OBITUARIES

Click on a name in the alphabetical list below.

Baker, John
Cuninghame-Green, Raymond
Flanders, Harley
Ghaffari, Abolghassem
Halberstam, Heini
Jones, Douglas
Norman, Christopher
Orchel, Andrzej
Rees, David
Rees, Joan
Watson, John
Wilson, John

Earlier death notices can be found in the Published Issues.

 


 

 

CHRISTOPHER NORMAN

Published online 25 March 2014

Chris NormanChristopher W. Norman, who was elected a member of the London Mathematical Society on 20 June 1963, died on 25 January 2014, aged 76.

Eira Scourfield writes:  Chris was born on 23 April 1937 and spent his childhood in Bedfordshire.  He was an undergraduate at the University of Birmingham, graduating in Mathematics in 1958, before becoming a research student at Balliol College, University of Oxford, and working in algebraic topology under the supervision of Professor Ioan M. James.  He was awarded his DPhil in 1961 before taking up a lecturing position at Westfield College, University of London.  He remained there until 1984 when the reorganization of the University of London saw him and seven mathematical colleagues transferred to Royal Holloway.  He was promoted to Senior Lecturer in 1997 and retired in 2001.

Research in algebra at Westfield College was strengthened when Dan Hughes was appointed in the mid 60’s, so Chris decided to switch his research to this area.  He published some thirteen research papers, mostly in algebra; his only joint paper was with Fred Piper.  He had two research students.  Chris became particularly interested in problems concerning canonical forms and Jordan forms and bases which culminated in three papers in the 1990’s and one in 2008.  In addition he wrote two undergraduate textbooks in algebra based on his lectures at Westfield College and Royal Holloway; one at first year level was published in 1986 and another for the next two levels appeared in 2012.  Chris was highly regarded as a teacher by his students, and they appreciated his exceptionally well prepared lectures, his excellent handwriting and his willingness to help them. Several students remained in contact with him for years after they graduated.  He was a valued colleague, always willing to do reliably, efficiently and without fuss whatever administrative tasks were asked of him.

Chris met his wife Lucy (formerly Wyatt) when she joined the French Department at Westfield College and they married in 1969. They had one son Timothy and a granddaughter arrived in 2013.  From 1984 the family home was in Ascot and Chris enjoyed tending his garden.  He learnt to play the organ as a teenager and this interest continued throughout his life. When at Westfield College he played the organ at church services nearby, and then afterwards he was a church organist in Bracknell for 25 years. Chris became ill in August 2013 and died of cancer less than six months later.

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JOHN BAKER

Published online 25 March 2014

John BakerDr John W. Baker, who was elected a member of the London Mathematical Society on 21 December 1961, died on 8 November 2013, aged 75.

John Pym writes: John Baker was born on 31 March 1938 in Finsbury, London. From the Trinity School of John Whitgift, Croydon, he went to the University of Reading, leaving in 1961 with an MSc (by research). There he met his future wife, Sally,and they moved together to the University of Wales at Swansea, John as Assistant Lecturer and Sally as Research Fellow. John's initial research, and his first five papers, were in summability theory. His PhD was awarded in 1966.

At this point he switched interests to functional analysis, an area for which Swansea was renowned. John was drawn into generalisations of group algebras. His success led to his appointment at the University of Sheffield in 1969, where he was soon promoted to senior lecturer. Perhaps his most substantial achievement was in a series of three papers in the LMS Journal written jointly with Sally. He proposed what, with hindsight, was obviously the correct generalisation of the group algebra to locally compact semigroups, presenting elegant alternative characterisations of this algebra and developing its theory.  He went on to write over 40 research papers.  He contributed a survey to The Analytical and Topological Theory of Semigroups (1990), one described by a reviewer as the `most scholarly’ in the book.

That remark captures one of John's invaluable qualities. If he was tasked with doing a job, he did it conscientiously and effectively.  Of his research students, three have become academics with strong publication lists. He taught well everything the department asked of him.  His qualities as an administrator were `rewarded' with the problems of becoming Head of Pure Mathematics.

After early retirement in 2000, John continued serving the community as a leading trustee of a Sheffield charity which exists to help refugees integrate into British society. He is survived by a daughter, Sandra, and a son, Simon.

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HEINI HALBERSTAM

Published online 6 February 2014

Heini Halberstam

Professor Heini Halberstam, who was elected a member of the London Mathematical Society on 25 November 1954, died 25 January 2014 in Champaign, Illinois, aged 87.

Harold Diamond writes: Born in Brux, Czechoslovakia, Heini came to Britain in the Kindertransport program in 1939.  With the care and support of Anne Welsford, Heini attended University College, London, where he earned his PhD degree in 1952 under the direction of T. Estermann.  In 1987, he was elected a Fellow of University College.

After positions in Exeter, Royal Holloway, and Dublin, Heini moved in 1964 to Nottingham, where he served at times as Department Head and Dean of Faculty.  Heini came to the University of Illinois in Urbana-Champaign in 1980, was eight years Department Head, and retired as an emeritus professor in 1996.  He also held several visiting positions.

Heini's research ranged over several areas of analytic number theory, most importantly, sieve theory.  His conjecture with P.D.T.A. Elliott about the distribution of prime numbers in arithmetic progressions is one of the outstanding open problems in this area.  Heini was an author of several influential research monographs.  Sequences, with K.F. Roth, made accessible such areas as sums of integers from given sequences and the probabilistic method of Erdös and Renyi. Sieve Methods, with H.E. Richert, provided accounts (some for the first time) of important work of Brun, Selberg, Rosser-Iwaniec, and J.R. Chen.  A Higher Dimensional Sieve Method grew out of his research with Richert and H. Diamond.

Heini supervised 14 PhD.s and many masters students and post-docs, several of whom are now distinguished number thorists.  He also was a force for mathematical education in both Nottingham and the U.S.

Heini was active in the LMS and served as a Vice President and as Secretary of the LMS Journal.  Also, he was a long-time member and a Fellow of the American Mathematical Society.  He was on the editorial board of several journals and wrote over 150 Mathematical Reviews. Heini edited or co-edited the collected mathematical papers of W.R. Hamilton, H. Davenport, J.E. Littlewood, and L.K. Hua, and he co-edited the proceedings of two conferences.

Heini's first wife, Heather, died in 1971. He is survived by his second wife, Doreen, who lives in Champaign, IL; by two children living in the U.S.; by two children and two step children in Britain; and by eight grandchildren, all in Britain.

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ANDRZEJ WOJCIECH ORCHEL

Published online 17 January 2014


Andrzej Wojciech Orchel

Dr Andrzej W. Orchel, who was elected a member of the London Mathematical Society on 22 November 1969, died on 22 January 2012, aged 65.

Jack Orchel writes: Andrzej (Andrew) Orchel was born in Edinburgh on 16 January 1947. The second of four sons of Dr Eugeniusz and Rozalia Orchel (née Wasylkowska), he attended St Mary’s RC College in Middlesbrough where his interest in projective geometry was ignited by his mathematics teacher Fred Jackson.

Andrew’s undergraduate and postgraduate studies were pursued at Queen Elizabeth College in London from 1966 to 1972. There he was inspired by Dr Otto Wagner. Working alone for several years Andrew eventually produced a doctoral thesis entitled Finite Groups and Associated Mathematical Spaces in which he solved a challenging problem first proposed by Wagner in 1961, later associated with a conjecture of Marshall Hall. Andrew was awarded his PhD and elected a member of the London Mathematical Society in 1979.   Unfortunately, he was burdened with a chronic debilitating illness which had become apparent in his early twenties. This interfered with his advanced studies and prevented him from pursuing an academic career.

Writing in December 1983 Professor W.B. Bonnor of Queen Elizabeth College, London, stated that whilst at QEC Andrew ‘was a brilliant student, especially on the pure mathematical side, and his (undergraduate) marks in Galois theory still rank among the best we have ever had...When he left the college (in 1972) he continued his researches and, in spite of serious ill health which necessitated several operations, he was awarded the PhD of London University...’ Professor Bonnor also described Andrew as a ‘friendly, kindly man, with a strong sense of humour’ and ‘many other excellent qualities, among them persistence, determination and courage.’

Andrew worked briefly for ICI on Teesside but was forced to lead a reclusive lifestyle at the family home in Linthorpe where he was happiest. He was a keen student of nature, a talented amateur photographer and artist and read widely. He devoted much time to studying P shapes and delighted in making discoveries in this field. His legacy lies in his huge archive of photographs and diaries which documents the life of the Orchel family. He died suddenly of a heart attack on 22 January 2012 a few days after his 65th birthday.

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DOUGLAS JONES

Published online 17 January 2014


Douglas Jones

Professor Douglas Samuel Jones, FRS, FRSE, who was elected a member of the London Mathematical Society on 18 May 1979, died on 26 November 2013, aged 91.

Brian Sleeman writes: Douglas Jones was born in Corby, Northants, on 10 January 1922. He won a scholarship to Wolverhampton Grammar School where he became Senior Prefect, Captain of both Chess and Cricket as well as Vice-Captain of Soccer. In 1940 Douglas won an open scholarship to Corpus Christi College, Oxford. As was the experience of many young men of that period Douglas's University career was interrupted by call up for war service. He joined the Royal Air Force and in 1942, as a Signals radar officer with the rank of Flight Lieutenant, led a research unit of about 100 people engaged in designing and commissioning new equipment for night fighter operations. In recognition of his abilities Douglas was ‘Mentioned in Dispatches’ in 1943 and awarded an MBE in 1945. In the same year he returned to Oxford graduating MA in 1947. 

Following a year as a Commonwealth Fellow at MIT, Douglas was appointed to an assistant lectureship at Manchester University rising to Senior Lecturer in 1955. It was during this period that Douglas made fundamental contributions to diffraction theory and demonstrated his phenomenal abilities as an analyst. In 1957 he moved to the Chair of Mathematics at the University of Keele where his reputation as a world leader was established with the publication of his monumental book The Theory of Electromagnetism. In 1965 Douglas was appointed to the Ivory Chair of Applied Mathematics at the University of Dundee, a position he held with great distinction until his retirement in 1992, at which point he was made Emeritus Professor.

Douglas's style and approach to mathematical research is nicely encapsulated by the following remark of Sir James Lighthill relating to the theory of generalised functions made at the 1992 Dundee conference to mark his 70th birthday. It concerns Douglas's book The Theory of Generalised Functions.

“I have moreover been overjoyed that my tiny 80-page Introduction to Fourier Analysis and Generalised Functions, which concentrates on functions of just one variable, has proved to be a suitable appetite-whetting ‘starter’, as it were, leading up to Douglas's superbly concocted ‘main dish’ in 540 pages which extends all the results in a comprehensive fashion and includes the corresponding properties of functions of many variables.”

During his career his achievements have been recognised by numerous honours; Fellowship of the Royal Society, Fellowship of the Royal Society of Edinburgh and Honorary DSc of the University of Strathclyde. He was also elected an Honorary Fellow of Corpus Christi College Oxford, recipient of the Naylor Prize and Lectureship in Applied Mathematics of the London Mathematical Society, the Marconi prize of the Institute of Electrical Engineers, the van der Pol Gold Medal of the International Union of Radio Science and the Keith Prize of the Royal Society of Edinburgh.

Douglas was a tireless champion and campaigner for the promotion of mathematics and that of the professional mathematician. He was chairman of the UGC (now HEFCE) mathematics sub-committee. Within the wider community Douglas was a founding member of the Institute of Mathematics and its Applications (IMA) served on Council and was appointed President in 1988. It was during his Presidency that he led the negotiations with the Privy Council which resulted in the IMA being incorporated by Royal Charter and then subsequently granted the right to award Chartered Mathematician status.

Douglas was a fine man, a friend and mentor and is greatly missed. He was pre-deceased by his wife Ivy and is survived by his sisters Dot and Joyce.

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ABOLGHASSEM GHAFFARI

Published online 3 January 2014


Abolghassem Ghaffari

Dr Abolghassem Ghaffari, who was elected a member of the London Mathematical Society on 22 May 1947, died on 5 November 2013, aged 106.

Vida Ghaffari writes: born in Tehran in 1907, he was educated at Darolfonoun School (Tehran). In 1929, he went to France and studied Mathematics and Physics at Nancy University, where he took his L-es-Sc. in Mathematics in 1932. After obtaining post-graduate diplomas in Physics, Astronomy, and Higher Analysis, he obtained in 1936 his doctorate from the Sorbonne (Doctor of Sciences with mention très honorable) for basic research on Mathematical Study of Brownian Motion.

Dr Ghaffari lectured as a Research Associate at King’s College, London, where he received his PhD from the Mathematics Department on the Velocity-Correction Factors and the Hodograph Method in Gas Dynamics. As a Fulbright Scholar, he worked at Harvard University as a Research Associate to lecture on Differential Equations and to continue his research on Gas Dynamics.

He was a Research Associate in Mathematics at Princeton University, and at the Institute for Advanced Study, he worked in the early 1950s with Albert Einstein on the Unified Field Theory of Gravitation and Electromagnetism. J. Robert Oppenheimer, who headed the US atom bomb program during World War II, was director of the Institute at the time and interviewed Ghaffari before the latter became a member of the Institute (Oppenheimer later befriended Ghaffari).

He lectured as a Professor of Mathematics at American University in Washington, DC and at Tehran University, where he joined the Faculty of Sciences and was appointed full Professor of Higher Analysis from 1941-56.

In 1956, Ghaffari moved permanently to the US to take up a position as a senior mathematician at the US National Bureau of Standards. Part of his work there involved calculations of the motion of artificial satellites.

In 1964, three years into the manned space program, he joined, as aerospace scientist, the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center, where he studied the mathematical aspects of different optimization techniques involved in the Earth-Moon trajectory problems, and different analytical methods for multiple midcourse manoeuvres in interplanetary guidance. He later investigated the effects of solar radiation pressure on the Radio Astronomy Explorer Satellite Booms as well as the effects of General Relativity on the orbits of Artificial Earth Satellites.

He was awarded in Iran the Imperial Orders of the late Mohammad Reza Shah Pahlavi, and the US Special Apollo Achievement award (1969) at a White House ceremony with President Nixon. He published more than 50 papers on pure and applied mathematics in American, British, French, and Persian periodicals. In addition to two textbooks, he is author of The Hodograph Method in Gas Dynamics (1950).

In 2005, Ghaffari received the Distinguished Scholar award from the Association of Professors and Scholars of Iranian Heritage (APSIH) at UCLA. In 2007, he received a proclamation from former Beverly Hills mayor and current Goodwill Ambassador Jimmy Delshad acknowledging his numerous lifetime achievements. He also recently was appointed as a Hall of Fame inductee by SINA (Spirit of Noted Achievers) at Harvard University.

He was a past member of the Iranian National Commission of UNESCO. Ghaffari was a Fellow of the New York Academy of Sciences, the Washington Academy of Sciences, and the American Association for the Advancement of Sciences and a member of the London Mathematical Society, the American Mathematical Society, The Mathematical Association of America, and the American Astronomical Society.

He is survived by his wife, Mitra, and his two daughters, Ida and Vida. He is interred at Pierce Brothers Valhalla Memorial Park in Burbank, California. In lieu of flowers, his one wish was to have a scholarship in his name for young Iranians studying Mathematics or Science. Details on the scholarship will be soon announced. 

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JOHN WATSON

Published online 22 October 2013


John Watson

Dr John Waton, who was elected a member of the London Mathematical Society on 17 February 1995, died on 16 July 2013, aged 83.

Trevor Stuart writes: John Watson was born in 1930 in the Scottish County of Fife, living as a child in Cellardyke, which is close to Anstruther on the Firth of Forth. His father was the captain of a fishing boat from Anstruther. His mother, whom I met in 1958 in Cellardyke during a break from the International Congress of Mathematicians in Edinburgh, was very hospitable. He had two brothers. After attending a primary school in Fife, John entered Robert Gordon’s College in Aberdeen for his secondary education and followed this by joining the University of Aberdeen to study mathematics, which was by far his major love academically. It was in Aberdeen that he met his future wife, Eve, who hailed from the Orkneys and whom he married in 1955. After graduation from Aberdeen he was awarded a scholarship to study for a post graduate degree in Aeronautical Engineering in the University of Cambridge, following which he joined the National Physical Laboratory (NPL) in its Aerodynamics Division, which was natural in view of his studies in Cambridge. It was there that I first met John in 1954, as he and I worked in the same Theoretical Section. From 1966 until his retirement in 1995 he was a member of the Faculty of the School of Mathematics (initially the school of Mathematics and Physics) at the University of East Anglia, where he was a dedicated teacher who was well-liked by all his students; there he showed a preference for the purer aspects of mathematics, which was ironic as his research achievements lay in applied mathematics, as is emphasized below. During the 1960s John spent a year as a visitor at the Rensselaer Polytechnic Institute in Troy, New York, where he pursued his research and commenced teaching of mathematics. .

In his research John was primarily distinguished for his work on nonlinear instability waves in fluid flows, as one possible precursor to turbulence; in this he followed in the tradition of the theoretical physicist L.D. Landau in the early 1940s and the present writer in the late 1950s. They had outlined the way in which nonlinear waves might be studied by means of an amplitude equation. Details were left to other mathematicians to study and to clarify, one of whom was John, who took up the challenge and was, I believe, the first to calculate higher-order terms beyond the cubic term in an equation of the form dA[t]/dt = aA  + higher powers of A and |A| for the amplitude A of the wave, where a is a known parameter. This was a fine achievement, which is regularly quoted today (much to the astonishment of John, who was so modest).

John was such a likeable, albeit modest, man, who was respected by all who met him and who will be long remembered for his personal qualities as well as for his research achievements.

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JOHN WILSON
Published online 01 October 2013

John Wilson

Dr John P. Wilson, who was elected a member of the London Mathematical Society on 16 December 1964, died on 9 August 2013, aged 76.

John Dyke writes: John first worked for the Open University in the North Region in 1973 and taught on our initial mathematics foundation course, M100.  He taught a range of courses there up to his departure to Bishops Castle.  His contribution to both North Region and Wales were highly valued and he came with excellent recommendation to us in Wales. 

In Wales, John taught the History of Mathematics Course, MA290, from 1994 up to his retirement in 2002.  His tutoring was of the highest calibre and he was well liked by both staff and students.  His enthusiasm and passion for the history of mathematics were passed on to many of his students.  I remember talking to an arts student who had studied the history of mathematic course with John, as an arts course.  He said that he had developed a great interest in mathematics, a subject he had previously feared, and would be pursuing it further in his studies.   

In 2002 John told us of his illness and his intention to resign at the conclusion of the current year.  We were saddened by the bad news of his illness and also at losing a valued colleague. 

John Bolton and Derek Wilson write: John was born in Northampton in 1937, and read Mathematics at Liverpool University. After graduating in 1959, he took an MSc at Liverpool, and was then appointed as lecturer at Aberystwyth where he also studied for his PhD - successfully completing this in 1965. It was here that he met and subsequently married Margaret.

John was then appointed to a lectureship at Durham, where he took a keen interest in both his teaching and research. His research interests were in Topology and Differential Geometry, particularly of Homogeneous Spaces. He was also a talented linguist; indeed, he followed language courses to A-level at school, and, at the request of publishers, he translated Russian mathematical papers and also several volumes of Bourbaki from French to English. This took many hours of his time for several years in the 1970s. In the 1980s, John became interested in computer languages and simulation as a means of solving problems in industry, completing an MSc in Computing Science (at Newcastle) in 1983. For many years he was also a pastoral tutor at residential colleges for students of Durham University, firstly St Cuthbert's Society, and later at St Chad's and St Mary's. In the late sixties, he spent some time at the University of Ife in Nigeria (now called the Obafemi Awolowo University), helping them to develop their mathematical programme. He took early retirement from Durham in 1995 due to ill health.

John suffered several years of ill-health. However, his love of geometry persisted to the end, which caused much puzzlement for the non-mathematically minded nurses!

He is survived by his wife Margaret, sons Mark and Alexander and two grandchildren.

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JOAN REES

Published online 01 October 2013


Joan Rees

Dr Joan Sybil Rees, née Cushen, who was elected a member of the LMS on 15 June 1972, died on 28 August 2013, aged 89.

David Oates, aided by Mary and Sarah Rees, writes: born to a school-teaching family in Portsmouth on 25 August 1924 and after some war-time disruption, Joan took up a scholarship at Girton College in 1942.  Taught by Mary Cartwright and Bertha Jeffreys, and the only woman to get a mathematics first for two years, she began a PhD on Algebraic Geometry with Hodge. This was completed under Dan Pedoe at Royal Holloway College, where the duties of her lectureship included playing the double bass left by the previous incumbent.

Returning to a Fellowship at Girton, she entered into a lifetime as an enthusiastic and inspiring teacher and friend, much loved by her students and colleagues. The Fellowship had to be relinquished on marriage to David Rees in 1952 and Joan continued as a supervisor between the births of the first three of their four daughters.

After their move to Exeter in 1958, she devoted herself to the needs of the family, eventually taking a post teaching at the Maynard School.  In 1965 Joan began 19 years lecturing in David’s Department.  Here, as in everything, she was the ideal complement to David’s quiet authority. Differential geometry was a particular joy to her, aided by models including a paint-stiffened pair of tights to demonstrate saddle points.

Joan was quite profoundly deaf from childhood.  However, very few even noticed how heavily dependent she was on her expert lip reading.  Reflections following a near-fatal attack of scarlet fever engendered a deep religious faith and a lifelong devotion to the high end of Anglicanism – ‘anything a bit spiky’, as she put it. After the family had left home she fulfilled a long-held ambition to convert to Roman Catholicism, subsequently taking a great interest in the local RC schools.

Joan was an accomplished watercolourist and many friends have pictures from her exhibitions decorating their walls. Having been a Cambridge blue for swimming (and lacrosse and squash), she became a great devotee of sea bathing – often in weather that would make others shudder. For many, the typical image was of a well-wrapped Joan sitting at an easel on Dawlish Warren beach in a howling gale painting happily away.

Joan was a great friend and inspiration to many, remaining her active and enthusiastic self until just the last few months.

Joan’s husband David died just twelve days earlier; they are survived by their daughters Mary, Rebecca, Sarah and Deborah.

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DAVID REES

Published online 30 August 2013

David Rees

David Rees FRS, who was elected a member of the London Mathematical Society on 23 May 1946 and who was awarded the Society’s Pólya Prize in 1993, died on 16 August 2013, aged 95.       

Rodney Sharp writes: David’s undergraduate studies during 1936-39 at Sidney Sussex College, Cambridge, were supervised by Gordon Welchman.  Although David began postgraduate work, on semigroup theory, in autumn 1939, the war intervened.  Gordon Welchman recruited David and other young Cambridge mathematicians to work at Bletchley Park, the British codebreaking centre, where they became part of a team that broke the Enigma code. 

After the war, David was appointed to an Assistant Lectureship at Manchester University, and then, in 1948, to a University Lectureship at Cambridge and a Fellowship at Downing College.  While at Manchester, and for his first years as a Cambridge fellow, he worked on semigroups and other non-commutative algebra.  Rees factor semigroups and Rees matrix semigroups are named after David.

His life changed following a very successful working seminar in Cambridge, organized by Douglas Northcott, on Weil’s book Foundations of algebraic geometry.  First, David Rees was so inspired by the seminar that he became a commutative algebraist. Second, another participant in the seminar was Joan Cushen, and David and Joan were married in 1952.

In David’s first paper in commutative algebra, written jointly with Douglas Northcott about 60 years ago, they introduced the concept of reduction of an ideal in a local ring.  Even in this 21st century, hardly a conference on commutative algebra passes without several mentions of reductions of ideals. 

David Rees left Cambridge in 1958 to take up a chair at the University of Exeter, where he remained until his retirement in 1983.  He carried out his duties as head of department with care and consideration. The associated administrative tasks reduced the time he had available for research, but he had a burst of research activity after his retirement.

David’s fundamental work on valuations associated with local rings and ideals, and on grade, and his above-mentioned work on reductions of ideals, together with the familiar (at least for commutative algebraists) expressions ‘Rees ring’ and ‘Artin–Rees Lemma’, ensure that his legacy to commutative algebra will be lasting.

David's wife Joan survived him by just twelve days; they are survived by their daughters Mary, Rebecca, Sarah and Deborah.

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RAYMOND CUNINGHAME-GREEN

Published online 28 August 2013


Raymond Cuninghame-Green

Professor Raymond Cuninghame-Green MA, PhD, DSc, FBCS, FIMA who was elected a member of the London Mathematical Society on 18 May 1961, died on 9 June 2013, shortly before his 80th birthday.

Peter Butkovic writes: Ray was Professor of Industrial Mathematics at the School of Mathematics in Birmingham 1975-99 and the Head of School 1994-97. He lay the foundations of management mathematics at Birmingham. Ray retired in 1999 but remained research active.

Ray Cuninghame-Green is known as one of the first pioneers of max-algebra, today also known as tropical mathematics. His first paper on max-algebra was published in 1960. Ray was probably the first who realised that the maximum cycle mean of a matrix is its principal max-eigenvalue (1962). He achieved fundamental results in the theory of max-linear systems, including linear independence, tropical rank, residuation, duality, maxpolynomials, the discovery of the characteristic maxpolynomial, rational functions and the proofs of several results for irreducible or finite matrices proved in full generality in the 1980s and 1990s by other authors, such as the complete description of (max-algebraic) eigenspaces, the cyclicity theorem or spectral projector. Most of these appear in his publication Minimax Algebra, Lecture Notes in Economics and Math. Systems 166, Berlin: Springer, 1979. This work has been cited by hundreds of authors worldwide and contains material that is still relevant for researchers in tropical linear algebra today.

Ray was a kind, tolerant and highly respected man. He will be missed very much by his family, friends, colleagues and former students.

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HARLEY FLANDERS

Published online 28 August 2013


Harley Flanders

Professor Harley M. Flanders, who was elected a member of the London Mathematical Society on 16 January 1958, died on 26 July 2013, aged 87.

Zvi Flanders writes: Harley completed his PhD in mathematics at the University of Chicago in 1949. Until 1960 he was a professor at the University of California, Berkeley. During part of this time he was a National Science Foundation Fellow at both Cambridge and Hebrew Universities. In 1960 he was appointed full professor at Purdue and later at Tel Aviv University. In 1977 he returned to the United States where he held several positions, most recently as a visiting scholar at the University of Michigan.

Harley authored an important book Differential Forms with Applications to the Physical Sciences (Academic Press), nearly 100 scientific papers as well as a number of textbooks on algebra, trigonometry, calculus and Scientific Pascal. From 1958-63 he was the Associate Editor of the Transactions of the American Mathematical Society. Between 1966 to 1973 he served first as Associate Editor and later as Editor-in-Chief of the American Mathematical Monthly. He was the recipient of the NCRIPTAL/EDUCOM Distinguished Software Award for his MicroCalc educational software program.

Harley is survived by his ex-wife, M. June Flanders; sons Daveed and Zvi; three grandchildren Tal, Nathan and Louis; and two great-grandchildren, Yosef and Batsheva.

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LMS NEWSLETTER ONLINE
Published online 28 January 2014

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