Karl Pearson FRS (27 March 1857 – 27 April 1936) was an influential English mathematician who has been credited for establishing the discipline of mathematical statistics.

In 1911 he founded the world's first university statistics department at University College London. He was a proponent of eugenics, and a protégé and biographer of Sir Francis Galton.

A sesquicentenary conference was held in London on 23 March 2007, to celebrate the 150th anniversary of his birth.

Carl Pearson, later known as Karl Pearson (1857 – 1936), was born to William Pearson and Fanny Smith, who had three children, Aurthur, Carl (Karl) and Amy. William Pearson also sired an illegitimate son, Frederick Mockett.

Pearson's mother, Fanny Pearson née Smith, came from a family of master mariners who sailed their own ships from Hull; his father read law at Edinburgh and was a successful barrister and Queen's Counsel (QC). William Pearson's father's family came from the North Riding of Yorkshire.

"Carl Pearson" inadvertently became "Karl Pearson" when he enrolled at the University of Heidelberg in 1879, which changed the spelling. He used both variants of his name until 1884 when he finally adopted Karl — supposedly also after Karl Marx, though some argue otherwise. Eventually he became universally known as "KP".

He was also an accomplished historian and Germanist. He spent much of the 1880s in Berlin, Heidelberg, Vienna Saig bei Lenzkirch and Brixlegg. He wrote on Passion plays, religion, Goethe, Werther, as well as sex related themes, and was a founder of the Men and Women's Club.

In 1890 he married Maria Sharpe, who was related to the Kenrick, Reid, Rogers and Sharpe families, late 18th century and 19th century non - conformists largely associated with north London; they included:

• Samuel Rogers, poet (1763 – 1855)
• Sutton Sharpe (1797 – 1843), barrister
• Samuel Sharpe, Egyptologist and philanthropist (1799 – 1881)
• John Kenrick, a non - Conformist minister (1788 – 1877)

Karl and Maria Pearson had two daughters, Sigrid Loetitia Pearson and Helga Sharpe Pearson, and one son, Egon Sharpe Pearson. Egon Pearson became an eminent statistician himself, establishing the Neyman - Pearson lemma. He succeeded his father as head of the Applied Statistics Department at University College.

Karl Pearson was educated privately at University College School, after which he went to King's College, Cambridge, in 1876 to study mathematics, graduating in 1879 as Third Wrangler in the Mathematical Tripos. He then traveled to Germany to study physics at the University of Heidelberg 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 Emil du Bois - Reymond on Darwinism (Emil 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 16th 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 Germanics post at Kings College, Cambridge.

On returning to England in 1880, Pearson first went to Cambridge:

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

In his first book, The New Werther, Pearson gives a clear indication of why he studied so many diverse subjects:

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.

Pearson then returned to London to study law so that he might, like his father, be called to the Bar. Quoting Pearson's own account:

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.

His next career move was to Inner Temple, where he read law until 1881 (although he never practiced). After this, he returned to mathematics, deputizing for the mathematics professor at King's College London in 1881 and for the professor at University College London in 1883. In 1884, he was appointed to the Goldsmid Chair of Applied Mathematics and Mechanics at University College London. Pearson became the editor of Common Sense and the Exact Sciences (1885) when William Kingdon Clifford passed on. 1891 saw him also appointed to the professorship of Geometry at Gresham College; here he met Walter Frank Raphael Weldon, a zoologist who had some interesting problems requiring quantitative solutions. The collaboration, in biometry and evolutionary theory, was a fruitful one and lasted until Weldon died in 1906. Weldon introduced Pearson to Charles Darwin's cousin Francis Galton, who was interested in aspects of evolution such as heredity and eugenics. Pearson became Galton's protégé — his "statistical heir" as some have put it — at times to the verge of hero worship.

After Galton's death in 1911, Pearson embarked on producing his definitive biography — a three volume tome of narrative, letters, genealogies, commentaries, and photographs — published in 1914, 1924 and 1930, with much of Pearson's own financing paying for their print runs. The biography, done "to satisfy myself and without regard to traditional standards, to the needs of publishers or to the tastes of the reading public", triumphed Galton's life, work and personal heredity. He predicted that Galton, rather than Charles Darwin, would be remembered as the most prodigious grandson of Erasmus Darwin.

When Galton died, he left the residue of his estate to the University of London for a Chair in Eugenics. Pearson was the first holder of this chair — the Galton Chair of Eugenics, later the Galton Chair of Genetics — in accordance with Galton's wishes. He formed the Department of Applied Statistics (with financial support from the Drapers' Company), into which he incorporated the Biometric and Galton laboratories. He remained with the department until his retirement in 1933, and continued to work until his death in 1936.

When the 23 year old Albert Einstein started a study group, the Olympia Academy, with his two younger friends, Maurice Solovine and Conrad Habicht, he suggested that the first book to be read was Pearson's The Grammar of Science. This book covered several themes that were later to become part of the theories of Einstein and other scientists. Pearson asserted that the laws of nature are relative to the perceptive ability of the observer. Irreversibility of natural processes, he claimed, is a purely relative conception. An observer who travels at the exact velocity of light would see an eternal now, or an absence of motion. He speculated that an observer who traveled faster than light would see time reversal, similar to a cinema film being run backwards. Pearson also discussed antimatter, the fourth dimension, and wrinkles in time.

Pearson's relativity was based on idealism, in the sense of ideas or pictures in a mind. "There are many signs," he wrote, "that a sound idealism is surely replacing, as a basis for natural philosophy, the crude materialism of the older physicists." (Preface to 2nd Ed., The Grammar of Science) Further, he stated, "... science is in reality a classification and analysis of the contents of the mind...." "In truth, the field of science is much more consciousness than an external world." (Ibid., Ch. II, § 6) "Law in the scientific sense is thus essentially a product of the human mind and has no meaning apart from man." (Ibid., Ch. III, § 4)

A eugenicist who applied his social Darwinism to entire nations, Pearson saw "war" against "inferior races" as a logical implication of his scientific work on human measurement: "My view – and I think it may be called the scientific view of a nation," he wrote, "is that of an organized whole, kept up to a high pitch of internal efficiency by insuring that its numbers are substantially recruited from the better stocks, and kept up to a high pitch of external efficiency by contest, chiefly by way of war with inferior races." He reasoned that, if August Weismann's theory of germ plasm is correct, the nation is wasting money when it tries to improve people who come from poor stock.

Weismann claimed that acquired characteristics could not be inherited. Therefore, training benefits only the trained generation. Their children will not exhibit the learned improvements and, in turn, will need to be improved. "No degenerate and feeble stock will ever be converted into healthy and sound stock by the accumulated effects of education, good laws and sanitary surroundings. Such means may render the individual members of a stock passable if not strong members of society, but the same process will have to be gone through again and again with their offspring, and this in ever - widening circles, if the stock, owing to the conditions in which society has placed it, is able to increase its numbers." (Introduction, The Grammar of Science).

"History shows me one way, and one way only, in which a high state of civilization has been produced, namely, the struggle of race with race, and the survival of the physically and mentally fitter race. If you want to know whether the lower races of man can evolve a higher type, I fear the only course is to leave them to fight it out among themselves, and even then the struggle for existence between individual and individual, between tribe and tribe, may not be supported by that physical selection due to a particular climate on which probably so much of the Aryan's success depended . . ." (Karl Pearson, National Life from the Standpoint of Science [London, 1905])

Pearson was known in his lifetime as a prominent "freethinker" and socialist. He gave lectures on such issues as "the woman's question" (this was the era of the suffragist movement in the UK) and upon Karl Marx. His commitment to socialism and its ideals led him to refuse the offer of being created an OBE (Officer of the Order of the British Empire) in 1920 and also to refuse a knighthood in 1935.

Pearson achieved widespread recognition across a range of disciplines and his membership of, and awards from, various professional bodies reflects this:

• 1896: elected FRS: Fellow of the Royal Society
• 1898: awarded the Darwin Medal
• 1911: awarded the honorary degree of LLD from the University of St Andrews
• 1911: awarded a DSc from University of London
• 1920: offered (and refused) the OBE
• 1932: awarded the Rudolf Virchow medal by the Berliner Anthropologische Gesellschaft
• 1935: offered (and refused) a knighthood

He was also elected an Honorary Fellow of King's College Cambridge, the Royal Society of Edinburgh, University College London and the Royal Society of Medicine, and a Member of the Actuaries' Club.

Pearson's work was all-embracing in the wide application and development of mathematical statistics, and encompassed the fields of biology, epidemiology, anthropometry, medicine and social history. In 1901, with Weldon and Galton, he founded the journal Biometrika whose object was the development of statistical theory. He edited this journal until his death. Among those who assisted Pearson in his research were a number of female mathematicians who included Beatrice Mabel Cave - Browne - Cave and Frances Cave - Browne - Cave. He also founded the journal Annals of Eugenics (now Annals of Human Genetics) in 1925. He published the Drapers' Company Research Memoirs largely to provide a record of the output of the Department of Applied Statistics not published elsewhere.

Pearson's thinking underpins many of the 'classical' statistical methods which are in common use today. Examples of his contributions are:

• Correlation coefficient. The correlation coefficient (first conceived by Francis Galton) was defined as a product - moment, and its relationship with linear regression was studied.
• Method of moments. Pearson introduced moments, a concept borrowed from physics, as descriptive statistics and for the fitting of distributions to samples.
• Pearson's system of continuous curves. A system of continuous univariate probability distributions that came to form the basis of the now conventional continuous probability distributions. Since the system is complete up to the fourth moment, it is a powerful complement to the Pearsonian method of moments.
• Chi distance. A precursor and special case of the Mahalanobis distance.
• P-value. Defined as the probability measure of the complement of the ball with the hypothesized value as center point and chi distance as radius.
• Foundations of the statistical hypothesis testing theory and the statistical decision theory. In the seminal "On the criterion..." paper, Pearson proposed testing the validity of hypothesized values by evaluating the chi distance between the hypothesized and the empirically observed values via the p-value, which was proposed in the same paper. The use of preset evidence criteria, so called alpha type-I error probabilities, was later proposed by Jerzy Neyman and Egon Pearson.
• Pearson's chi - squared test. A hypothesis test using normal approximation for discrete data.
• Principal component analysis. The method of fitting a linear subspace to multivariate data by minimizing the chi distances.