite his poor publication record, Whitehead was promoted to a Lectureship at Cambridge in 1888. He took up additional teaching duties by accepting a teaching position at Girton College. All the signs at this time would point to him having decided that his strength was in teaching and not in publishing. A rather remarkable change came, however, when he married Evelyn Wade in London on 16 December 1890 [6]:-

Whereas he was quiet and restrained, she was active and outgoing.

He had become interested in pure mathematics and he started work on Treatise on Universal Algebra in January 1891, just weeks after his marriage. The work would take him seven years to complete, not finally being published until 1898. Whitehead's wife, Evelyn Wade, was the daughter of Captain A Wade, and they had three children, two sons and a daughter. The younger of the two sons, Eric Alfred Whitehead, became a second Lieutenant in the Royal Flying Corps (which was set up in 1912 and later became part of the Royal Air Force) and died while on a flying patrol in France in 1918.

Other changes in Whitehead's life took place around the time of his marriage. We have already indicated that Whitehead's father was an Anglican vicar and, of course, Whitehead was brought up as an Anglican. However around 1889-90 he began to move towards the Roman Catholic Church. He debated with himself for seven years whether to remain an Anglican or join the Roman Catholic Church. In the end he chose neither and became an agnostic around the mid 1890s. He himself stated that the biggest factor in his becoming an agnostic was the rapid developments in science; particularly his view that Newton's physics was false. It may seem surprising to many that the correctness of Newton's physics could be a major factor in deciding anyone's religious views. However one has to understand the complex person that Whitehead was, and in particular the interest which he was developing in philosophy and metaphysics.

We should return to the story of the Treatise on Universal Algebra which Whitehead worked on for much of the 1890s. Perhaps the first comment we should make is that the work is not on the modern topic of universal algebra for the term 'universal algebra' had quite a different meaning to Whitehead. In fact the name was taken from a paper published by Sylvester fourteen years earlier. In the Preface to the treatise he writes that his aim is:-

... to present a thorough investigation of the various systems of symbolic reasoning allied to ordinary algebra ... . The chief examples of such systems are Hamilton's Quaternions, Grassmann's Calculus of Extension, and Boole's Symbolic Algebra.

Also in the Preface Whitehead also gives his views on the nature on mathematics and the philosophy of mathematics:-

Mathematics in its widest signification is the development of all types of formal, necessary, deductive reasoning. The reasoning is formal in the sense that the meaning of propositions forms no part of the investigation. The sole concern of mathematics is the inference of proposition from proposition. ... The ideal of mathematics should be to erect a calculus to facilitate reasoning in connection with every providence of thought, or external experience, in which the succession of thoughts, or of events can be definitely ascertained and precisely stated. So that all serious thought which is not philosophy, or inductive reasoning, or imaginative literature, shall be mathematics developed by means of a calculus.

Although Whitehead became very productive after his marriage, he never considered himself a creator of new areas of mathematics, but rather as a developer of ideas introduced by others. This does not mean that his contribution should be considered any less important because of this but certainly Cambridge seems to have undervalued his contribution. In 1894 Whitehead became an examiner for the Mathematical Tripos. In 1903 he was promoted to Senior Lecturer, a position which had only just been established at Cambridge.

Whitehead is perhaps best known for his collaboration with Bertrand Russell. We shall give details of this collaboration below, but first we shall complete the details of Whitehead's career. He remained at Cambridge until 1910 but, in some sense, having not made the grade in mathematics and, having little prospects of a mathematics chair at Cambridge, he moved to the University of London. This explanation of his move is almost certainly basically correct and this indeed was the motivation behind Whitehead's thinking; on the face of it, however, rather different and dramatic events ended his association with Cambridge.

In 1910 Andrew Forsyth, who had been a close friend of Whitehead's since his student days, had a love affair with Marion Amelia Boys, the wife of C V Boys, and the scandal forced him to resign his chair at Cambridge. Whitehead did everything he could to ensure that Forsyth kept his Fellowship. The decision as to whether he could keep the Fellowship was taken by the Council of Trinity and Whitehead, as a member of that Council, argued strongly that Forsyth should be allowed to remain a Fellow of Trinity. Whitehead was outvoted on the Council, however, and shortly after this he resigned his Senior Lectureship and his Fellowship.

The Council then voted that Whitehead had served as a Lecturer for over 25 years (the maximum period) so must leave his post. Whitehead's appointment as Senior Lecturer still had three years to run but he did not stay to argue his case. He moved to London in the summer of 1910 with no job to go to. In 1914, after four years without a proper position, he became Professor of Applied Mathematics at the Imperial College of Science and Technology in London. He accepted a chair in philosophy at Harvard University in 1924, and he taught at Harvard until his retirement in 1937.

Bertrand Russell entered Cambridge in 1890 and immediately Whitehead, as examiner for the entrance examinations, spotted Russell's brilliance in his examination papers. Whitehead argued that Russell should be awarded a more prestigious scholarship than his marks would have merited and indeed this was agreed. When Russell was in his second year as an undergraduate he was taught by Whitehead. Their collaboration on Principia Mathematica appears to have begun near the end of 1900, although both men failed to remember the exact time their collaboration began when interviewed late in their lives. In fact they had attended the International Congress of Mathematicians in Paris in 1900 and there they had learnt about Peano's work on the foundations of mathematics. This led to them study Peano's papers and this must have been a major factor in getting their collaboration started.

At the time they began collaborating, Whitehead was working on his article Memoir on the algebra of symbolic logic while Russell was close to finishing the first draft of his Principles of mathematics. Whitehead was planning a second volume of Treatise on Universal Algebra but both their plans were somewhat disrupted in 1901 when Russell discovered his famous set theory paradox. After the initial worry over the paradox they joined forces on Volume 2 of Russell's work so, by 1903, Whitehead was working simultaneously on two different second volumes. Realising that this was not the optimal course for him he abandoned the second volume of his own work to concentrate on his collaboration with Russell. Their joint work attempted to construct the foundations of mathematics on a rigorous logical basis and it was carried out with Russell as the philosopher on the project and Whitehead as the mathematician.

Working with Russell did not occupy Whitehead completely for he continued to produce work of his own. In 1906 he published The axioms of projective geometry and, in the following year, The axioms of descriptive geometry. The first volume of Principia Mathematica was published in 1910, the second in 1912, and the third in 1913. He also wrote the popular mathematics book An introduction to mathematics which was published in 1911, between Volumes 1 and 2 of the Principia.

As the Principia Mathematica neared completion, Whitehead turned his attention to the philosophy of science. This interest arose out of the attempt to explain the relation of formal mathematical theories in physics to their basis in experience, and was sparked by the revolution brought on by Einstein's general theory of relativity. In The Principle of Relativity (1922), Whitehead presented an alternative to Einstein's views.

Science and the Modern World (1925), a series of lectures given in the United States, served as an introduction to his later metaphysics. Whitehead's most important book, Process and Reality (1929), took this theory to a level of even greater generality.

Whitehead received many honours throughout his career. Elected to the Royal Society in 1903, he was awarded the Society's Sylvester Medal in 1925 because of his work on the foundations of mathematics and his studies of physical concepts. The Royal Society of Edinburgh awarded him their James Scott Prize in 1922 (he was the first recipient). Columbia university awarded him their Butler Medal in 1930 and in the following year he was elected to the British Academy. He was awarded the Order of Merit in 1945. Many universities awarded him an honorary degree including Manchester, St Andrews, Wisconsin, Harvard, Yale and Montreal.