# Karl Pearson

### Born: 27 March 1857 in London, England

Died: 27 April 1936 in Coldharbour, Surrey, England

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**Karl Pearson**'s mother Fanny Smith and his father William Pearson were both from Yorkshire families. William was a barrister of the Inner Temple [26]:-

William and Fanny named their second child Carl and he used this name until he was about 23 years old when he changed the spelling to Karl. In this article we shall refer to him either as Karl or as Pearson.He was a man of great ability, with exceptional mental and physical energy and a keen interest in historical research, traits which his son also exhibited.

Karl, together with his one older brother and one younger sister, were brought up in an upper-middle class family. After being educated at home up to the age of nine years, he was sent to University College School, London. He studied there until he was sixteen, but he was then forced to leave due to illness. A private tutor was engaged to teach him at home and he took the Cambridge Scholarship Examinations in 1875 and, coming second in the examinations, he won a scholarship to King's College.

At Cambridge he was taught by Stokes, Maxwell, Cayley and Burnside. His coach was perhaps the most famous of all the Cambridge coaches, namely Routh. He spoke of his undergraduate years saying (see [3]):-

But these were days of great happiness for Pearson [22]:-At Cambridge I studied mathematics under Routh, Stokes, Cayley, and Clerk Maxwell, but read papers on Spinoza.

As he indicates in these quotations, his studies at Cambridge were unusually broad. He read Goethe, Dante, and Rousseau, read about the history of religious thought, and enjoyed debating with students of moral philosophy about their subject.There was pleasure in the friendships, there was pleasure in the fights, there was pleasure in the coaches' teaching, there was pleasure in searching for new lights as well in mathematics as in philosophy and religion.

Pearson was never one to accept authority and this comes out clearly during his undergraduate years at Cambridge. At that time divinity lectures and attendance at chapel were compulsory. Pearson was deeply interested in religion yet hated the compulsory nature of these activities. He argued successfully to have the University regulations changed so that attendance was no longer compulsory at divinity lectures and, having won this battle, fought the second battle on compulsory chapel with his father's help. Having won, he surprised the University authorities by continuing to attend chapel but, of course, to Pearson there was a world of difference between attending voluntarily and compulsory attendance.

He graduated from Cambridge University in 1879 as Third Wrangler in the Mathematical Tripos (meaning that he was ranked third among those who gained a First Class degree). He then travelled to Germany to study at the University of Heidelberg. There he studied physics under G H Quincke and metaphysics under Kuno Fischer. He next visited the University of Berlin, where he attended the lectures of the famous physiologist Émile du Bois-Reymond on Darwinism (Émile was a brother of Paul du Bois-Reymond, the mathematician). Other subjects which he studied in Berlin included Roman Law, taught by Bruns and Mommsen, medieval and 16

^{th}century German Literature, and Socialism. He was strongly influenced by the courses he attended at this time and he became sufficiently expert on German literature that he was offered a post in the German Department of Cambridge University. On his return to England in 1880, Pearson first went to Cambridge [3]:-

His first book,Back in Cambridge, I worked in the engineering shops, but drew up the schedule in Mittel- and Althochdeutsch for the Medieval Languages Tripos.

*The New Werther*, was published at this time. In it Pearson gives a clear indication of why he studied so many diverse subjects (see for example [17] or [26] or

*The New Werther):-*

Despite the feelings he expresses in this quote, Pearson decided to study law so that he might, like his father, be called to the Bar. Again quoting Pearson's own account [3]:-I rush from science to philosophy, and from philosophy to our old friends the poets; and then, over-wearied by too much idealism, I fancy I become practical in returning to science. Have you ever attempted to conceive all there is in the world worth knowing - that not one subject in the universe is unworthy of study? The giants of literature, the mysteries of many-dimensional space, the attempts of Boltzmann and Crookes to penetrate Nature's very laboratory, the Kantian theory of the universe, and the latest discoveries in embryology, with their wonderful tales of the development of life - what an immensity beyond our grasp! ... Mankind seems on the verge of a new and glorious discovery. What Newton did to simplify the planetary motions must now be done to unite in one whole the various isolated theories of mathematical physics.

Despite being called to the Bar in 1882, Pearson never practised law. During 1882-84 he lectured around London on a wide variety of topics such as German social life, the influence of Martin Luther, and historical topics. He also wrote essays, articles and reviews as well as substituting for professors of mathematics at King's College and University College London.Coming to London, I read in chambers in Lincoln's Inn, drew up bills of sale, and was called to the Bar, but varied legal studies by lecturing on heat at Barnes, on Martin Luther at Hampstead, and on Lasalle and Marx on Sundays at revolutionary clubs around Soho.

He spent most of his career at University College, London, after he was appointed to the Chair of Applied Mathematics in 1885 as Goldsmid Professor. One of his former pupils writes in [3]:-

From 1884 to 1890 Pearson was highly productive. As well as giving lectures on statics, dynamics and mechanics, he completed the unfinished first volume of Clifford'sHe was no "textbook" teacher, and could instil an understanding of the fundamentals of a subject with greater ease and in a shorter time than any mathematical lecturer I have since known. His personal appearance was arresting: the typical Greek athlete, with finely cut features and a magnificent physique. ... He was a pertinacious controversialist, but in any personal discussion his humorous twinkle was disarming.

*The Common Sense of the Exact Sciences*(published in 1885), completed and edited the half written first volume of Todhunter's

*History of the Theory of Elasticity*, began working on the second volume which had hardly been started by Todhunter, and published many papers on applied mathematics. He also lectured on

*The Ethic of Free Thought*, and undertook research on a number of historical topics such as the evolution of Western Christianity. In 1885 he was a founder member of the Men and Women Club dedicated to discussion of the role of men and women in society, and at meetings of the club he met Maria Sharpe. Their marriage in 1890 produced three children; Egon Pearson (born 1895) who followed his father's profession, and two daughters Sigrid Loetitia who was three years older than Egon and Helga Sharpe who was three years younger.

It is worth pausing to realise that Pearson is known as one of the founders of statistics, yet we have reached 1890 and the 33 year old professor of applied mathematics, although having a high reputation in a wide variety of areas, had still not begun to work on statistical problems. As Aldrich writes in [6]:-

Two events changed the course of his career. The first was the publication by Galton of his book... his contribution to statistical methodology overshadowed his contribution to any substantive field. His statistical contributions can be divided into ways of arranging numerical facts - univariate and multivariate - estimation and testing.

*Natural Inheritance*in 1889. The second was the appointment of Weldon as Professor of Zoology at University College London in 1890. Walker writes in [26]:-

Through Weldon and Galton's book, Pearson became interested in developing mathematical methods for studying the processes of heredity and evolution. From 1893 to 1912 he wrote 18 papers entitledThe importance for science of the intense personal friendship which soon sprang up between Pearson and Weldon, then both in their early thirties, can scarcely be exaggerated. Weldon asked the questions that drove Pearson to some of his most significant contributions.

*Mathematical Contributions to the Theory of Evolution*which contain his most valuable work. These papers contain contributions to regression analysis, the correlation coefficient and includes the chi-square test of statistical significance (1900). His chi-square test was produced in an attempt to remove the normal distribution from its central position.

His book

*The Grammar of Science*(1892) was remarkable in that it anticipated some of the ideas of relativity theory. It was wide ranging and attempted to extend the influence of science into all aspects. Pearson coined the term 'standard deviation' in 1893. His work was influenced by the work of Edgeworth while he in turn influenced the work of Yule.

Pearson was a co-founder, with Weldon and Galton, of the statistical journal

*Biometrika*. This came about because he had presented a paper to the Royal Society, of which he had been elected a Fellow in 1896 and received its Darwin Medal in 1898, in 1900. The paper looked at heredity and argued using a mathematical analysis of large amounts of collected data. Biologists in the Royal Society were not, however, prepared to accept biological conclusions based on mathematical analysis. Weldon, in a letter to Pearson on 16 November 1900, suggested solving the problem of getting such papers published by setting up their own journal. Pearson was enthusiastic and suggested they name the journal

*Biometrika*. The first volume appear in October 1901 with Pearson as its editor, a role he continued to hold until his death 35 years later.

From around 1906 Pearson put a large effort into setting up a postgraduate centre. He did this (see [17]):-

He was the first Galton Professor of Eugenics, holding the chair from 1911 to 1933. Galton had set up the Eugenics Record Office in 1904 and in 1906 he put Pearson in charge. Pearson already ran the Biometric Laboratory and in 1911 the two laboratories were combined into the Department of Applied Statistics in University College. Galton had expressed the wish that Pearson should be offered the chair, so becoming head of the new Department. In so doing Pearson gave up his Goldsmid chair.... to make statistics a branch of applied mathematics with a technique and nomenclature of its own, to train statisticians as men of science ... and in general to convert statistics in this country from being the playing field of dilettanti and controversialists into a serious branch of science, which no man could attempt to use effectively without adequate training, and more than he could attempt to use the differential calculus, being ignorant of mathematics.

Pearson had a long, bitter, and very public dispute with Fisher. At first they exchanged friendly letters after Pearson received a manuscript from Fisher in September 1914 of a paper he was submitting for publication. Pearson's initial response was to say (see [18]):-

Again a week later [18]:-I congratulate you very heartily on getting out the actual distribution form ... if the analysis is correct which seems highly probable, I should be delighted to publish the paper in Biometrika.

Pearson then offered to have his staff at the Galton Laboratories work on a tabulation of values for the frequency curves arising in Fisher's paper to test the exact distribution produced by Fisher against previously known approximations. By May 1916 they were still corresponding in a friendly manner. However Pearson misunderstood the assumptions of Fisher's maximum likelihood method, and criticised it unfairly in the May 1917I have now read your paper fully and think it marks a distinct advance.

*Cooperative Study*paper which he co-authored with his staff concerning tabulating the frequency curves. Fisher, believing that Pearson's criticism was unwarranted, responded with a paper which criticised examples in the

*Cooperative Study*to the extent of ridiculing them. Fisher had looked again at his earlier correspondence with Pearson, noticed that many of his papers had been rejected, and concluded that Pearson had been responsible.

Although both were strong advocates of statistical methods their approach was rather different. Pearson used large samples which he measured and the tried to deduce correlations in the data. Fisher, on the other hand, followed Gosset in trying to use small samples and, rather than deduce correlations, to find causes. The dispute became bad enough to have Fisher turn down the post of Chief Statistician at the Galton Laboratory in 1919 since it would have meant working under Pearson. The dispute continued to grow in intensity with each taking every opportunity to attack the other's views.

Maria, Pearson's wife, died in 1928 and he remarried Margaret Victoria Child, a co-worker in his department, in the following year. Pearson resigned from the Galton Chair in the summer of 1933 and University College decided to split his Department into two. His son Egon Pearson became head of the Department of Statistics, while Fisher was appointed to the Galton Chair to succeed Pearson as head of the Department of Eugenics.

Greenwood writes of Pearson's character in [9]:-

Walker sums up Pearson's importance in [26] as follows:-Pearson was among the most influential university teachers of his time; he took great pains to be intelligible and could hold a large audience either of students or merely casual hearers who were without special interest in his topics. In the smaller circle of his research pupils he inspired enthusiastic personal affection; no head of a department repaid loyal service more generously. ... He had some of the defects of his qualities; he was dominating, ... he had an intense and genuine belief in freedom of thought but was apt to attribute intellectual differences of opinion to stupidity or even moral obliquity. Personal relations between him and his pupils were sometimes painfully interrupted for years; but it is pleasant to record that eventually most of these broken friendships were happily resumed. Only intellectual differences disturbed harmony; in the ordinary social relations of life he was a charming host, guest, or travelling companion. Pearson's influence upon those who only knew him through his writings was also great. He was admired and feared, rather than loved, by many; in some he aroused bitter hostility.

We have mentioned above some of the honours which Pearson received. Let us also note that he received an honorary degree from the University of St Andrews and from the University of London. He was also elected a fellow of the Royal Society of Edinburgh.Although Pearson made contributions to statistical technique that now appear to be of enduring importance, these techniques are of less importance than what he did in arousing the scientific world from a state of sheer interest in statistical studies to one of eager effort by a large number of well-trained persons, who developed new theory, gathered and analysed statistical data from every field, computed new tables, and re-examined the foundations of statistical philosophy. This is an achievement of fantastic proportions. His laboratory was a world centre in which men from all countries studied. Few men in all the history of science have stimulated as many other people to cultivate and to enlarge the fields they themselves had planted. he provided scientists with the concept of a general methodology underlying all science, one of the great contributions to modern thought.

**Article by:** *J J O'Connor* and *E F Robertson*

**Click on this link to see a list of the Glossary entries for this page**

**List of References** (28 books/articles)
**Some Quotations** (4)

**A Poster of Karl Pearson**
**Mathematicians born in the same country**

**Additional Material in MacTutor**

- Karl Pearson's Introduction to William Clifford's
*Common Sense* - Obituary: RSE
- Obituary: The Times
- Multiple entries in
*The Mathematical Gazetteer of the British Isles*

**Honours awarded to Karl Pearson**

(Click the link below for those honoured in this way)

1. | Fellow of the Royal Society | 1896 | |

2. | Fellow of the Royal Society of Edinburgh | 1934 | |

3. | Popular biographies list | Number 166 |

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