A Brief History of the UCL Department of Mathematics
Since its founding in the early nineteenth century, the Department of Mathematics at UCL has been home to pioneering teachers, world-leading researchers, and students who have gone on to shape science, society, and industry. Marking the bicentennial of UCL’s founding, we trace the Department’s history from the University’s radical beginnings as a secular institution, through the development of pure and applied mathematics, to the vibrant, international department it is today.
Founding the University and the Chair of Mathematics (1826–1828)
University of London—eventually University College London (UCL)—was founded on 11 February 1826. UCL was founded as the first secular university in England, providing access to higher learning irrespective of religious denomination. This stood in contrast to the universities in Oxford and Cambridge, where membership of the Church of England remained a requirement for full participation well into the nineteenth century.[i] From its beginning, mathematics was considered central to the curriculum at UCL, and the history of the department reflects both the growth of the discipline in Britain and the shifting ideals of modern universities.
When the College Council first began appointing professors in 1826, mathematics was given a particular emphasis as it offered an opportunity to confer prestige on the new University. The Council initially advertised two chairs in mathematics: Elementary Mathematics and Higher Mathematics. More than thirty applications were received.[ii] They included Henry Moseley, later the first Professor of Natural and Experimental Philosophy at King’s College London, who was shortlisted but missed his interview when the invitation arrived too late; Thomas Grainger Hall, later appointed as the first Professor of Mathematics also at King’s, who withdrew when he learned that accepting the chair would forfeit his Cambridge fellowship; John Radford Young, who went on to a distinguished career as a mathematics professor at Belfast College; as well as two individuals who were offered other professorships at UCL: Dionysius Lardner as Chair of Natural Philosophy and Astronomy, and Thomas Hewitt Key as Chair of Latin.
At the same time, the Council directly approached two prominent scientific figures of the time hoping to entice them into the Mathematics Chair, a perhaps ambitious step for a newly formed and yet untested institution. In 1827, Charles Babbage, already famous for his Difference Engine, a mechanical calculator, was invited to become Professor of Higher Mathematics and Mathematical Physics.[iii] Babbage appears to have rejected the offer and was shortly after appointed Lucasian Professor of Mathematics at Cambridge. The Council then approached John Herschel, another well-known natural philosopher and astronomer, with an offer to become Professor of Higher Mathematics. Herschel declined, but the Council persisted, suggesting that no teaching would be required for the first two or three years.[iv] However, Herschel, whose work at the time was leaning more towards astronomy, declined again, stating that he had no interest in even a temporary position that would require him to “resign as soon as its duties become (I will not say bothersome, but) real”, adding “To teaching I have a positive dislike, and would certainly engage in no office in which it formed any part of the duties expected of me.”[v]
With Babbage and Herschel out of reach, the Council ultimately abandoned the idea of two separate chairs for Mathematics. Instead, they focused on fielding the applicants who had indicated a preference for the Higher or either Chair, likely as their skills would be more suitable for all levels of mathematics, eliminating all those who applied only for the Elementary professorship.[vi]
On 23 February 1828, the Council appointed Augustus De Morgan (1806–1871), a young Cambridge graduate, as Chair of Mathematics. At just twenty-one, he was the youngest of UCL’s founding professors and quickly set the tone for mathematical education in the new university. Although young, De Morgan had already distinguished himself at Cambridge, graduating as Fourth Wrangler in the Mathematical Tripos of 1827.[vii] The testimonials submitted on his behalf praised both his depth of knowledge and his unusual aptitude for teaching, qualities that convinced the Council to entrust him with the responsibility of shaping mathematics at the new institution.[viii]
De Morgan’s First Tenure (1828-1831)
Originally urged by his mother to study law after Cambridge, De Morgan had instead seized on the opportunity to pursue his passion for mathematics. According to his wife, Sophia: “Mr. De Morgan welcomed the opening of the College, as not only meeting a great want of the time, but as offering to himself a prospect of leaving the study of Law, which he did not like, for the teaching and pursuit of Science.”[ix] At the same time, De Morgan embodied the cause of the new secular institution. Though Anglican, he had refused to subscribe to the Thirty-Nine Articles of the Church of England on principle, thereby forfeiting the chance of a Cambridge fellowship.[x] His appointment at UCL was, therefore, both an academic opportunity and a vindication of the new college’s secular ideals.
De Morgan’s inaugural lecture, delivered on 5 November 1828, titled On the Study of Mathematics, argued that mathematical reasoning was fundamental to intellectual development and social progress. He declared that “the success of every individual in the world must depend on his power of reasoning”.[xi] Sophia later described this lecture as “an essay upon the progress of knowledge, the need of knowledge, the right of everyone to as much knowledge as can be given to him, and the place in mental development which the culture of reasoning power ought to hold.”[xii]
De Morgan’s courses were immediately popular. Ninety-one students enrolled in his first year, and ninety-four in his second.[xiii] The programme’s entry requirement was only a basic knowledge of arithmetic, but the curriculum was ambitious. First-year students studied plane and solid geometry, descriptive geometry, algebra, and plane and spherical trigonometry. Second-year courses introduced conic sections, transcendental algebra, theory of projections, algebraic geometry, differential and integral calculus, and probability theory.[xiv]
During this time, De Morgan also pursued his own original research, producing influential works across several mathematical fields such as The Elements of Algebra (1828), Elements of Arithmetic (1830), and The Study and Difficulty of Mathematics (1831).
However, after only three years in the role, De Morgan abruptly resigned his chair in protest after the College Council dismissed the anatomist Granville Sharp Pattison. Pattison’s lectures had collapsed amid protests, with students citing “unusual ignorance of old notions, and total ignorance of and disgusting indifference to new anatomical views and researches … he is ignorant, or, if not ignorant, indolent, careless, and slovenly, and, above all, indifferent to the interests of the science.”[xv] Even so, De Morgan believed that dismissing a professor without proven misconduct threatened the integrity of the institution. In his resignation letter, he made it clear that the precedent was unacceptable, writing “Here is distinctly laid down the principle that a Professor may be removed, and, as far as you can do it, disgraced, without any fault of his own. This being understood, I should think it discreditable to hold a Professorship under you one moment longer. I have, therefore, the honour to resign my Professorship.”[xvi]
This opinion was not unexpected; De Morgan had previously warned that precarious tenure would undermine both teaching and the institution itself. “If a Professor is easily removable,” he cautioned, “he will endeavour to secure something else of a more certain tenure … to the manifest detriment of his class”. Without this security, he added, “the University will become a nursery of Professors for better conducted institutions … [and risk] the eventual loss of its reputation as a place of education.”[xvii] Essentially, he was suggesting that this would result in a continuously revolving faculty that would compromise both educational quality and institutional prestige.
The Tenure of George James Pelly White (1831-1836)
After De Morgan’s sudden resignation, the Council sought stability for the mathematics programme and once again publicised the role. This time, only twelve applications were received. The Council quickly settled on George James Pelly White (c.1806-1836), a near contemporary of De Morgan at Trinity College, Cambridge. White had studied under the prominent scholar William Whewell and graduated as Sixth Wrangler in 1829. Although he had no publications to his name, White came with strong testimonials from several leading figures including Whewell, mathematician George Peacock, and astronomer George Biddell Airy, and the Council regarded him as the closest substitute for De Morgan they could secure on such short notice.[xviii]
With only a fortnight before the start of term, White produced a carefully considered syllabus which significantly reorganised the course structure. Rather than allowing students to join at any level (subject to adequate preparation) as De Morgan had, White divided students into separate “divisions”, one more elementary and the other more technical. Students in the first division would “find themselves capable of understanding the principles of Mechanics, Optics, Hydrostatics &c […] in fact sufficient for most of the purposes of a practical life.” Those in the second division would find “the methods recommended will be more analytical & scientific” with the highest classes able “to extend the Student’s views of the principles of Mathematics & to lead him to the very summits where he can command the sublimest discoveries of Physical Astronomy.”[xix]
Tragically White’s promising career ended suddenly in 1836, when he drowned in a boating accident returning from Guernsey.[xx] Although his tenure was brief, he provided much needed stability and continuity at a critical moment in the department’s early history.
De Morgan’s Return and Second Tenure (1836-1866)
Upon White’s death, De Morgan initially offered to cover the mathematics courses on a temporary basis until a replacement could be found. However, he soon began to consider a more permanent return, although not without reassurances that recent administrative changes had done enough to address his previous concerns. Shortly after his resignation, the creation of a professorial Senate in 1832 had reformed UCL’s governance, giving professors a stronger voice. De Morgan sought advice from his friend and lawyer Sir Harris Nicolas on whether new regulations had given more security to the position. De Morgan also confessed that financially he would “lose rather than gain for a time” from the position but admitted the prospect of resuming teaching was “in itself pleasant to me, and which has some few pleasing associations.”[xxi]
Encouraged by his former colleagues, and reassured that these reforms brought security to the role, De Morgan agreed to return to the Chair. On 17 October 1836, the Council unanimously resolved that he should be reappointed,[xxii] beginning a thirty-year second tenure during which he firmly established mathematics at UCL.
During his second tenure as Chair of Mathematics, De Morgan’s reputation grew rapidly. He was admired as a lecturer of wit and clarity, whose lessons in algebra and logic fascinated his students. Among these were William Stanley Jevons, later a founder of modern economics, and Walter Bagehot, journalist and political thinker.[xxiii]
Alongside his teaching, De Morgan had a prolific output of research and writing that helped to define nineteenth-century British mathematics. Through his work on symbolic logic, he formulated the mathematical rules that would be called “De Morgan’s Laws”, which showed how “and” and “or” reversed under negation. He also helped to shape modern algebra by introducing new terminology and exploring the relationships between real and complex numbers.[xxiv] Beyond his mathematical contributions, De Morgan wrote extensively on the history of science, producing essays on Isaac Newton, Edmond Halley, and the origins of algebra, as well as compiling bibliographies that laid the foundations for modern mathematical historiography.[xxv]
In 1865, De Morgan played a central role in the founding of the London Mathematical Society (LMS). LMS, inspired by specialist organisations such as the Royal Astronomical Society, Chemical Society, and Geological Society, was established at UCL by a group of his former students, including his son George De Morgan. George asked his father to take up the leadership of the new society and De Morgan was appointed as the first President. For the first time, mathematicians in Britain had a dedicated forum for publishing research, exchanging ideas, and fostering professional identity.[xxvi] LMS’s Proceedings, launched soon after, became the leading publication for mathematical research in the UK.
In 1866, De Morgan suddenly resigned again, this time also in protest. De Morgan felt that the Council’s refusal to appoint a candidate, James Martineau, whom the Senate had recommended, had been based on religious prejudice. As such, De Morgan considered the decision a betrayal of UCL’s founding secular principles.[xxvii] His departure marked the end of an era, closing a formative period for the Department shaped by De Morgan’s influence.
Reorganisation of the Department and Growth (1867-1902)
In 1867, De Morgan was succeeded by Thomas Archer Hirst (1830-1892), a respected geometer who was already a professor of mathematical physics at UCL.[xxviii] At first Hirst held the title of Professor of Pure and Applied Mathematics and was expected to cover the higher branches of mathematical physics in addition to pure mathematics. However, the load quickly proved overwhelming, and in 1868 the department was reorganised into two separate chairs: Pure Mathematics (retained by Hirst) and Applied Mathematics and Mechanics, taken up by Benjamin Theophilus Moore (1830-1899). Moore’s remit included Mechanics, Hydrostatics, and Astronomy for candidates preparing for London BSc and BA degrees, as well as Applied Mechanics for engineering students.[xxix]
Even this lighter division of work left Hirst overstretched. He complained that his professorial duties left him with no time for research and was taxing his physical strength.[xxx] After only three years in the post, he resigned his chair in 1870 to take up an administrative position as Assistant Registrar of the University of London. Later, from 1873 to 1883, he served as Director of Naval Studies at the Royal Naval College, Greenwich.[xxxi] The division between pure and applied mathematics at UCL, however, remained in place well into the twentieth century.
Following this reorganisation into Pure and Applied mathematics, the department was led by a series of notable figures who gave it stability and growing prestige. In 1870 Hirst was succeeded in Pure Mathematics by Olaus Henrici (1840-1918), a German-trained mathematician whose ingenious mechanical models brought complex curves and surfaces to life for students,[xxxii] for example, by using physical linkages and moving apparatus to make abstract geometrical relationships more tangible.
On the Applied side, Moore’s tenure was also short. Dissatisfied with the low attendance to his classes, and struggling with the low income, at the time still tied to student fees, he also resigned in 1870. The College Council considered abolishing the Applied Mathematics chair altogether due to a lack of funds.[xxxiii] However, its future was secured in 1871 when lawyer, politician, and philanthropist, Sir Francis Goldsmid offered to endow the Chair of Applied Mathematics with £200 per annum, specifically to bring William Kingdon Clifford (1845-1879) to UCL. It was subsequently renamed the Goldsmid Chair, a designation that continues today.
Clifford was already a notable figure, and his appointment gave prestige to the new Goldsmid Chair and to mathematics at UCL. Clifford’s work on geometry was a significant precursor to Einstein’s general relativity—as early as 1870 he proposed that matter and energy might be understood as the curvature of space.[xxxiv] He also developed what are now called “Clifford algebras,” concepts that would later become central to modern physics. He wrote widely for general audiences, linking UCL mathematics to the wider intellectual culture of nineteenth century Britain.[xxxv] Although Goldsmid initially only offered five years of funding, he renewed the arrangement in 1876, then, upon his death, secured the position with a significant endowment to the University.[xxxvi] This benefaction guaranteed applied mathematics a permanent place at UCL.
Following Clifford’s early death in 1879, Henrici briefly moved across to the Goldsmid Chair before it passed in 1884 to Karl Pearson (1857-1936), one of the founders of biometry and modern statistics. Pearson established the Biometric Laboratory, applying mathematics to biology and medicine, and is remembered for methods such as the Pearson Significance Test,[xxxvii] used to determine whether the relationship between two variables is statistically meaningful. Yet his work was also deeply connected to eugenics, and in 2021 UCL issued a formal apology for its historical role in “the development, propagation and legitimisation of eugenics.”[xxxviii]
Meanwhile, in Pure Mathematics, Micaiah John Muller Hill (1856-1929) was appointed to the Chair in 1884 and went on to serve for nearly forty years. Hill’s research ranged across hydrodynamics, differential equations, and theory of proportion, and he is best remembered for discovering Hill’s vortex and for his influential reformulation of Euclid’s theory of proportion.[xxxix] In 1902, famous New York immigrant William Waldorf Astor endowed two Chairs at UCL: History and Pure Mathematics, to be renamed the “Astor Chairs”.[xl] Accordingly, the existing Pure Mathematics chair was formally renamed the Astor Chair of Pure Mathematics shortly after with Hill continuing in the position. The endowment of both chairs now ensured that mathematics at UCL entered the twentieth century on a stable footing.
Early Twentieth-Century (1902-1950s)
The early twentieth century was both a time of continuity and change. In Pure Mathematics, Hill’s long tenure was followed in 1924 by George Barker Jeffery (1891-1957) who made contributions to general relativity and to the mathematics of elasticity.[xli] His name endures in the “Jeffery equations”, or “Jeffery–Hamel flow”, of fluid dynamics, which describe how a fluid moves through a narrowing or widening space between two flat surfaces.
In Applied Mathematics, Pearson, who went on to the new Department of Applied Statistics, was succeeded by Louis Napoleon George Filon (1875-1937) in 1912, who built an international reputation in classical mechanics and strength of materials. Filon also served as Vice-Provost of UCL, helping steer the college through the difficult interwar years.[xlii]
The two World Wars caused significant disruption to the University. During the First World War, many students and staff joined the armed forces, while others contributed to the war effort through research in mechanics and ballistics. Teaching continued, but often under strained conditions.[xliii] The impact of the Second World War was even greater. In 1939, UCL’s campus had to be evacuated as central London became unsafe under threat of bombing, with the mathematics department going to Bangor, in north Wales. Classes continued and were held in makeshift rooms with staff living in temporary accommodation. Despite these difficulties, the department maintained a strong programme of teaching and mathematical research.[xliv]
Another distinguished figure of this era was Sir Harrie Massey (1908-1983), who held the Goldsmid Chair of Applied Mathematics from 1938 to 1950 before moving to Physics. Massey was already a leading authority on atomic collisions and went on to play a central role in Britain’s space research programme, including early satellite projects.[xlv] His career illustrates both the strength of UCL Mathematics in the interwar and postwar years and its close ties to neighbouring sciences.
A Unified Department of Mathematics and International Recognition (1950s-2000)
The postwar years consolidated UCL’s place at the forefront of international mathematics. In Pure Mathematics, Harold Davenport (1907-1969) became the Astor Professor in 1945. A leading figure on analytic number theory, Davenport helped to establish London as a global centre for research in the field.[xlvi] Davenport also founded the journal Mathematika in 1954. At a time when Britain had few specialist journals in pure mathematics, Mathematika quickly gained international recognition, and continues to be published by the Department today. Among his most distinguished students was Klaus Friedrich Roth, a UCL Mathematics PhD (1950) and later professor in the department, who in 1958 was awarded the Fields Medal for his work on Diophantine approximation,[xlvii] the approximation of real numbers by fractions.
Applied Mathematics also flourished in this period, particularly in the field of fluid dynamics. William Reginald Dean (1896-1973), Goldsmid Professor from 1952 to 1964, made fundamental contributions to fluid mechanics, particularly the study of flow in curved channels.[xlviii] In 1964, he was succeeded by Keith Stewartson (1925–1983), described as “one of the most mathematically profound of this century’s great applied mathematicians active in mechanics of fluids”.[xlix]
Through the first half of the century, Pure and Applied Mathematics had remained effectively separate departments. However, by mid-century, the two strands of mathematics at UCL were unified into a single Department of Mathematics, with administrative department heads distinct from the chairs. The first such head was Claude Ambrose Rogers (1920-2005), alumnus of the department and Astor Professor of Pure Mathematics from 1958 to 1986. A world-class analyst in the geometry of numbers and functional analysis,[l] Rogers supervised a generation of students and guided the department for nearly three decades and into the modern era. He was also a central figure in the London Mathematical Society, reflecting UCL’s continuing role in the wider mathematical community.
Women in UCL Mathematics
In 1878, all classes at UCL, except those in the Faculty of Medicine, were opened to women. This change responded to a growing demand that had been developing over several decades. Opportunities for women had been expanding through institutions such as Bedford College—now merged with Royal Holloway—founded in 1849 as the first higher education institution for women in Britain. Bedford College had from its establishment offered mathematical instruction, with De Morgan teaching there in its founding year. From 1868, the London Ladies’ Educational Association had begun organising lectures for women delivered by UCL professors. Initially only offered outside university premises, in 1871 these were brought into UCL itself, although the Association maintained responsibility for the lectures.[li]
Prior to the open admission of women into the University, some departments at UCL, including mathematics, had already started allowing women to be admitted but only by gaining special permission from the College Council.
A pioneering figure in the opening of UCL mathematics classes to women was Ellen Martha Watson (1856–1880). In 1876, she wrote to George Carey Foster, at the time Chair of Physics and also one of the first to lecture for the Ladies’ Educational Association in 1868,[lii] to ask for advice on furthering her studies in physics.[liii] Watson had previously studied at the North London Collegiate School where she lived with the founder and headmistress, Frances Mary Buss. In 1872 she had passed the Cambridge Senior Examination in the First Honours Class and won an Exhibition to Bedford College but declined it to care for her younger siblings. In 1874, she had sat the London University Women’s Examination, placing second among those who passed in the Honours Division and winning a Gilchrist Scholarship to Girton College, which she also declined to remain at home.[liv] Foster was so struck by the intellect displayed in her letters that he offered her a place in the Physical Laboratory at UCL.[lv] Later that year, with the strong support of Foster and William Kingdon Clifford, at the time Chair of Applied Mathematics, Watson received special permission from the College Council to enrol in physics and mathematics classes.[lvi] In October 1876 she became the first woman to officially enrol in mathematics at UCL.[lvii]
Watson was an outstanding student. In 1877, she won both the principal prize in applied mathematics and the Mayer de Rothschild Exhibition, the highest prize in pure mathematics.[lviii] On announcing the awards, Clifford declared: “A few more students like Miss Watson would […] certainly raise University College to a status surpassing that of institutions twenty times as rich, and which had been two hundred years longer in existence.”[lix] In 1879, only a year after the University of London formally allowed women to obtain degrees, Watson sat the First B.Sc. examination, passing in the first division.[lx] She had long suffered from a lung disease, and shortly after, her health began to decline rapidly. On her doctors’ advice she travelled with her brother to Grahamstown in the Eastern Cape, South Africa.[lxi] Her health did not stop her ambition and there she took up a teaching post at the Diocesan School for Girls and organised evening classes for women in botany and arithmetic.[lxii] She died there on 3 December 1880, aged just twenty-four. In her memory, colleagues and admirers established the Ellen Watson Memorial Scholarship, one of the earliest academic prizes founded to honour achievements in mathematics regardless of gender.[lxiii] The scholarship remains active in the UCL Department of Mathematics today, awarded annually to the best final-year student in Applied Mathematics.
Watson’s enrolment opened the door for other women in mathematics at UCL. In 1877-78, she was joined in applied mathematics by several notable women,[lxiv] including Edith Prance, who worked with educational pioneer Frances Mary Buss;[lxv] Mary Everest Boole, a self-taught mathematician and educator married to mathematician George Boole, who later published several books including The Preparation of the Child for Science (1904) and Philosophy and Fun of Algebra (1909);[lxvi] Lucy Everest Boole, daughter of Mary Boole, who would go on to become the first woman to undertake research in pharmaceutical chemistry in Britain and, in 1894, was elected the first female fellow of the Royal Institute of Chemistry;[lxvii] and Thomazine Mary Browne (later Lady Lockyer), who later co-founded College Hall with her sister Annie Leigh Browne to provide accommodation for women studying in London,[lxviii] and was later elected a Fellow of the Royal Astronomical Society in 1923.[lxix]
By 1878–79, the first session in which women could enrol at UCL without special permission, at least twenty-two women were enrolled in mathematics courses.[lxx] Notable figures included “Mrs. H. Fawcett”, possibly Millicent Garrett Fawcett, a leading suffragist and co-founder of Newnham College, Cambridge, who later led the National Union of Women’s Suffrage Societies and played a central role in the campaign for women’s voting rights.[lxxi] And Mary Kilgour, also a suffragist, who was active in the Women’s Local Government Society.[lxxii]
Other early figures in the Department included Millicent Fawcett’s daughter, Philippa Garrett Fawcett (1868-1948), who attended mathematics courses at UCL from 1885-1887 before winning a scholarship to continue her studies at Newnham College, Cambridge. She gained significant recognition in 1890 when she placed “above Senior Wrangler” in the Cambridge Mathematical Tripos, even though Cambridge still refused to grant degrees to women.[lxxiii] And Alice Elizabeth Lee (1858–1939), who studied mathematics at Bedford College before attending Pearson’s statistics classes at UCL. Pearson soon hired her as an assistant in the Biometric Laboratory while she conducted research for her DSc in the 1890s. She later became a lecturer in mathematics and physics at Bedford College.[lxxiv]
Alongside these developments at UCL, women associated with institutions in the wider University of London made significant contributions to mathematics. Charlotte Angas Scott (1858-1931) who would have been eighth wrangler at Cambridge in 1880 had women been allowed to be ranked, received her mathematics degree externally from the University of London in 1885. Eventually she emigrated to the United States, where she became the first head of mathematics at Bryn Mawr College and a pioneer of graduate training for women.[lxxv] Sophie Willock Bryant (1850-1922), educated at Bedford College, earned her BSc in 1881 with first class honours in moral and mental science and second class honours in mathematics. In 1884 she became the first woman in England to be awarded a DSc in moral and mental philosophy,[lxxvi] and that same year she became the first woman to publish an article in the Proceedings of the London Mathematical Society.[lxxvii]
In the twentieth century, Susan Brown (1937–2017), renowned for her outstanding contributions in fluid mechanics, was appointed Professor of Mathematics at UCL in 1986, one of the first women in the UK to hold a mathematics professorship. Brown was respected as both a scholar and a teacher, and she became an inspirational figure for students and colleagues in the department. In 2019, her colleagues remembered her outstanding commitment to teaching and the sense of possibility her example gave to women in mathematics: “I belong here.”[lxxviii]
More recently, Helen Wilson, a specialist in complex fluids, became the first woman to head the UCL Department of Mathematics (2018–2023) and was the first woman to be President of the British Society of Rheology (2015–2017).
The Department Today
Throughout its history, UCL Mathematics has attracted scholars of the highest calibre. Three Fields Medallists have been associated with the department: Klaus Roth (1958) and Alan Baker (1970), both department alumni, and Timothy Gowers (1998), who conducted significant early work at UCL. Among recent members of the department was one of the century’s greatest theorists in fluid mechanics: Sir James Lighthill. Prior to coming to UCL he held the Lucasian chair at Cambridge which was once held by Newton and more recently by Stephen Hawking.
The department today is home to around eighty-four academic staff, including thirty-nine full professors, and a number of honorary staff, supported by a professional services team of twenty-five. Its community also includes around thirty-six Postdoctoral Research Fellows, around ninety PhD students, and fifty-four MSc students. The department also welcomes a regular stream of distinguished visiting academics from home and abroad. The broad range of research interests is reflected in the large choice of courses available in the third and fourth years of the degree programmes, from computational geometry to fluid mechanics and from mathematical ideas in biology to cosmology. The department continues to publish Mathematika, which retains its international reputation as a venue for high-quality research.
The department has been joined by CORU (the Clinical Operational Research Unit) which applies mathematics to a wide range of medically oriented research topics. Additionally, the department participates in CoMPLEX (Centre for the application of Mathematics and Physics in the Life sciences and EXperimental biology).
The department is also involved with the London School of Geometry and Number Theory (LSGNT), which is an EPSRC Centre for Doctoral Training that offers a 4-year PhD programme. This is a joint venture with Imperial College London and King’s College London. The LSGNT is made up of about 40 mathematicians in three London Universities, with interests in different aspects of number theory, geometry and topology, and they admit 14-15 students per year over a 10-year period; the first intake was in September 2014.
Conclusion
As one of the founding departments of UCL, the Department of Mathematics has grown from its early beginnings under De Morgan into a major internationally renowned centre of research and teaching. Its history has been shaped by an unwavering commitment to UCL’s founding principles, as well as through pioneering research and contributions in areas including algebra, geometry, statistics, and fluid dynamics. It has proudly represented UCL’s tradition of inclusivity, with a long record of welcoming women as students, faculty, and leaders. The department has been home to some of the most distinguished mathematicians of their time; two centuries on, its staff and students continue to build on this legacy, maintaining its place at the forefront of international mathematics.
[i] For the history of UCL, see: Negley Harte et al., The World of UCL (UCL Press, 2018).
[ii] Adrian Rice, ‘Augustus De Morgan and the Development of University Mathematics in London in the Nineteenth Century’ (PhD diss., Middlesex University, 1997), 38. Some of the original applications and testimonials are still held in the UCL archives in UCLCA/APPL Box 21 – Maths 1827/28.
[iii] Henry Brougham to Charles Babbage, 20 Feb 1827, British Library Add. MS 37183, f.454.
[iv] Henry Brougham to John Herschel, 30 Jun 1827, Royal Society HS/4/303.
[v] Draft letter from John Herschel to Henry Brougham, Jul 1827, Royal Society HS/4/306, emphasis in original.
[vi] Rice, ‘Augustus De Morgan and the Development of University Mathematics in London in the Nineteenth Century’, 48.
[vii] Rice, ‘Augustus De Morgan and the Development of University Mathematics in London in the Nineteenth Century’, 34.
[viii] Some of the testimonials submitted on De Morgan’s behalf are contained in UCLCA/APPL Box 21 – Maths 1827/28
[ix] Sophia Elizabeth De Morgan, Memoir of Augustus De Morgan (London: Longmans, Green, and Co., 1882), 24.
[x] Rice (1993), p. 121.
[xi] Augustus De Morgan, On the Study of Mathematics, UCL Archives, MS ADD 3, f.8.
[xii] De Morgan, Memoir of Augustus De Morgan, 29.
[xiii] Rice, ‘Augustus De Morgan and the Development of University Mathematics in London in the Nineteenth Century’, 78.
[xiv] Rice, ‘Augustus De Morgan and the Development of University Mathematics in London in the Nineteenth Century’, 74-76.
[xv] Quoted in Hugh Hale Bellot, University College London 1826-1926, (London: University of London Press, 1929), 197-198.
[xvi] Letter from De Morgan to the Council, 24 Jul 1831, reprinted in De Morgan, Memoir of Augustus De Morgan, 39.
[xvii] Letter from De Morgan to the Council, 15 Jul 1831, reprinted in De Morgan, Memoir of Augustus De Morgan, 36.
[xviii] Rice, ‘Augustus De Morgan and the Development of University Mathematics in London in the Nineteenth Century’, 132-133.
[xix] Mathematical course outline by White, 17 Oct. 1831, UCL College Correspondence No. 2255.
[xx] De Morgan, Memoir of Augustus De Morgan, 69.
[xxi] Letter from De Morgan to Sir Harris Nicolas, 10 Oct 1836, reprinted in De Morgan, Memoir of Augustus De Morgan, 70-73.
[xxii] Rice, ‘Augustus De Morgan and the Development of University Mathematics in London in the Nineteenth Century’, 153.
[xxiii] Harte et al., The World of UCL, 39.
[xxiv] Leslie Stephen and I. Grattan-Guinness, ‘Morgan, Augustus De (1806–1871), Mathematician and Historian’, Oxford Dictionary of National Biography, 23 September 2004, http://www.oxforddnb.com/view/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-7470.
[xxv] Adrian Rice, ‘Augustus De Morgan: Historian of Science’, History of Science 34, no. 2 (1996): 201–40, https://doi.org/10.1177/007327539603400203.
[xxvi] Adrian Rice et al., ‘From Student Club to National Society: The Founding of the London Mathematical Society in 1865’, Historia Mathematica 22, no. 4 (1995): 402–21, https://doi.org/10.1006/hmat.1995.1032.
[xxvii] De Morgan, Memoir of Augustus De Morgan, 338-339.
[xxviii] Robin J. Wilson, ‘Hirst, Thomas Archer (1830–1892), Mathematician’, Oxford Dictionary of National Biography, 23 September 2004, http://www.oxforddnb.com/view/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-13364.
[xxix] Rice, ‘Augustus De Morgan and the Development of University Mathematics in London in the Nineteenth Century’, 285-286.
[xxx] Rice, ‘Augustus De Morgan and the Development of University Mathematics in London in the Nineteenth Century’, 288.
[xxxi] Wilson, ‘Hirst, Thomas Archer (1830–1892), Mathematician’.
[xxxii] Adrian Rice, ‘Henrici, Olaus Magnus Friedrich Erdmann (1840–1918), Mathematician’, Oxford Dictionary of National Biography, 23 September 2004, https://www.oxforddnb.com/view/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-39487.
[xxxiii] Rice, ‘Augustus De Morgan and the Development of University Mathematics in London in the Nineteenth Century’, 292-294.
[xxxiv] Clifford first presented this idea at a meeting of the Cambridge Philosophical Society on 21 February 1870; the abstract was later published: W. K. Clifford, ‘On the Space-Theory of Matter’, in Proceedings of the Cambridge Philosophical Society, vol. 2 (Cambridge: Cambridge University Press, 1876).
[xxxv] Albert C. Lewis, ‘Clifford, William Kingdon (1845–1879), Mathematician and Philosopher of Science’, Oxford Dictionary of National Biography, 23 September 2004, https://www.oxforddnb.com/view/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-5667.
[xxxvi]Memoir of Sir Francis Henry Goldsmid, 2nd ed. (London: Kegan Paul, Trench, & Co., 1882), 73-74.
[xxxvii] Joanne Woiak, ‘Pearson, Karl [Formerly Carl] (1857–1936), Statistician and Eugenicist.’, Oxford Dictionary of National Biography, 23 September 2004, https://www.oxforddnb.com/view/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-35442.
[xxxviii] See: ‘UCL Makes Formal Public Apology for Its History and Legacy of Eugenics’, 7 January 2021, https://www.ucl.ac.uk/news/2021/jan/ucl-makes-formal-public-apology-its-history-and-legacy-eugenics.
[xxxix] Adrian Rice, ‘Hill, Micaiah John Muller (1856–1929), Mathematician’, Oxford Dictionary of National Biography, 23 September 2004, http://www.oxforddnb.com/view/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-39485.
[xl] University College, London: Report of the Council, Financial Statements, and Other Documents to Be Presented to the Members of the College at the Annual General Meeting on Wednesday, 25th February, 1903 (London: Taylor and Francis, 1903), 22.
[xli] J. J. O’Connor and E. F. Robertson, ‘George Barker Jeffery’, MacTutor, 2020, https://mathshistory.st-andrews.ac.uk/Biographies/Jeffery/.
[xlii] George Barker Jeffery, ‘Louis Napoleon George Filon, 1875-1937’, Obituary Notices of Fellows of the Royal Society 2, no. 7 (1939): 501–9, https://doi.org/10.1098/rsbm.1939.0010.
[xliii] Harte et al., The World of UCL, 153-157.
[xliv] Harte et al., The World of UCL, 201-210; and O’Connor and Robertson, ‘George Barker Jeffery’.
[xlv] Richard Staley, ‘Massey, Sir Harrie Stewart Wilson (1908–1983), Physicist’, Oxford Dictionary of National Biography, 23 September 2004, https://www.oxforddnb.com/view/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-31419.
[xlvi] Heini Halberstam, ‘Davenport, Harold (1907–1969), Mathematician’, Oxford Dictionary of National Biography, 23 September 2004, http://www.oxforddnb.com/view/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-32722.
[xlvii] Alex May, ‘Roth, Klaus Friedrich (1925–2015), Mathematician’, Oxford Dictionary of National Biography, 10 January 2019, http://www.oxforddnb.com/view/10.1093/odnb/9780198614128.001.0001/odnb-9780198614128-e-111795.
[xlviii] A. M. Binnie, ‘Some Notes on the Study of Fluid Mechanics in Cambridge, England’, Annual Review of Fluid Mechanics 10, no. 1 (1978): 1–11, https://doi.org/10.1146/annurev.fl.10.010178.000245, 4.
[xlix] Michael James Lighthill, ‘Keith Stewartson, 20 September 1925 - 7 May 1983’, Biographical Memoirs of Fellows of the Royal Society 31 (1985): 545–69, https://doi.org/10.1098/rsbm.1985.0019, 545.
[l] Kenneth Falconer et al., ‘Claude Ambrose Rogers. 1 November 1920 — 5 December 2005’, Biographical Memoirs of Fellows of the Royal Society 61 (January 2015): 403–35, https://doi.org/10.1098/rsbm.2015.0007.
[li] Harte et al., The World of UCL, 89.
[lii] Harte et al., The World of UCL, 89.
[liii] Anna Buckland, ed., A Record of Ellen Watson (London: Macmillan and Co., 1884), 30.
[liv] Buckland, A Record of Ellen Watson, 14-22.
[lv] Buckland, A Record of Ellen Watson, 30-34.
[lvi] The Council adopted the recommendation of the Senate for “ladies to be admitted to the Higher Senior Class of Mathematics and the Class of Mineralogy”: College Council minutes, 4 Nov 1876, UCLCA/3/1/7. These were not the only classes open to women; the Slade School had allowed women to enrol since it was founded in 1871, see: Harte et al., The World of UCL, 89. Additionally, earlier in the year, the Council had agreed to allow women to be admitted to the classes of “Roman Law, Jurisprudence, Geology and Political Economy”: College Council minutes, 17 Jun 1876, UCLCA/3/1/7.
[lvii] Professors’ Fees Book 1876-77, UCLCA/2/6/1/45, folio 80.
[lviii]UCL Calendar 1877-1878 (London: Taylor and Francis, 1877), 93.
[lix] ‘Distribution of Prizes at University College’, Daily News (London), 23 June 1877.
[lx] Buckland, A Record of Ellen Watson, 78.
[lxi] Buckland, A Record of Ellen Watson, 76-77.
[lxii] Letter from Ellen Watson to Lucy Clifford, 2 Feb 1880, CLIF/B1/6, Trinity College Library, Cambridge.
[lxiii] ‘Dean’s Report’, in UCL Calendar for 1882-83 (London: Taylor and Francis, 1882), lv; and ‘University and Educational Intelligence’, Nature 23, no. 594 (1881): 474, https://doi.org/10.1038/023473b0.
[lxiv] Permission was extended for women to attend mathematics classes: College Council minutes, 5 May 1877, UCLCA/3/1/7. The Professors’ Fees book for 1877-78 shows several women enrolled in mathematics: Professors’ Fees Book 1877-78, UCLCA/2/6/1/46, folio 78.
[lxv] See, Annie E. Ridley, Frances Mary Buss and Her Work for Education (London: Longmans, Green, & Co., 1895), 81; and more recently, Elizabeth Coutts, ‘Buss, Frances Mary’, Oxford Dictionary of National Biography, 5 January 2006, https://www.oxforddnb.com/view/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-37249.
[lxvi] See, Mary R. S. Creese, ‘Boole [Née Everest], Mary (1832–1916), Scholar and Educationist’, Oxford Dictionary of National Biography, 23 September 2004, https://www.oxforddnb.com/view/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-38817.
[lxvii] See, Creese, ‘Boole [Née Everest], Mary (1832–1916)’.
[lxviii] Harte et al., The World of UCL, 90.
[lxix] See, ‘Mary Thomasina Lockyer’, MNRAS 104, no. 2 (1944): 91–92, https://doi.org/10.1093/mnras/104.2.91b.
[lxx] Professors’ Fees Book 1878-79, UCLCA/2/6/1/47, folios 93-95.
[lxxi] For recent work on Fawcett, see: Elizabeth Crawford, ‘Millicent Fawcett (1847–1929): The Making of a Politician’, in The British Women’s Suffrage Campaign (Routledge, 2020); and Melissa Terras and Elizabeth Crawford, eds, Millicent Garret Fawcett: Selected Writing (UCL Press, 2022).
[lxxii] See: Elaine Kaye, ‘Kilgour, Mary Stewart (1851–1955), Educationist and Feminist’, Oxford Dictionary of National Biography, 23 September 2004, https://www.oxforddnb.com/view/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-48593.
[lxxiii] Rita McWilliams Tullberg, ‘Fawcett, Philippa Garrett (1868–1948), Mathematician and Civil Servant’, Oxford Dictionary of National Biography, 23 September 2004, https://www.oxforddnb.com/view/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-39169.
[lxxiv] Chris Renwick, ‘Lee, Alice Elizabeth (1858–1939), Statistician and Eugenicist’, Oxford Dictionary of National Biography, 12 July 2018, http://www.oxforddnb.com/view/10.1093/odnb/9780198614128.001.0001/odnb-9780198614128-e-39491.
[lxxv] J. J. Gray, ‘Scott, Charlotte Angas (1858–1931), Mathematician’, Oxford Dictionary of National Biography, 23 September 2004, https://www.oxforddnb.com/view/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-38823.
[lxxvi] Sheila Fletcher, ‘Bryant [Née Willock], Sophie (1850–1922), Educationist and Suffragist’, Oxford Dictionary of National Biography, 23 September 2004, https://www.oxforddnb.com/view/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-37237.
[lxxvii] Sophie Bryant, ‘On the Ideal Geometrical Form of Natural Cell-Structure’, Proceedings of the London Mathematical Society s1-16, no. 1 (1884): 311–17, https://doi.org/10.1112/plms/s1-16.1.311.
[lxxviii] ‘De Morgan Association Newsletter 2019/20’, UCL Department of Mathematics, 2020, 20.
Bibliography:
Bellot, Hugh Hale. University College London 1826-1926. London: University of London Press, 1929.
Binnie, A. M. ‘Some Notes on the Study of Fluid Mechanics in Cambridge, England’. Annual Review of Fluid Mechanics 10, no. 1 (1978): 1–11. https://doi.org/10.1146/annurev.fl.10.010178.000245.
Buckland, Anna, ed. A Record of Ellen Watson. London: Macmillan and Co., 1884.
Bryant, Sophie. ‘On the Ideal Geometrical Form of Natural Cell-Structure’. Proceedings of the London Mathematical Society s1-16, no. 1 (1884): 311–17. https://doi.org/10.1112/plms/s1-16.1.311.
Clifford, W. K. ‘On the Space-Theory of Matter’. In Proceedings of the Cambridge Philosophical Society, vol. 2. Cabridge: Cambridge University Press, 1876.
Coutts, Elizabeth. ‘Buss, Frances Mary’. Oxford Dictionary of National Biography, 5 January 2006. https://www.oxforddnb.com/view/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-37249.
Crawford, Elizabeth. ‘Millicent Fawcett (1847–1929): The Making of a Politician’. In The British Women’s Suffrage Campaign. Routledge, 2020.
Creese, Mary R. S. ‘Boole [Née Everest], Mary (1832–1916), Scholar and Educationist’. Oxford Dictionary of National Biography, 23 September 2004. https://www.oxforddnb.com/view/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-38817.
Daily News (London). ‘Distribution of Prizes at University College’. 23 June 1877.
De Morgan Association Newsletter 2019/20. 2020. https://www.ucl.ac.uk/mathematical-physical-sciences/sites/mathematical_physical_sciences/files/demorgan_newsletter_2019.pdf.
De Morgan, Sophia Elizabeth. Memoir of Augustus De Morgan. London: Longmans, Green, and Co., 1882.
‘Dean’s Report’. In UCL Calendar for 1882-83. London: Taylor and Francis, 1882.
Falconer, Kenneth, Peter M. Gruber, Adam Ostaszewski, and Trevor Stuart. ‘Claude Ambrose Rogers. 1 November 1920 — 5 December 2005’. Biographical Memoirs of Fellows of the Royal Society 61 (January 2015): 403–35. https://doi.org/10.1098/rsbm.2015.0007.
Fletcher, Sheila. ‘Bryant [Née Willock], Sophie (1850–1922), Educationist and Suffragist’. Oxford Dictionary of National Biography, 23 September 2004. https://www.oxforddnb.com/view/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-37237.
Gray, J. J. ‘Scott, Charlotte Angas (1858–1931), Mathematician’. Oxford Dictionary of National Biography, 23 September 2004. https://www.oxforddnb.com/view/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-38823.
Halberstam, Heini. ‘Davenport, Harold (1907–1969), Mathematician’. Oxford Dictionary of National Biography, 23 September 2004. http://www.oxforddnb.com/view/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-32722.
Harte, Negley, John North, and Georgina Brewis. The World of UCL. UCL Press, 2018.
Jeffery, George Barker. ‘Louis Napoleon George Filon, 1875-1937’. Obituary Notices of Fellows of the Royal Society 2, no. 7 (1939): 501–9. https://doi.org/10.1098/rsbm.1939.0010.
Kaye, Elaine. ‘Kilgour, Mary Stewart (1851–1955), Educationist and Feminist’. Oxford Dictionary of National Biography, 23 September 2004. https://www.oxforddnb.com/view/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-48593.
Lewis, Albert C. ‘Clifford, William Kingdon (1845–1879), Mathematician and Philosopher of Science’. Oxford Dictionary of National Biography, 23 September 2004. https://www.oxforddnb.com/view/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-5667.
Lighthill, Michael James. ‘Keith Stewartson, 20 September 1925 - 7 May 1983’. Biographical Memoirs of Fellows of the Royal Society 31 (1985): 545–69. https://doi.org/10.1098/rsbm.1985.0019.
‘Mary Thomasina Lockyer’. MNRAS 104, no. 2 (1944): 91–92. https://doi.org/10.1093/mnras/104.2.91b.
May, Alex. ‘Roth, Klaus Friedrich (1925–2015), Mathematician’. Oxford Dictionary of National Biography, 10 January 2019. http://www.oxforddnb.com/view/10.1093/odnb/9780198614128.001.0001/odnb-9780198614128-e-111795.
Memoir of Sir Francis Henry Goldsmid. 2nd edn. London: Kegan Paul, Trench, & Co., 1882.
O’Connor, J. J., and E. F. Robertson. ‘George Barker Jeffery’. MacTutor, 2020. https://mathshistory.st-andrews.ac.uk/Biographies/Jeffery/.
Renwick, Chris. ‘Lee, Alice Elizabeth (1858–1939), Statistician and Eugenicist’. Oxford Dictionary of National Biography, 12 July 2018. http://www.oxforddnb.com/view/10.1093/odnb/9780198614128.001.0001/odnb-9780198614128-e-39491.
Rice, Adrian. ‘Augustus De Morgan and the Development of University Mathematics in London in the Nineteenth Century’. PhD diss., Middlesex University, 1997.
Rice, Adrian. ‘Augustus De Morgan: Historian of Science’. History of Science 34, no. 2 (1996): 201–40. https://doi.org/10.1177/007327539603400203.
Rice, Adrian. ‘Henrici, Olaus Magnus Friedrich Erdmann (1840–1918), Mathematician’. Oxford Dictionary of National Biography, 23 September 2004. https://www.oxforddnb.com/view/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-39487.
Rice, Adrian. ‘Hill, Micaiah John Muller (1856–1929), Mathematician’. Oxford Dictionary of National Biography, 23 September 2004. http://www.oxforddnb.com/view/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-39485.
Rice, Adrian, Robin J. Wilson, and J. Helen Garner. ‘From Student Club to National Society: The Founding of the London Mathematical Society in 1865’. Historia Mathematica 22, no. 4 (1995): 402–21. https://doi.org/10.1006/hmat.1995.1032.
Ridley, Annie E. Frances Mary Buss and Her Work for Education. London: Longmans, Green, & Co., 1895.
Staley, Richard. ‘Massey, Sir Harrie Stewart Wilson (1908–1983), Physicist’. Oxford Dictionary of National Biography, 23 September 2004. https://www.oxforddnb.com/view/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-31419.
Stephen, Leslie, and I. Grattan-Guinness. ‘Morgan, Augustus De (1806–1871), Mathematician and Historian’. Oxford Dictionary of National Biography, 23 September 2004. http://www.oxforddnb.com/view/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-7470.
Terras, Melissa, and Elizabeth Crawford, eds. Millicent Garret Fawcett: Selected Writing. UCL Press, 2022. https://doi.org/10.14324/111.9781787358638.
Tullberg, Rita McWilliams. ‘Fawcett, Philippa Garrett (1868–1948), Mathematician and Civil Servant’. Oxford Dictionary of National Biography, 23 September 2004. https://www.oxforddnb.com/view/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-39169.
UCL Calendar 1877-1878. London: Taylor and Francis, 1877.
‘UCL Makes Formal Public Apology for Its History and Legacy of Eugenics’. 7 January 2021. https://www.ucl.ac.uk/news/2021/jan/ucl-makes-formal-public-apology-its-history-and-legacy-eugenics.
‘University and Educational Intelligence’. Nature 23, no. 594 (1881): 473–74. https://doi.org/10.1038/023473b0.
University College, London: Report of the Council, Financial Statements, and Other Documents to Be Presented to the Members of the College at the Annual General Meeting on Wednesday, 25th February, 1903. London: Taylor and Francis, 1903.
Wilson, Robin J. ‘Hirst, Thomas Archer (1830–1892), Mathematician’. Oxford Dictionary of National Biography, 23 September 2004. http://www.oxforddnb.com/view/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-13364.
Woiak, Joanne. ‘Pearson, Karl [Formerly Carl] (1857–1936), Statistician and Eugenicist.’ Oxford Dictionary of National Biography, 23 September 2004. https://www.oxforddnb.com/view/10.1093/ref:odnb/9780198614128.001.0001/odnb-9780198614128-e-35442.