**L N G Filon** was French-born English mathematician, best known for his work on classical mechanics and elasticity.

- He taught at the lycées in Nice and Grenoble, and was a prolific author and theatre critic sometimes writing under the pseudonym Pierre Sandrié.
- She appeared as Sparkeion in Thespis, or The Gods Grown Old, Gilbert and Sullivan's first collaboration, at the Gaiety Theatre in London, premièred on 26 December 1871.
- Augustin Filon suffered a severe illness in 1877 which left him almost completely blind.
- In 1878 he settled permanently in England, living first at Margate.
- He began Latin and Greek before he was six.
- His ambition was to be a sailor.
- He was always drawing pictures of boats at sea, and some good models of ships he made at this time are still in existence.
- In 1888 Filon began his studies at Herne House School in Margate.
- This boarding school for boys opened in 1881, founded by William Taylor Jones who was the headmaster.
- At the time of the 1891 census, Filon is a 'scholar' at this school and is living at home in the Thanet district of Margate with his parents.
- They have a general domestic servant, Grace Fanner.
- Filon and his parents are French subjects at this time and only later does Filon become naturalised British.
- While at Herne House School, Filon showed no interest in mathematics and when he entered University College, London in 1894 he started on the standard B.A. course.
- He won the medal for Greek but he had quickly showed that he had an exceptional talent for mathematics and graduated in 1896 with honours in mathematics.
- He also received the Ellen Watson Scholarship for Applied Mathematics, and the Malden Medal and Scholarship.
- He was awarded an M.A. in 1898 with the Gold Medal.
- He was taught by Karl Pearson who had been appointed as Goldsmid Professor of Applied Mathematics at University College in 1885.
- When he graduated Filon had thoughts of becoming a painter and he had already exhibited a considerable talent for this.
- Karl Pearson, however, had seen the abilities that his young student possessed and offered him a position as a Demonstrator in Applied Mathematics.
- Nowadays young people expect at least £250 a year in the same circumstances, but then they do not get the stimulus of a Karl Pearson, which was worth more to me than the difference.
- K.P. lectured to us on the 'Mathematical Theory of Statistics', and on one occasion wrote down a certain integral as zero, which it should have been on an accepted general principal.
- It was typical of K.P. that, the moment he was really convinced, he saw the full consequences of the result, proceeded at once to build up a new theory (which involved scrapping some previously published results) and generously associated me with himself in the resulting paper.
- The joint paper with Karl Pearson which Filon refers to in this quote is Mathematical contributions to the theory of evolution.
- IV: On the probable errors of frequency constants and on the influence of random selection on variation and correlation, an 82-page paper published in 1898 by the Royal Society.
- A certificate was issued on 1 March 1898 and after he signed the Oath of Allegiance on 4 March 1898 he became a naturalised British subject.
- Filon was awarded an 1851 Scholarship in 1898 by the Royal Commission for the Exhibition of 1851 which had originally the aim to "increase the means of industrial education and extend the influence of science and art upon productive industry" but in 1891 the emphasis had been changed to the support of individuals with the award of scholarships.
- With the support of the scholarship, Filon went to King's College, Cambridge, where he remained registered as an Advanced Student from 14 October 1898 to 1903.
- His research papers show a wide range of interests at this time: On certain diffraction fringes as applied to micrometric observations (1899); On the resistance to torsion of certain forms of shafting with special reference to the effect of keyways (1900); (with Karl Pearson) On the flexure of heavy beams subjected to continuous systems of load (1900); Reductions of photographs of Swift's comet (α 899) taken at Cambridge Observatory with a portrait lens (1902); and On the elastic equilibrium of circular cylinders under certain practical systems of load (1902).
- This last mentioned paper on elasticity marks the start of Filon's work on this topic on which he specialised throughout his career.
- While holding the Advanced Student status at Cambridge, he was also an Assistant Professor of Applied Mathematics at University College, London from 1899 to 1900 being awarded a B.Sc. from the University of London in 1900.
- He was resident at Cambridge during 1900-1902, his degree dissertation was approved in 1900 and Cambridge awarded him a B.A. in 1901.
- He was awarded a D.Sc. by the University of London in 1902.
- In 1903 he was appointed as a lecturer in pure mathematics at University College, London, in the department headed by M J M Hill.
- Micaiah John Muller Hill (1856-1929) had been appointed to the chair of mathematics at University College, London, in 1884 and continued to hold this position until he retired in 1924.
- They have a cook and a nurse.
- Filon was not a pure mathematician in the way that the term is understood today; for him mathematics was a tool to be used in solving physics problems.
- As a lecturer in pure mathematics he was expected to teach the subject but this led to difficulties when he proposed teaching a course on the differential equations of mathematical physics.
- He developed a liking for teaching geometry, particularly projective geometry.
- After a theoretical course on this topic he followed it with practical classes on making accurate drawings of projections.
- He was perhaps a little ashamed of this, for he realised that it was difficult to reconcile with his somewhat utilitarian attitude towards mathematics, and he took a special delight in producing examples, sometimes a little strained, of the application of projective geometry to problems of physics or astronomy.
- This interest led to him publishing the book An Introduction to Projective Geometry (1908).
- He had already undertaken joint research with M J M Hill on projective geometry and they had published the joint paper On the projection of two triangles on to the same triangle (1905).
- On 5 May 1910 Filon was elected a fellow of the Royal Society; G H Hardy was elected a fellow of the Royal Society on the same occasion.
- In 1911 Karl Pearson was appointed as the Galton Professor of Eugenics and head of the Department of Applied Statistics in University College.
- He had to give up the Goldsmid chair of Applied Mathematics and, in 1912, Filon was appointed as his successor in the Goldsmid chair of Applied Mathematics.
- This now meant he held a chair that fitted his interests perfectly and it gave him a new enthusiasm.
- George Barker Jeffery had been appointed as his research student and assistant in 1912 and, when Filon left for War Service, Jeffery became acting head of the Applied Mathematics Department.
- Filon had been a 2nd Lieutenant in the University of London Officers' Training Corps since January 1909, and had been promoted to Captain in December 1910.
- Britain declared war on Germany on 4 August 1914 and on the following day Filon attended the General Staff Office and was sent to France.
- He served in France from August 1914 to February 1915 when he was invalided and returned to London.
- He was made a temporary Major, in charge of the 2nd (Reserve) Battalion London Regiment on 11 March 1915.
- Although he was doing an excellent job with the London Regiment, he was not using his technical skills so, on 27 November 1916, he was seconded to the technical staff of the Admiralty.
- He was in charge of the School for Instruction of Officers in London and then head of the Instrument Section of the Technical Department of the Air Board.
- On 28 December 1917 he was seconded to the Royal Flying Corps, which was the air arm of the British Army.
- On 1 April 1918 the Royal Flying Corps merged with the Royal Naval Air Service to form the Royal Air Force and so Filon was in the R.A.F. from its formation.
- He was mentioned twice in War Office Communiqués "for valuable services rendered," first in the Communiqué of 24 February 1917 as Major in the London Regiment (Territorial Force) and for a second time in the Communiqué of 13 March 1918.
- Not surprisingly, Filon published no papers between 1914 and 1918, but after he returned to his chair of Applied Mathematics at University College London, he was again research active.
- Three of his papers appears in 1918, two in 1919 and another two in 1920.
- Papers were on his main topic of elasticity and on spherical aberration in a lens, topics he had worked on before the War.
- But now there were also the papers Investigations of stresses in aeroplane wing frameworks (1919) and Position fixing in aircraft during long distance flights over sea (1920) which were motivated by war work.
- The experiments were carried out by Mr Chakko and Air-Cadet McGowan, under the general supervision of Major A R Low, R.A.F., and Major L N G Filon, R.A.F. An account of these experiments has been given by Major A R Low in the 'Aeronautical Journal' for November 1918.
- The object of the investigation was to test a theory, due to Mr Harris Booth and Mr Harold Bolas, and further developed by Mr Arthur Berry, for calculating the stresses in the frameworks carrying aeroplane wings.
- This theory, of which an account is being published in the 'Transactions of the Royal Aeronautical Society', contains an extension of Clapeyron's well-known theorem of 'Three Moments', so as to include the effects of bending moment due to end-thrust.
- The fundamental assumption made in this theory is that the nodes of the framework, originally collinear and horizontal, remain collinear and horizontal when the load is applied, so that we can treat them, for mathematical purposes, as fixed points.
- The second half of the assumption - namely, that the nodes remain horizontal - is not essential, for we can, without sensible error to the order of approximation considered, measure deflections from the line of nodes.
- But the first assumption - namely, that the nodes remain collinear - is of primary importance.
- Although still very active as a researcher, Filon began to take a larger part in University affairs.
- In 1920 he was elected to the University of London senate and he continued to serve on this body for seventeen years until his death.
- Needless to say, his unswerving devotion to what he considered right, and his lack of that praiseworthy pliancy and useful obliquity which adorn some of our leading administrators, occasionally led him to oppose certain notable personalities, but, in spite of this, his services were so outstanding that he was elected vice-chancellor of the University in 1933-35, the period during which the foundation stone of the candid and considerable -may we say elephantine - University building was laid.
- Filon was a dedicated teacher and his interest in teaching led him to be an enthusiastic supporter of the Mathematical Association.
- He was elected President of the London Branch of the Mathematical Association for 1924-25 and delivered his Presidential Address on 31 January 1925 entitled The beginnings of arithmetic.
- Educational experience suggests that a similar process occurs in mental development, so that, generally speaking, ideas have to be introduced in the order of their historical occurrence, if unnecessary resistance is not to be encountered.
- A study of the early history of any branch of knowledge is therefore, apart from its interest to the curious, of practical importance to those concerned in teaching it.
- It is this consideration which has led me to select, as the subject of my remarks this afternoon, the primitive stages in the history of Arithmetic.
- He was elected President of the Mathematical Association for 1937-38 but died during his term of office, less than one week before the Annual Meeting of the Association at which he would have delivered his Presidential Address.
- He had a deep knowledge of the early history of astronomy, and gave an excellent course on the subject.
- he transformed the teaching of astronomy in his College.
- He found it largely theoretical in its treatment, though under his predecessor and revered teacher Karl Pearson practical instruction had been given in a small observatory in the College grounds.
- He left it as a highly developed subject in many of its branches and as Director of an active University Observatory at Mill Hill.
- Prepared with a characteristic thoroughness, they were delivered in a clear and unhesitating manner and illustrated by a supreme command of the blackboard.
- When in later life responsibilities crowded upon him, and his friends were amazed at the amount of work of different kinds that he could get through, nothing was allowed to diminish the care and attention he gave to his teaching work.
- Relativity, particularly the "general theory", seemed to him to rest on too slender an experimental basis.
- He regarded it as a kind of pure mathematics that had drifted out of touch with reality.
- He modified this attitude somewhat in later years and made serious efforts in his lectures to put the "special" theory into logical form.
- For the quantum theorists, however, he had nothing but scorn.
- Their constantly changing hypotheses seemed to him to be sheer madness and the negation of that logical structure he expected to find in mechanics.
- As it was gradually borne in on him that the theory was actually producing good results, he found it very difficult to understand how this could possibly be.
- A congenial companion and a warm-hearted friend, he occasionally indulged in short bursts of irascibility, which, if they arose suddenly, as suddenly subsided.
- These outbreaks, so well known to his friends, were purely superficial disturbances, for fundamentally Filon was one of the most generous and kindly of men, who would put himself to great trouble even for those who had small claims on him.
- Nobody could be a pleasanter speaker or a better host.
- At the age of 62, Filon died as a result of a typhoid epidemic which swept through Croydon.
- A fit man, he seemed to be well on the way to recovering when the disease suddenly overcame him.
- The epidemic was caused by a polluted water well and resulted in 341 residents of Croydon who received water from the well becoming ill, and Filon was one of 43 deaths from the epidemic.

Born 22 November 1875, Saint Cloud, near Paris, France. Died 29 December 1937, Croydon, Surrey, England.

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**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive