Hardy on the Tripos

Lest anyone think I’m uniquely deranged for my criticisms of the Cambridge University Mathematics Tripos examination, particularly during the 18th- and 19th-centuries, here is GH Hardy – perhaps Britain’s greatest 20th century pure mathematician – speaking in his Presidential Address to the Mathematics Association in 1926:

My own contribution to the discussion consisted merely in an expression of my feeling that the best thing that could happen to English mathematics, and to Cambridge mathematics in particular, would be that the Mathematical Tripos should be abolished. I stated this on the spur of the moment, but it is my considered opinion, and I propose to defend it at length to-day. And I am particularly anxious that you should understand quite clearly that I mean exactly what I say; that by “abolished” I mean “abolished”, and not “reformed”; that if I were prepared to co-operate, as in fact I have co-operated in the past, in “reforming” the Tripos, it would be because I could see no chance of any more revolutionary change; and that my “reforms” would be directed deliberately towards destroying the traditions of the examination and so preparing the way for its extinction.” [p. 134]
. . .
“I suppose that it would be generally agreed that Cambridge mathematics, during the last hundred years, has been dominated by the Mathematical Tripos in a way in which no first-rate subject in any other first-rate university [page-break] has ever been dominated by an examination. It would be easy for me, were the fact disputed, to justify my assertion by a detailed account of the history of the Tripos, but this is unnecessary, since you can find an excellent account, written by a man who was very much more in sympathy with the Tripos than I am, in Mr. Rouse Ball’s History of Mathematics in Cambridge. I must, however, call your attention to certain rather melancholy reflections which the history of Cambridge mathematics suggests. You will understand that when I speak of mathematics I mean primarily pure mathematics, not that I think that anything which I say about pure mathematics is not to a great extent true of applied mathematics also, but merely because I do not want to criticise where my competence as a critic is doubtful.
Mathematics at Cambridge challenges criticism by the highest standards. England is a first-rate country, and there is no particular reason for supposing that the English have less natural talent for mathematics than any other race; and if there is any first-rate mathematics in England, it is in Cambridge that it may be expected to be found. We are therefore entitled to judge Cambridge mathematics by the standards that would be appropriate in Paris or Gottingen or Berlin. If we apply these standards, what are the results?  I will state them, not perhaps exactly as they would have occurred to me spontaneously – though the verdict is one which, in its essentials, I find myself unable to dispute – but as they were stated to me by an outspoken foreign friend.
In the first place, about Newton there is no question; it is granted that he stands with Archimedes or with Gauss. Since Newton, England has produced no mathematician of the very highest rank. There have been English mathematicians, for example Cayley, who stood well in the front rank of the mathematicians of their time, but their number has been quite extraordinarily small; where France or Germany produces twenty or thirty, England produces two or three. There has been no country, of first-rate status and high intellectual tradition, whose standard has been so low; and no first-rate subject, except music, in which England has occupied so consistently humiliating a position. And what have been the peculiar characteristics of such English mathematics as there has been? Occasional flashes of insight, isolated achievements sufficient to show that the ability is really there, but, for the most part, amateurism, ignorance, incompetence, and triviality. It is indeed a rather cruel judgment, but it is one which any competent critic, surveying the evidence dispassionately, will find it uncommonly difficult to dispute.
I hope that you will understand that I do not necessarily endorse my friend’s judgment in every particular. He was a mathematician whose competence nobody could question, and whom nobody could accuse of any prejudice against England, Englishmen, or English mathematicians; but he was also, of course, a man developing a thesis, and he may have exaggerated a little in the enthusiasm of the moment or from curiosity to see how I should reply.  Let us assume that it is an exaggerated judgment, or one rhetorically expressed.  It is, at any rate, not a ridiculous judgment, and it is serious enough that such a condemnation, from any competent critic, should not be ridiculous. It is inevitable that we should ask whether, if such a judgment can really embody any sort of approximation to the truth, some share of the responsibility must not be laid on the Mathematical Tripos and the grip which it has admittedly exerted on English mathematics.
I am anxious not to fall into exaggeration in my turn and use extravagant language about the damage which the Tripos may have done, and it would no doubt be an extravagance to suggest that the most ruthless of examinations could destroy a whole side of the intellectual life of a nation. On the [page-break] other hand it is really rather difficult to exaggerate the hold which the Tripos has exercised on Cambridge mathematical life, and the most cursory survey of the history of Cambridge mathematics makes one thing quite clear; the reputation of the Tripos, and the reputation of Cambridge mathematics stand in correlation with one another, and the correlation is large and negative.  As one has developed, so has the other declined. As, through the early and middle nineteenth century, the traditions of the Tripos strengthened, and its importance in the eyes of the public grew greater and greater, so did the external reputation of Cambridge as a centre of mathematical learning steadily decay. When, in the years perhaps between 1880 and 1890, the Tripos stood, in difficulty, complexity, and notoriety, at the zenith of its reputation, English mathematics was somewhere near its lowest ebb. If, during the last forty years, there has been an obvious revival, the fortunes of the Tripos have experienced an equally obvious decline.” [pp. 135-137]
. . .
“It has often been said that Tripos mathematics was a collection of elaborate futilities, and the accusation is broadly true. My own opinion is that this is the inevitable result, in a mathematical examination, of high standards and traditions. The examiner is not allowed to content himself with testing the competence and the knowledge of the candidates; his instructions are to provide a test of more than that, of initiative, imagination, and even of some sort of originality. And as there is only one test of originality in mathematics, namely the accomplishment of original work, and as it is useless to ask a youth of twenty-two to perform original research under examination conditions, the examination necessarily degenerates into a kind of game, and instruction for it into initiation into a series of stunts and tricks. It was in any case certainly true, at the time of which I am speaking, that an undergraduate might study mathematics diligently throughout the whole of his career, and attain the very highest honours in the examination, without having acquired, and indeed without having encountered, any knowledge at all of any of the ideas which dominate modern mathematical thought. His ignorance of analysis would have been practically complete. About geometry I speak with less confidence, but I am sure that such knowledge as he possessed would have been exceedingly one-sided, and that there would have been whole fields of geometrical knowledge, and those perhaps the most fruitful and fascinating of all, of which he would have known absolutely nothing. A mathematical physicist, I may be told, would on the contrary have received an appropriate and an excellent education. It is possible; it would no doubt be very impertinent for me to deny it. Yet I do remember Mr. Bertrand Russell telling me that he studied electricity at Trinity for three years, and that at the end of them he had never heard of Maxwell’s equations; and I have also been told by friends whom I believe to be competent that Maxwell’s equations are really rather important in physics. And when I think of this I begin to wonder whether the teaching of applied mathematics was really quite so perfect as I have sometimes been led to suppose.” [p. 138]
. . .
“I shall judge the Tripos by its real or apparent influence on English mathematics. I have already told you that in my judgment this influence has in the past been bad, that the Tripos has done negligible good and by no means negligible harm, and that, so far from being the great glory of Cambridge mathematics, it has gone a very long way towards strangling its development.”  [p. 141]

G. H. Hardy [1926/1948]: Presidential Address: The Case against the Mathematical Tripos. The Mathematical Gazette, 32 (300): 134-145 (July 1948).

The Mathematical Tripos at Cambridge

From the 18th century until 1909, students at Cambridge University took a compulsory series of examinations, called the Mathematical Tripos, named after the three-legged stool that candidates originally sat on.  Until the mid-18th century, these examinations were conducted orally, and only became written examinations over faculty protests.   Apparently, not everyone believed that written examinations were the best or fairest way to test mathematical abilities, a view which would amaze many contemporary people – although oral examinations in mathematics are still commonly used in some countries with very strong mathematical traditions, such as Russia and the other states of the former USSR.
The Tripos became a notable annual public event in the 19th century, with The Times newspaper publishing articles and biographies before each examination on the leading candidates, and then, after each examination, the results.   There was considerable public interest in the event each year, not just in Cambridge or among mathematicians, and widespread betting on the outcomes.
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Charles Burney

This post is a history of the family of Charles Burney FRS (1726-1814), musician and musicologist, and his ancestors and descendants.
Sir MacBurney was one of the 60 Knights who participated in a jousting tournament, supervised by Geoffrey Chaucer on the orders of Richard II, held at Smithfield in London in 1390.
One James Macburney is said to have come south to London from Scotland with King James I and VI in 1603.   His descendant (likely a grandson), also James Macburney, was born around 1653 and had a house in Whitehall.   His son, also called James Macburney (1678-1749), was born in Great Hanwood, Shropshire, around 1678, and attended Westminster School in London.   In 1697, he eloped with Rebecca Ellis, against his father’s wishes. As a consequence, the younger James was not left anything when his father died.  The  younger man’s stepbrother, Joseph Macburney (born of a second wife) was left the entire estate of their father.
This younger James Macburney (1678-1749) was a dancer, violinist and painter, and was supposedly a wit and bon viveur.  He and Rebecca Ellis had 15 children over 20 years, of whom 9 survived into adulthood.   By 1720, he had moved to Shrewsbury,  and Rebecca had died.  He married again, to Ann Cooper, who apparently brought money to the union which helped her somewhat feckless husband. This second marriage produced 5 further children, among whom were Richard Burney (1723-1792) (christened “Berney”).  The last two children were twins, Charles Burney (1726-1814) and Susanna (1726-1734?), who died at the age of 8.  Their father James had apparently dropped the prefix “Mac” around the time of the birth of the  twins.
One of Charles’ half-brothers was James Burney (1710-1789), who was organist at St. Mary’s Church, Shrewsbury, for 54 years, from 1732 to 1786. Charles Burney worked as his assistant from 1742 until 1744.
For a period, Charles Burney and his family lived in Isaac Newton’s former house at 35 St Martin’s Street, Leicester Square, London.  Among Charles’ children were:

  • Esther Burney (1749-1832), harpsichordist, who married her cousin Charles Rousseau Burney (1747-1819), also a keyboardist and violinist.
  • Rear Admiral James Burney RN FRS (1750-1821), naval historian and sailor, who twice sailed around the world with Captain James Cook RN.
  • Fanny Burney, later Madame d’Arblay (1752-1840), novelist and playwright.
  • Rev. Charles Burney FRS (1757-1817), classical scholar.
  • Charlotte Ann Burney, later Mrs Broome (1761-1838), novelist.
  • Sarah Harriet Burney (1772-1844), novelist.

Charles’ nephew, Edward Francisco Burney (1760-1848), artist and violinist, was a brother to Charles Rousseau Burney, both sons of Richard Burney (1723-1792), Charles’s elder brother.  This is a self-portrait of Edward Francisco Burney (Creative Commons License from National Portrait Gallery, London):
In 1793, Fanny Burney married Alexandre-Jean-Baptiste Piochard D’Arblay (1754-1818), an emigre French aristocrat and soldier, and adjutant-general to Lafayette. Their son, Alexander d’Arblay (1794-1837), was a poet and keen chess-player, and was 10th wrangler in the Mathematics Tripos at Cambridge in 1818, where he was a friend of fellow-student Charles Babbage.  He was also a member of Babbage’s Analytical Society (forerunner of the Cambridge Philosophical Society), which sought to introduce modern analysis, including Leibnizian notation for the differential calculus, into mathematics teaching at Cambridge. d’Arblay was ordained and served as founding minister of Camden Town Chapel (later the Greek Orthodox All Saints Camden) from 1824-1837, and then served briefly at Ely Chapel in High Holborn, London. The founding organist at Camden Town Chapel was Samuel Wesley (1766-1837).
Not everyone was a fan of clan Burney. Here is William Hazlitt:

“There are whole families who are born classical, and are entered in the heralds’ college of reputation by the right of consanguinity. Literature, like nobility, runs in the blood. There is the Burney family. There is no end of it or its pretensions. It produces wits, scholars, novelists, musicians, artists in ‘numbers numberless.’ The name is alone a passport to the Temple of Fame. Those who bear it are free of Parnassus by birthright. The founder of it was himself an historian and a musician, but more of a courtier and man of the world than either. The secret of his success may perhaps be discovered in the following passage, where, in alluding to three eminent performers on different instruments, he says: ‘These three illustrious personages were introduced at the Emperor’s court,’ etc.; speaking of them as if they were foreign ambassadors or princes of the blood, and thus magnifying himself and his profession. This overshadowing manner carries nearly everything before it, and mystifies a great many. There is nothing like putting the best face upon things, and leaving others to find out the difference. He who could call three musicians ‘personages’ would himself play a personage through life, and succeed in his leading object. Sir Joshua Reynolds, remarking on this passage, said: ‘No one had a greater respect than he had for his profession, but that he should never think of applying to it epithets that were appropriated merely to external rank and distinction.’ Madame d’Arblay, it must be owned, had cleverness enough to stock a whole family, and to set up her cousin-germans, male and female, for wits and virtuosos to the third and fourth generation. The rest have done nothing, that I know of, but keep up the name.” (On the Aristocracy of Letters, 1822).

K. S. Grant: ” Charles Burney”, Grove Music Online. (Accessed 2006-12-10.)

Public speaking

While talking just now about excellent public speakers, I remembered that I had heard a superb speech last year at a University of London graduation ceremony.  In the USA, these ceremonies are often the occasion for great speeches from invited public figures.  My experience is that this is far less often the case elsewhere in the anglophone world – the speeches tend to the routine or mundane, and outsiders are not always invited to give addresses.  Perhaps this relates to the fact the American universities, alone among those in the anglophone world, still have Departments of Speech, with serious study of argumentation, rhetoric, and oratory.  Since the switch from oral to written mathematics examinations at Cambridge in the 18th century our universities mostly no longer train or exercise people in public speaking skills, despite their evident value for so many careers.  Moreover, writing speeches is often a form of policy formulation, as experienced speech-writers attest.

At a graduation ceremony last October in the Barbican I was fortunate to hear a superb speech by Thomas Clayton, President of the Student’s Union of King’s College London, speaking in his official capacity. The speech was original, clear, inspiring, and amusing, and was pitched just right for the audience and the occasion.  Clayton himself was enthusiastic and engaged, and his speech did not sound, as many at these events do, as if he was merely going through the motions. He is evidently someone to listen out for in future.


Thurston on mathematical proof

The year 2012 saw the death of Bill Thurston, leading geometer and Fields Medalist.   Learning of his death led me to re-read his famous 1994 AMS paper on the social nature of mathematical proof.   In my opinion, Thurston demolished the views of those who thought mathematics is anything other than socially-constructed.  This post is just to present a couple of long quotes from the paper.
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Most-viewed posts

The top 21 most-viewed posts on this blog, since its inception (in descending order):

(Photo of Paul Keating,  credit:  AFR).

The mechanical judiciary

In the tradition of Montaigne and Orwell, Rory Stewart MP has an extremely important blog post about the need for judicial decisions to be be made case-by-case, using humane wisdom, intuition, and discretion, and not by deterministic or mechanical algorithms. The same applies to most important decisions in our lives and our society. Sadly, his view runs counter to the thrust of modern western culture these last four centuries, as Stephen Toulmin observed.   Our obssessive desire for consistency in decision-making sweeps all before it, from oral examinations in mathematics to eurozone economic policy.

Stewart’s post is worth quoting at length:

What is the point of a parliamentary debate? It isn’t about changing MPs’ minds or their votes. It wasn’t, even in the mid-nineteenth century. In the 1860s Trollope describes how MPs almost always voted on party lines. But they and he still felt that parliamentary debate mattered, because it set the terms of the public discussion, and clarified the great national questions. The press and public galleries were often filled. Churchill, even as a young backbencher, could expect an entire speech, lasting almost an hour, to be reprinted verbatim in the Morning Post. MPs put enormous effort into their speeches. But in the five-hour debate today on the judicial sentencing council, the press gallery was empty, and for most of the time there was only one single person on the Labour benches – a shadow Minister who had no choice. And on our side, a few former judges, and barristers. For whom, and about what, were we speaking?
Continue reading ‘The mechanical judiciary’

The Matherati: Matthew Piers Watt Boulton

Matthew Piers Watt Boulton (1820-1894, pictured in portrait by Sir Francis Grant, ca. 1840) was the eldest grandson of the great engineer Matthew Boulton, and was named for James Watt, his grandfather’s partner-in-steam.   He inherited significant wealth and attended Eton and Trinity College, Cambridge, where his first tutor was the mathematician George Peacock (1791-1858), undergraduate friend of Charles Babbage and Alexander d’Arblay.    At Cambridge, Boulton studied mathematics, logic, and classics. He declined to apply for scholarships, despite his evident ability and in the face of entreaties from his tutor and his father, on the grounds that they bred unpleasant competitiveness – perhaps he was someone after my own heart.  It is likely that, for the same reason, he did not sit the Tripos examinations.

He was however of strong mathematical bent.  In 1868, he patented a method for lateral control of aircraft in flight, inventing what are now called ailerons.  Being a gentleman of wealth and leisure, he was able to read and write at will, and published translations of classic literature, some poetry, and pamphlets on solar energy, in addition to a work on aircraft stability.   Kinzer (2009) makes a compelling case for him also being the author of several works of philosophy published by someone calling himself “M. P. W. Bolton,” mostly in the 1860s.
Kinzer quotes the following words from Boulton’s paper,  “Has a Metaphysical Society any raison d’etre?”, read to a meeting of the Metaphysical Society, held at the Grosvenor Hotel on 9 April 1874 and chaired by William Gladstone:

There is no question, however apparently non-metaphysical, which may not be pursued till we come to the Metaphysical.  The question of whether Tarquin lived, and whether Lucretia committed suicide, is about as non-metaphysical as any question can be: yet disputants engaged in its discussion may persist till they open up the general question of the credibility of testimony; and this may open that of the credibility of memory, the nature of belief, what grounds we have for believing the existence of other persons, and an external world . . .  Whenever we try to bottom a question or subject, to use Locke’s word (the French word would be “approfondir”) then Metaphysics come in sight  . . . Every sentence involves, in some shape or other, the verb “to be”, and this, if pursued long enough, leads to the heart of Metaphysics  . . . Scientific persons often speak of Metaphysics  with scorn, calling them an Asylum Ignorantiae, useful enough to the vulgar, but in no way needed by themselves.  They imagine their science to be perfectly luminous, far above the lower regions where Metaphysical mists prevail.  But in reality they share the common lot:  the ideas of Force, Law, Cause, Substance, Causal or Active Matter, all dwell in the region of metaphysical twilight, not in the luminous ether. “

For some reason, reading the quoted passage brought to mind Richard Dawkins and memes.
I am grateful to Bruce Kinzer for some information here.
There is an index here to posts about members of the Matherati.
Billie Andrew Inman [1991]:  Pater’s Letters at the Pierpont Morgan Library.  English Literature in Transition, 1880-1920, 34 (4):401-417.
Bruce Kinzer [1979]: In search of M.P.W. Bolton. Notes and Queries, n.s., 26 (August 1979): 310-313.
Bruce Kinzer [2009]:  Flying under the radar:  The strange case of Matthew Piers Watt Boulton. Times Literary Supplement, 1 May 2009, pp. 14-15.

Oral culture

For about 300 years, and especially from the introduction of universal public education in the late 19th century, western culture has  been dominated by text and writing.  Elizabethan culture, by contrast, was primarily oral:  Shakespeare, for example, wrote his plays to be performed not to be read, and did not even bother to arrange definitive versions for printing.   One instance of the culture-wide turn from speech to text was a switch from spoken to written mathematics tests in the west which occurred at Cambridge in the late 18th century, as I discuss here.  There is nothing intrinsically better about written examinations over spoken ones, especially when standardized and not tailored for each particular student.  This is true even for mathematics, as is shown by the fact that oral exams are still the norm in university mathematics courses in the Russian-speaking world; Russia continues to produce outstanding mathematicians.
Adventurer and writer Rory Stewart, now an MP,  has an interesting post about the oral culture of the British Houses of Parliament, perhaps the last strong-hold of argument-through-speech in public culture.  The only other places in modern life, a place which is not quite as public, where speech reigns supreme, are court rooms.

The Matherati: Alexander d’Arblay

The photo shows the Greek Orthodox Cathedral of All Saints, at the corner of Pratt and Camden Streets in Camden, London. Before becoming an Orthodox Chuch in 1948, the building was an Anglican Church, most recently All Saints Camden. The building was designed by William Inwood and his son Henry Inwood in 1822-24, who had together earlier designed St. Pancras New Church in Euston, London. Both churches borrow from ancient Greek architecture, so it is fitting that one is now filled with Greek icons and text, and used for services in (modern) Greek. All Saints has a low-set but very deep choir balcony, extending from the entrance almost one-third the length of the church; this gives the church a quite intimate feel, despite the height of the main chapel. The current cathedral also has three large, low-hanging white glass chandeliers over the main chapel, which enhances the intimacy. I was reminded of the intimacy of Lloyd Wright’s Unity Temple in Chicago, a building which is similarly deceptive from the outside about the compactness of the space within.

When built, All Saints was called Camden Town Chapel, and its founding pastor was the Rev’d Alexander Charles Louis d’Arblay (1794-1837), son of the author Fanny Burney (1752-1840) and Alexandre-Jean-Baptiste Piochard D’Arblay (1754-1818), emigre French aristocrat and soldier, and adjutant-general to Lafayette. The Reverend d’Arblay was a poet and chess-player, and had been 10th wrangler in the Mathematics Tripos at Cambridge in 1818. He was a friend of fellow-student (but non-wrangler) Charles Babbage and of Senior Wrangler (1813) John Herschel, and a member of Babbage’s Analytical Society (forerunner of the Cambridge Philosophical Society).  Indeed, d’Arblay may have introduced Babbage to recent French mathematics. Alexander had been partly educated in France, and was aware of French trends in analysis, which in its rigour and formality was very different to the applied focus of British mathematics. From his time as an undergraduate, Babbage ran a campaign against the troglodytic British mathematics establishment, who were then opposed to rigour, formality and theory, and he sought to introduce modern analysis into mathematics teaching at Cambridge. British pure mathematics, as better mathematicians than I have argued, lost a century of progress as a result of its focus on certain types of applications at the expense of rigour.

Because of his First-Class degree, after his graduation d’Arblay was appointed a Fellow of Christ College Cambridge, which paid him a generous stipend his entire life (presumably while he remained unmarried). He had a remarkable ability to quickly learn and recite from memory long poems, and was obsessed with chess. He once missed an arranged meeting with his father when the latter was returning to France because he was engrossed in a chess game with his uncle, the admiral James Burney. d’Arblay was apparently bilingual, and wrote equally easily in English and French, and translated poetry and literary works from each language to the other. d’Arblay was ordained as a Church of England deacon in 1818, and as a priest on 11 April 1819 in St James’s Picadilly.  In the summer of 1821, he spent three months walking in Switzerland with Babbage and Herschel.

Through his mother, he was friends with the royal family and moved in high society.  For many years he was close friends with Mrs Clara Bolton (nee Clarissa Marion Verbeke) (1804-1839), who was, for a period, also a very close friend (and alleged mistress) of the young Benjamin Disraeli. She was the wife of George Buckley Bolton ( -1847), who was the Disraeli family doctor.  The evidence for the allegation that Mrs Bolton was a mistress of Disraeli does not convince me at all.

Ordained Reverend d’Arblay, d’Arblay served as minister of Camden Town Chapel from 1824-1837, and then briefly at Ely Chapel in High Holborn, London. He died of tuberculosis still unmarried, although engaged at the time of death to one Mary Anne Smith.  Thaning [1985] argues that d’Arblay was in unrequited love with Mrs Bolton, and that he proposed to her, unsuccessfully, shortly before becoming engaged to Mary Anne Smith.    The evidence Thaning presents for this claim, however, is not compelling.  Miss Smith became good friends with Madame d’Arblay, and lived with her after Alexander’s death.

Some of d’Arblay’s poetry is on the subject of chess. As the son of Fanny Burney, d’Arblay was the grandson of musician, composer and musicologist Charles Burney FRS (1726-1814), and thus from a remarkable family that included musicians, dancers, novelists, painters, historians, and an admiral.

Alongside d’Arblay, the founding organist at Camden Town Chapel was Samuel Wesley (1766-1837).

An index to posts about the Matherati is here.

POSTSCRIPT 1 [2011-12-24]: I have now seen d’Arblay’s poem, “Caissa Rediviva”, published anonymously in 1836. This is a long poem about a chess game. If there were any doubts about d’Arblay’s membership of the Matherati, this publication would allay them: The frontispiece to the poem poses a non-standard chess problem, which only someone with a subtle and agile mathmind could imagine: Given a particular chess board-configuration, find the precise sequence of 59 moves by White, each of which forces a single move by Black, and which ends with Black check-mating White with a particular move.

POSTSCRIPT 2 [2012-02-18]: Apparently, the Reverend d’Arblay suffered severely from depression for most of his adult life. Peter Sabor, in a recent talk at a conference in depression in the 18th century argues that d’Arblay’s depression may have arisen from his combination of great (and unrealistic) ambition and great indolence. But, of course, his apparent indolence may have been the result, not the cause, of his depression.

POSTSCRIPT 3 [2012-02-18]: d’Arblay was not the last member of the Matherati to become engrossed in intellectual pursuits. The most recent Senior Wrangler at Cambridge, Sean Eberhard (Tripos 2011), is described by his fellow collegians as, “most likely to neglect children to do crossword”.

POSTSCRIPT 4 [2017-11-11]: Clara Bolton is briefly mentioned (pages 68 and 78, footnote 61) as a friend and possible mistress of Benjamin Disraeli (1804-1881) by St. George [1995] in his fascinating history of the law firm, Norton Rose (now Norton Rose Fulbright).  However, St. George seems to have conflated Mrs Bolton with another close friend and possible mistress of Disraeli, Henrietta, Lady Sykes (c.1801-1846), wife of Sir Francis Sykes (1799-1843), third Baronet of Basildon.


An Amateur at Chess [Alexander C. L. d’Arblay] [1836]: Caissa Rediviva: Or the Muzio Gambit. London, UK: Sampson Low.

Peter Sabor [2008]: Frances Burney and Alexander d’Arblay: Creative and Uncreative Gloom. Invited Lecture at: Conference on Before Depression: 1600 – 1800.

Andrew St. George [1995]: A History of Norton Rose. London, UK: Granta Editions.

Kaj Thaning [1985]: Hvem var Clara? Grundtvig Studier, 37 (1).