Recently, I posted a salute to Mervyn Pragnell, a logician who was present in the early days of computer science. I was reminded of the late Malcolm Rennie, the person who introduced me to formal logic, and whom I acknowledged here. Rennie was the most enthusiastic and inspiring lecturer I ever had, despite using no multi-media wizardry, usually not even an overhead projector. Indeed, he mostly just sat and spoke, moving his body as little as possible and writing only sparingly on the blackboard, because he was in constant pain from chronic arthritis. He was responsible for part of an Introduction to Formal Logic course I took in my first year (the other part was taken by Paul Thom, for whom I wrote an essay on the notion of entailment in a system of Peter Geach). The students in this course were a mix of first-year honours pure mathematicians and later-year philosophers (the vast majority), and most of the philosophers struggled with non-linguistic representations (ie, mathematical symbols). Despite the diversity, Rennie managed to teach to all of us, providing challenging questions and discussions with and for both groups. He was also a regular entrant in the competitions which used to run in the weekly Nation Review (and a fellow-admirer of the My Sunday cartoons of Victoria Roberts), and I recall one occasion when a student mentioned seeing his name as a competition winner, and the class was then diverted into an enjoyable discussion of tactics for these competitions.
Continue reading ‘Australian logic: a salute to Malcolm Rennie’
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Great mathematical ideas
Normblog has a regular feature, Writer’s Choice, where writers give their opinions of books which have influenced them. Seeing this led me recently to think of the mathematical ideas which have influenced my own thinking. In an earlier post, I wrote about the writers whose books (and teachers whose lectures) directly influenced me. I left many pure mathematicians and statisticians off that list because most mathematics and statistics I did not receive directly from their books, but indirectly, mediated through the textbooks and lectures of others. It is time to make amends.
Here then is a list of mathematical ideas which have had great influence on my thinking, along with their progenitors. Not all of these ideas have yet proved useful in any practical sense, either to me or to the world – but there is still lots of time. Some of these theories are very beautiful, and it is their elegance and beauty and profundity to which I respond. Others are counter-intuitive and thus thought-provoking, and I recall them for this reason.
- Euclid’s axiomatic treatment of (Euclidean) geometry
- The various laws of large numbers, first proven by Jacob Bernoulli (which give a rational justification for reasoning from samples to populations)
- The differential calculus of Isaac Newton and Gottfried Leibniz (the first formal treatment of change)
- The Identity of Leonhard Euler: exp ( i * \pi) + 1 = 0, which mysteriously links two transcendental numbers (\pi and e), an imaginary number i (the square root of minus one) with the identity of the addition operation (zero) and the identity of the multiplication operation (1).
- The epsilon-delta arguments for the calculus of Augustin Louis Cauchy and Karl Weierstrauss
- The non-Euclidean geometries of Janos Bolyai, Nikolai Lobachevsky and Bernhard Riemann (which showed that 2-dimensional (or plane) geometry would be different if the surface it was done on was curved rather than flat – the arrival of post-modernism in mathematics)
- The diagonalization proofof Gregor Cantor that the Real numbers are not countable (showing that there is more than one type of infinity) (a proof-method later adopted by Godel, mentioned below)
- The axioms for the natural numbers of Guiseppe Peano
- The space-filling curves of Guiseppe Peano and others (mapping the unit interval continuously to the unit square)
- The axiomatic treatments of geometry of Mario Pieri and David Hilbert (releasing pure mathematics from any necessary connection to the real-world)
- The algebraic topology of Henri Poincare and many others (associating algebraic structures to topological spaces)
- The paradox of set theory of Bertrand Russell (asking whether the set of all sets contains itself)
- The Fixed Point Theorem of Jan Brouwer (which, inter alia, has been used to prove that certain purely-artificial mathematical constructs called economies under some conditions contain equilibria)
- The theory of measure and integration of Henri Lebesgue
- The constructivism of Jan Brouwer (which taught us to think differently about mathematical knowledge)
- The statistical decision theory of Jerzy Neyman and Egon Pearson (which enabled us to bound the potential errors of statistical inference)
- The axioms for probability theory of Andrey Kolmogorov (which formalized one common method for representing uncertainty)
- The BHK axioms for intuitionistic logic, associated to the names of Jan Brouwer, Arend Heyting and Andrey Kolmogorov (which enabled the formal treatment of intuitionism)
- The incompleteness theorems of Kurt Godel (which identified some limits to mathematical knowledge)
- The theory of categories of Sam Eilenberg and Saunders Mac Lane (using pure mathematics to model what pure mathematicians do, and enabling concise, abstract and elegant presentations of mathematical knowledge)
- Possible-worlds semantics for modal logics (due to many people, but often named for Saul Kripke)
- The topos theory of Alexander Grothendieck (generalizing the category of sets)
- The proof by Paul Cohen of the logical independence of the Axiom of Choice from the Zermelo-Fraenkel axioms of Set Theory (which establishes Choice as one truly weird axiom!)
- The non-standard analysis of Abraham Robinson and the synthetic geometry of Anders Kock (which formalize infinitesimal arithmetic)
- The non-probabilistic representations of uncertainty of Arthur Dempster, Glenn Shafer and others (which provide formal representations of uncertainty without the weaknesses of probability theory)
- The information geometry of Shunichi Amari, Ole Barndorff-Nielsen, Nikolai Chentsov, Bradley Efron, and others (showing that the methods of statistical inference are not just ad hoc procedures)
- The robust statistical methods of Peter Huber and others
- The proof by Andrew Wiles of The Theorem Formerly Known as Fermat’s Last (which proof I don’t yet follow).
Some of these ideas are among the most sublime and beautiful thoughts of humankind. Not having an education which has equipped one to appreciate these ideas would be like being tone-deaf.
Nicolas Fatio de Duillier
Nicolas Fatio de Duillier (1664-1753) was a Genevan mathematician and polymath, who for a time in the 1680s and 1690s, was a close friend of Isaac Newton. After coming to London in 1687, he became a Fellow of the Royal Society (on 1688-05-15), as later did his brother Jean-Christophe (on 1706-04-03). He played a major part in Newton’s feud with Leibniz over who had invented the differential calculus, and was a protagonist all his life for Newton’s thought and ideas.
Continue reading ‘Nicolas Fatio de Duillier’
Guerrilla logic: a salute to Mervyn Pragnell
When a detailed history of computer science in Britain comes to be written, one name that should not be forgotten is Mervyn O. Pragnell. As far as I am aware, Mervyn Pragnell never held any academic post and he published no research papers. However, he introduced several of the key players in British computer science to one another, and as importantly, to the lambda calculus of Alonzo Church (Hodges 2001). At a time (the 1950s and 1960s) when logic was not held in much favour in either philosophy or pure mathematics, and before it became to be regarded highly in computer science, he studied the discipline not as a salaried academic in a university, but in a private reading-circle of his own creation, almost as a guerrilla activity.
Pragnell recruited people for his logic reading-circle by haunting London bookshops, approaching people he saw buying logic texts (Bornat 2009). Among those he recruited to the circle were later-famous computer pioneers such as Rod Burstall, Peter Landin (1930-2009) and Christopher Strachey (1916-1975). The meetings were held after hours, usually in Birkbeck College, University of London, without the knowledge or permission of the college authorities (Burstall 2000). Some were held or continued in the neighbouring pub, The Duke of Marlborough. It seems that Pragnell was employed for a time in the 1960s as a private research assistant for Strachey, working from Strachey’s house (Burstall 2000). By the 1980s, he was apparently a regular attendee at the seminars on logic programming held at the Department of Computing in Imperial College, London, then (and still) one of the great research centres for the application of formal logic in computer science.
Pragnell’s key role in early theoretical computer science is sadly under-recognized. Donald MacKenzie’s fascinating history and sociology of automated theorem proving, for example, mentions Pragnell in the text (MacKenzie 2001, p. 273), but manages to omit his name from the index. Other than this, the only references I can find to his contributions are in the obituaries and personal recollections of other people. I welcome any other information anyone can provide.
UPDATE (2009-09-23): Today’s issue of The Guardian newspaper has an obituary for theoretical computer scientist Peter Landin (1930-2009), which mentions Mervyn Pragnell.
UPDATE (2012-01-30): MOP appears also to have been part of a production of the play The Way Out at The Little Theatre, Bristol in 1945-46, according to this web-chive of theatrical info.
UPDATE (2013-02-11): In this 2001 lecture by Peter Landin at the Science Museum, Landin mentions first meeting Mervyn Pragnell in a cafe in Sheffield, and then talks about his participation in Pragnell’s London reading group (from about minute 21:50).
UPDATE (2019-07-05): I have learnt some further information from a cousin of Mervyn Pragnell, Ms Susan Miles. From her, I understand that MOP’s mother died in the Influenza Pandemic around 1918, when he was very young, and he was subsequently raised in Cardiff in the large family of a cousin of his mother’s, the Miles family. MOP’s father’s family had a specialist paint manufacturing business in Bristol, Oliver Pragnell & Company Limited, which operated from 25-27 Broadmead. This establishment suffered serious bomb damage during WW II. MOP was married to Margaret and although they themselves had no children, they kept in close contact with their relatives. Both are remembered fondly by their family. (I am most grateful to Susan Miles, daughter of Mervyn Miles whose parents raised MOP, for sharing this information.)
References:
Richard Bornat [2009]: Peter Landin: a computer scientist who inspired a generation, 5th June 1930 – 3rd June 2009. Formal Aspects of Computing, 21 (5): 393-395.
Rod Burstall [2000]: Christopher Strachey – understanding programming languages. Higher-Order and Symbolic Computation, 13: 51-55.
Wilfrid Hodges [2001]: A history of British logic. Unpublished slide presentation. Available from his website.
Peter Landin [2002]: Rod Burstall: a personal note. Formal Aspects of Computing, 13: 195.
Donald MacKenzie [2001]: Mechanizing Proof: Computing, Risk, and Trust. Cambridge, MA, USA: MIT Press.
Alan Turing
Yesterday, I reported on the restoration of the world’s oldest, still-working modern computer. Last night, British Prime Minister Gordon Brown apologized for the country’s treatment of Alan Turing, computer pioneer. In the words of Brown’s statement:
Turing was a quite brilliant mathematician, most famous for his work on breaking the German Enigma codes. It is no exaggeration to say that, without his outstanding contribution, the history of World War Two could well have been very different. He truly was one of those individuals we can point to whose unique contribution helped to turn the tide of war. The debt of gratitude he is owed makes it all the more horrifying, therefore, that he was treated so inhumanely. In 1952, he was convicted of ‘gross indecency’ – in effect, tried for being gay. His sentence – and he was faced with the miserable choice of this or prison – was chemical castration by a series of injections of female hormones. He took his own life just two years later.”
It might be considered that this apology required no courage of Brown.
This is not the case. Until very recently, and perhaps still today, there were people who disparaged and belittled Turing’s contribution to computer science and computer engineering. The conventional academic wisdom is that he was only good at the abstract theory and at the formal mathematizing (as in his “schoolboy essay” proposing a test to distinguish human from machine interlocuters), and not good for anything practical. This belief is false. As the philosopher and historian B. Jack Copeland has shown, Turing was actively and intimately involved in the design and construction work (mechanical & electrical) of creating the machines developed at Bletchley Park during WWII, the computing machines which enabled Britain to crack the communications codes used by the Germans.
Perhaps, like myself, you imagine this revision to conventional wisdom would be uncontroversial. Sadly, not. On 5 June 2004, I attended a symposium in Cottonopolis to commemorate the 50th anniversary of Turing’s death. At this symposium, Copeland played a recording of an oral-history interview with engineer Tom Kilburn (1921-2001), first head of the first Department of Computer Science in Britain (at the University of Manchester), and also one of the pioneers of modern computing. Kilburn and Turing had worked together in Manchester after WW II. The audience heard Kilburn stress to his interviewer that what he learnt from Turing about the design and creation of computers was all high-level (ie, abstract) and not very much, indeed only about 30 minutes worth of conversation. Copeland then produced evidence (from signing-in books) that Kilburn had attended a restricted, invitation-only, multi-week, full-time course on the design and engineering of computers which Turing had presented at the National Physical Laboratories shortly after the end of WW II, a course organized by the British Ministry of Defence to share some of the learnings of the Bletchley Park people in designing, building and operating computers. If Turing had so little of practical relevance to contribute to Kilburn’s work, why then, one wonders, would Kilburn have turned up each day to his course.
That these issues were still fresh in the minds of some people was shown by the Q&A session at the end of Copeland’s presentation. Several elderly members of the audience, clearly supporters of Kilburn, took strident and emotive issue with Copeland’s argument, with one of them even claiming that Turing had contributed nothing to the development of computing. I repeat: this took place in Manchester 50 years after Turing’s death! Clearly there were people who did not like Turing, or in some way had been offended by him, and who were still extremely upset about it half a century later. They were still trying to belittle his contribution and his practical skills, despite the factual evidence to the contrary.
I applaud Gordon Brown’s courage in officially apologizing to Alan Turing, an apology which at least ensures the historical record is set straight for what our modern society owes this man.
POSTSCRIPT #1 (2009-10-01): The year 2012 will be a centenary year of celebration of Alan Turing.
POSTSCRIPT #2 (2011-11-18): It should also be noted, concerning Mr Brown’s statement, that Turing died from eating an apple laced with cyanide. He was apparently in the habit of eating an apple each day. These two facts are not, by themselves, sufficient evidence to support a claim that he took his own life.
POSTSCRIPT #3 (2013-02-15): I am not the only person to have questioned the coroner’s official verdict that Turing committed suicide. The BBC reports that Jack Copeland notes that the police never actually tested the apple found beside Turing’s body for traces of cyanide, so it is quite possible it had no traces. The possibility remains that he died from an accidental inhalation of cyanide or that he was deliberately poisoned. Given the evidence, the only rational verdict is an open one.
Social forecasting: Doppio Software
Five years ago, back in the antediluvian era of Web 2.0 (the web as enabler and facilitator of social networks), we had the idea of social-network forecasting. We developed a product to enable a group of people to share and aggregate their forecasts of something, via the web. Because reducing greenhouse gases were also becoming flavour-du-jour, we applied these ideas to social forecasts of the price for the European Union’s carbon emission permits, in a nifty product we called Prophets-360. Sadly, due mainly to poor regulatory design of the European carbon emission market, supply greatly outstripped demand for emissions permits, and the price of permits fell quickly and has mostly stayed fallen. A flat curve is not difficult to predict, and certainly there was little value in comparing one person’s forecast with that of another. Our venture was also felled.
But now the second generation of social networking forecasting tools has arrived. I see that a French start-up, Doppio Software, has recently launched publicly. They appear to have a product which has several advantages over ours:
- Doppio Software is focused on forecasting demand along a supply chain. This means the forecasting objective is very tactical, not the long-term strategic forecasting that CO2 emission permit prices became. In the present economic climate, short-term tactical success is certainly more compelling to business customers than even looking five years hence.
- The relevant social network for a supply chain is a much stronger community of interest than the amorphous groups we had in mind for Prophets-360. Firstly, this community already exists (for each chain), and does not need to be created. Secondly, the members of the community by definition have differential access to information, on the basis of their different positions up and down the chain. Thirdly, although the interests of the partners in a supply chain are not identical, these interests are mutually-reinforcing: everyone in the chain benefits if the chain itself is more successful at forecasting throughput.
- In addition, Team Doppio (the Doppiogangers?) appear to have included a very compelling value-add: their own automated modeling of causal relationships between the target demand variables of each client and general macro-economic variables, using semantic-web data and qualitative modeling technologies from AI. Only the largest manufacturing companies can afford their own econometricians, and such people will normally only be able to hand-craft models for the most important variables. There are few companies IMO who would not benefit from Doppio’s offer here.
Of course, I’ve not seen the Doppio interface and a lot will hinge on its ease-of-use (as with all software aimed at business users). But this offer appears to be very sophisticated, well-crafted and compelling, combining social network forecasting, intelligent causal modeling and semantic web technologies.
Well done, Team Doppio! I wish you every success with this product!
PS: I have just learnt that “doppio” means “double”, which makes it a very apposite name for this application – forecasts considered by many people, across their human network. Neat! (2009-09-16)
Article in The Observer (UK) about Doppio 2009-09-06 here. And here is an AFP TV news story (2009-09-15) about Doppio co-founder, Edouard d’Archimbaud. Another co-founder is Benjamin Haycraft.
Thinkers of renown
The recent death of mathematician Jim Wiegold (1934-2009), whom I once knew, has led me to ponder the nature of intellectual influence. Written matter – initially, hand-copied books, then printed books, and now the Web – has been the main conduit of influence. For those of us with a formal education, lectures and tutorials are another means of influence, more direct than written materials. Yet despite these broadcast methods, we still seek out individual contact with others. Speaking for myself, it is almost never the knowledge or facts of others, per se, that I have sought or seek in making personal contact, but rather their various different ways of looking at the world. In mathematical terminology, the ideas that have influenced me have not been the solutions that certain people have for particular problems, but rather the methods and perspectives they use for approaching and tackling problems, even when these methods are not always successful.
To express my gratitude, I thought I would list some of the people whose ideas have influenced me, either directly through their lectures, or indirectly through their books and other writings. In the second category, I have not included those whose ideas have come to me mediated through the books or lectures of others, which therefore excludes many mathematicians whose work has influenced me (in particular: Newton, Leibniz, Cauchy, Weierstrauss, Cantor, Frege, Poincare, Pieri, Hilbert, Lebesque, Kolmogorov, and Godel). I have also not included the many writers of poetry, fiction, history and biography whose work has had great impact on me. These two categories also exclude people whose intellectual influence has been manifest in non-verbal forms, such as through visual arts or music, or via working together, since those categories need posts of their own.
Teachers & lecturers I have had who have influenced my thinking include: Leo Birsen (1902-1992), Sr. Claver Butler RSM (ca. 1930-2009), Burgess Cameron (1922-2020), Sr. Clare Castle RSM (ca. 1920- ca. 2000), John Coates (1945-2022), Dot Crowe, James Cutt, Bro. Clive Davis FMS, Tom Donaldson (1945-2006), Aleksandr Doronin, Gary Dunbier, Sol Encel (1925-2010), Felix Fabryczny de Leiris, Claudio Forcada, Richard Gill (1941-2018), Myrtle Hanley (1909-1984), Sr. Jennifer Hartley RSM, Chip Heathcote (1931-2016), Hope Hewitt (1915-2011), Alec Hope (1907-2000), John Hutchinson, Marg Keetles, Joe Lynch, Robert Marks, John McBurney (1932-1998), David Midgley, Lindsay Morley, Leopoldo Mugnai, Terry O’Neill, Jim Penberthy* (1917-1999), Malcolm Rennie (1940-1980), John Roberts, Gisela Soares, Brian Stacey (1946-1996), James Taylor, Frank Torpie (1934-1989), Neil Trudinger, David Urquhart-Jones, Frederick Wedd (1890-1972), Gary Whale (1943-2019), Ted Wheelwright (1921-2007), John Woods and Alkiviadis Zalavras.
People whose writings have influenced my thinking include: John Baez, Ole Barndorff-Nielsen (1935-2022), Charlotte Joko Beck (1917-2011), Johan van Bentham, Mark Evan Bonds, John Cage (1912-1992), Albert Camus (1913-1960), Nikolai Chentsov (1930-1992), John Miller Chernoff, Stewart Copeland, Sam Eilenberg (1913-1998), Paul Feyerabend (1924-1994), George Fowler (1929-2000), Kyle Gann, Alfred Gell (1945-1997), Herb Gintis, Jurgen Habermas, Charles Hamblin (1922-1985), Vaclav Havel (1936-2011), Lafcadio Hearn (1850-1904), Jaakko Hintikka (1929-2015), Eric von Hippel, Wilfrid Hodges, Christmas Humphreys (1901-1983), Jon Kabat-Zinn, Herman Kahn (1922-1983), John Maynard Keynes (1883-1946), Andrey Kolmogorov (1903-1987), Paul Krugman, Imre Lakatos (1922-1974), Trevor Leggett (1914-2000), George Leonard (1923-2010), Brad de Long, Donald MacKenzie, Saunders Mac Lane (1909-2005), Karl Marx (1818-1883), Grant McCracken, Henry Mintzberg, Philip Mirowski, Michel de Montaigne (1533-1592), Michael Porter, Charles Reich (1928-2019), Jean-Francois Revel (1924-2006), Daniel Rose, Bertrand Russell (1872-1970), Pierre Ryckmans (aka Simon Leys) (1935-2014), Oliver Sacks (1933-2015), Gunther Schuller (1925-2015), George Shackle (1903-1992), Cosma Shalizi, Rupert Sheldrake, Raymond Smullyan (1919-2017), Rory Stewart, Anne Sweeney (d. 2007), Nassim Taleb, Henry David Thoreau (1817-1862), Stephen Toulmin (1922-2009), Scott Turner, Roy Weintraub, Geoffrey Vickers VC (1894-1982), and Richard Wilson.
FOOTNOTES:
* Which makes me a grand-pupil of Nadia Boulanger (1887-1979).
** Of course, this being the World-Wide-Web, I need to explicitly say that nothing in what I have written here should be taken to mean that I agree with anything in particular which any of the people mentioned here have said or written.
A more complete list of teachers is here.
Newton and scientific publication
While on the subject of Isaac Newton, here are several statements by historian Scott Mandelbrote on Newton’s attitude to the public dissemination of his work. The more we know of Newton, the less we should consider him a scientist in the modern meaning of the word.
His [theological investigation] was a voyage of personal discovery; even the Principia required Halley’s exertions as a midwife to bring them to light. Newton might share his religious opinions with other members of the remnant, as he did in his letters to Locke, but he worried about the consequences of their wider dissemination: ‘I was of opinion my papers had lain still & am sorry to heare there is news about them. Let me entreat you to stop their translation & impression so soon as you can for I designe to suppress them.’ Newton’s concern may have reflected fear of being discovered to hold unorthodox opinions, but it was also the product of religious motives. Not everyone could be expected to comprehend ‘strong meat’, which was intended for personal consumption, and which might be wasted on others.” (p.299)
His [Newton’s] theology pervaded his alchemy, in his analysis of the Emerald Tablets of Hermes Trismegistus, and in turn his alchemy suggested to him how matter might be understood physically. A true understanding of the uses of language enabled Newton to introduce astronomical calculation into his chronological writings, and to complete his mathematical arguments with theological references:
[pagebreak]
. . . .
Mathematics was God’s language; the language of the prophets communicated God’s purposes and ‘times’ to men. Newton felt it was his duty to understand and to reconcile the two, to decipher the hieroglyphs which corrupted religion and learning had obscured. The problems of mathematics ended in the solutions of divine majesty, and mathematical language solved the theological problem of describing Newton’s Arian interpretation of the relations within the Trinity:
. . .
Newton’s natural philosophical and theological discoveries removed the obscurities from divine language, in the books of nature and of scripture. In the life of the true believer, the two could not be separated. But most had to be content with the milk for babes, because Newton’s own language was beyond them.” (pp. 300-301).
Reference:
Scott Mandelbrote [1993]: ‘A dute of the greatest moment’: Isaac Newton and the writing of biblical criticism. British Journal of the History of Science, 26: 281-302.
A salute to Thomas Harriott
Thomas Harriott (c. 1560-1621) was an English mathematician, navigator, explorer, linguist, writer, and astronomer. As was the case at that time, he worked in various branches of physics and chemistry, and he was probably the first modern European to learn a native American language. (As far as I have been able to discover, this language was Pamlico (Carolinian Algonquian), a member of the Eastern Algonquian sub-family, now sadly extinct.) He was among those brave sailors and scientists who traversed the Atlantic, in at least one journey in 1585-1586, during the early days of the modern European settlement of North America. Because of his mathematical and navigational skills, he was employed variously by Sir Walter Raleigh and by Henry Percy, 9th Earl of Northumberland, both of whom were rumoured to have interests in the occult and in the hermetic sciences. Harriott was the first person to use a symbol to represent the less-than relationship (“<“), a feat which may seem trivial, until you realize this was not something that Babylonian, Egyptian, Greek, Islamic, Indian, or Chinese mathematicians ever did; none of these cultures were slouches, mathematically.
Yesterday, 26 July 2009, was the 400th anniversary of Harriott’s drawing of the moon using a telescope, the first such drawing known. In doing this, he beat Galileo Galilei by a year. The Observer newspaper yesterday honoured him with a brief editorial.
Interestingly, Harriott was born about the same year as the poet Robert Southwell, although I don’t know if they ever met. Southwell spent most of his teenage years and early adulthood abroad, and upon his return to England was either living in hiding or in prison. So a meeting between the two was probably unlikely. But they would have each known of each other.
Previous posts in this series are here. An index to posts about the Matherati is here.
The French Member of the English Language Committee of the IMO
The International Mathematics Olympiad is a famous international competition for mathematics students. This is an excerpt from the diary of the Chairman of the English Language Committee (ELC) of the 2005 IMO , Geoff Smith:
In the evening I prepare for the English language committee which I will chair next day. This means I slope off to my room early and try to cast the questions in perfect English myself, in order to have something to start with. The committee meets first thing in the morning. These days everyone is welcome in the ELC, including its most important member, the leader of France. We like to have simple sentences in IMO questions; ones which ideally can be translated almost word for word into as many languages as possible. French is rather special, and does not allow the rather free word order and grammatical latitude of English. Therefore the English language version has to be designed so that it can be easily translated into French. As each English sentence is suggested, we turn to FRA7, Claude Deschamps, to receive either a blessing (a shrug which indicates that all is well) or a sad shaking of the head which indicates that a particular piece of Anglo-Saxon thuggery simply cannot be expressed in French.”