# Thomas Scott Blyth

### Quick Info

Newburgh, Fife, Scotland

Strathkinness, Fife, Scotland

**Tom Blyth**published around 150 works, mainly on ordered algebraic structures and on semigroups. He wrote a number of important monographs and undergraduate textbooks.

### Biography

**Thomas Scott Blyth**(known as TSB or Tom Blyth) was the son of Robert Duncan Blyth (1909-1969) and Alice Wallace Scott (1911-1970). Robert Blyth was born in Newburgh, Fife, and became a linoleum factory worker. Alice Scott was born in Lochgelly, Fife and became a hospital seamstress. Robert and Alice Blyth were married in Newburgh in 1934 and lived at 45 High Street, Newburgh. They had three children, all born in Newburgh: David Blyth (born 1936); Thomas S Blyth (born 1938), the subject of this biography; and Elizabeth A Blyth (1949-2019).

Tom attended Newburgh Primary School but his mother Alice, who was very musical, was keen that he should also have musical training so she sent Tom to Perth for violin lessons. In 1950 Tom began his secondary education at Bell Baxter High School in Cupar, Fife. Tom is in the Class 1A1 photograph and, we note, so is Elizabeth Mary Farmer. Six years later, Tom would be the Dux of Science, while Elizabeth would be the Dux of Arts. Elizabeth Farmer later married Alex Craik who was in the same undergraduate mathematics class as Tom at the University of St Andrews.

Let us return to Tom's time at Bell Baxter High School. When he moved up to Bell Baxter in Cupar, he continued with the violin, eventually becoming leader of the school orchestra which led to his lifelong love of classical music. He was taught mathematics by Ken Nicol who had joined the staff at Bell Baxter in 1949. Tom was always grateful to Ken Nicol for giving him a solid start in mathematics. He did, however, teach himself some advanced calculus since he believed the curriculum was moving far too slowly for him. Barbara Miller related the following in [21]:-

Tom knew that not all his fellow pupils shared his passion for mathematics and science so one day, when he was unexpectantly put in charge of a chemistry class as the teacher was absent, he decided to encourage the youngsters to melt down their protractors, which he believed they would have no further need for, to create nail varnish. There is no record of what the head teacher thought of this particular venture.In 1955-56 Tom was a prefect at Bell Baxter and, as we noted above, was Dux in Science in 1956. Later that year, in October, he began his studies at the University of St Andrews. Having sat the University of St Andrews Bursary Competition, he had been awarded an entrance bursary. He went straight into Special Mathematics, the second year mathematics course, but took first year courses in applied mathematics and physics. Four other outstanding students began their university studies in the same Special Mathematics class, namely Patrick D L Constable, Alex D D Craik, Michael Moss and Grant Walker. One further outstanding student Bruce L R Shawyer was also in this Special Mathematics class, but he had started his university studies one year earlier and had won the Class Medal for the General Mathematics course in 1955-56. This was a remarkable year with the six we have mentioned all going on to become outstanding mathematics teachers in universities.

A picture of the Senior Honours Class of 1959/60 is at THIS LINK.

Before continuing to describe Tom Blyth's career, let us record at this point a few details of the careers of Tom's five fellow students.

Bruce Shawyer (1937-2021), was influenced by David Borwein to become an analyst and, with David Borwein as his thesis advisor, was awarded a Ph.D. from the University of St Andrews in 1963. After teaching at the University of Nottingham he went to Canada in 1966 where he spent the rest of his career, first at the University of Western Ontario (1966-1985) and then at Memorial University (1985-2002). Patrick D L Constable joined the statistics staff at the University of St Andrews teaching there until 1969. He later joined the Department of Statistics at the University of Leeds. Alex D D Craik studied for a Ph.D. at the University of Cambridge, and then was appointed as a lecturer in the Department of Applied Mathematics at the University of St Andrews in 1963. He became a leading expert on fluid mechanics and, towards the end of his career, an outstanding historian of mathematics. Michael Moss and Grant Walker both studied for a Ph.D. in topology at the University of Cambridge, advised by Frank Adams. Michael Moss taught at the University of Stirling, while Grant Walker taught at the University of Manchester.

We have given details of Tom Blyth's five fellow students who went on to academic careers to show what a talented group of mathematicians he joined in 1956. They were taught by excellent lecturers who included Edward Copson, who was the Regius Professor of Mathematics, Dan Rutherford, David Borwein, Arthur Hinton Read and Ronald Mitchell. Blyth studied the Junior Honours course in 1957-58 then spent two years taking Senior Honours courses, both in 1958-59 and 1959-60. In 1959 he was awarded the Duncan Prize in Applied Mathematics. As was customary at this time, he sat all the honours examinations papers at the end of his final year. He sat the papers: Geometry and Algebra; Algebra and Foundations; General Analysis; Statics; Dynamics; Fluid Dynamics; and Abstract Algebra. He was awarded a First Class honours degree in Mathematics and graduated in July 1960.

An outstanding undergraduate performance led to Blyth being awarded a NATO research scholarship to study in Paris at Sorbonne University. It was Dan Rutherford who had encouraged Blyth to go abroad for his doctoral studies and it was certainly advice that Blyth appreciated since the experience would define the style and topics that Blyth would spend rest of his life studying. He wrote about his experiences in [5]:-

It was Dan Rutherford who suggested that I should follow the old Scottish tradition of doing research on the Continent. (I discovered somewhat later that he, who had a doctorate from Amsterdam, was the only example of this old tradition that I could find!) Thus he arranged for me to go to Paris with a NATO scholarship, to be supervised by Madame Dubreil-Jacotin. This was my first trip out of the UK and it was arranged that I meet her at the Institut Henri Poincaré at 5 pm on the day after I arrived in Paris. Equipped with only high school French (most of which I had forgotten during my undergraduate years), and feeling as hopeless as an illegal immigrant, I managed to find my way there with the aid of a borrowed map of the Métro. The meeting was memorable. Naturally the first thing I asked was if she spoke English, to which she replied simply 'En France, on parle Français'. After an hour or so, during which my French improved dramatically, she told me to accompany her in her car since she had to go to the Place Vendôme to meet her husband. On reaching the ground floor of the Institut Poincaré we encountered a throng of students which parted for her as did the sea for Moses. Scurrying along in her wake, I realised that this was no ordinary Professor. On arriving at the Place Vendôme she told me to see her again in two weeks, after I had enjoyed discovering some of the niceties of Paris. A handshake and an au revoir left me to find my own way back to the Collège Franco-Britannique where I was staying. Luckily I had that Métro map!As we have learnt from this quote, in Paris he studied at the Institut Henri Poincaré, part of the Sorbonne University, advised by Marie-Louise Dubreil-Jacotin. He quickly learnt to speak French, acquired a lifelong appreciation for red wine and made several good friends including James Galway now known as "The Man with the Golden Flute". Blyth undertook research on ordered algebraic structures. He quickly obtained new results and published the two-part paper

Supervision by her was a joy. She claimed that she could not easily read my writing (in truth it was the other way round) and gave me a portable typewriter to prepare the material for her inspection. We met every two or three weeks in the late afternoon, either in her office or at her house in the 16th arrondissement. This was invariably followed by dinner, often in restaurants that I could never hope to afford.

I last met her in 1970. At the International Congress in Nice there was a splinter group on Semigroups, chaired by her husband Paul Dubreil. At the beginning of one of the sessions he called the rabble audience to order. In our thus interrupted conversation she wryly commented to me 'il y a des professeurs qui sont les dictateurs' to which I could not resist the reply 'oui, et il y en a qui sont les dictatrices!' Her jovial acceptance of this will always remain with me.

I owe her, and her husband Paul Dubreil, my entire subsequent career and memories of them stir great affection.

*La forme générale des structures algébriques résiduées*Ⓣ which appeared in the Academy of Sciences'

*Comptes Rendus*in 1962. He was awarded a Docteur en Science 'Très Honourable' for his thesis

*Contribution à la théorie de la résiduation dans les structures algébriques ordonnées*Ⓣ (1963). Details are available in the review [7].

Blyth returned to St Andrews to take up an appointment as a Lecturer in Mathematics in October 1963. In session 1964-65 he delivered the Special Topic course

*Ordered Algebraic Structures*. I [EFR] took this course which was given in the style of Bourbaki. The lectures were carefully prepared and Blyth presented much material which had evolved from his own research. The class was quite small and the lectures were delivered in the Mathematics Class Library. For me the course was exciting, introducing me for the first time to the cutting edge of research in an algebraic topic.

As was common at that time, many newly appointed lecturers were appointed as a subwarden in a university residence. Blyth became a subwarden in St Regulus Hall of residence and became friendly with the cook Jane Pairman [21]:-

Tom Blyth married Jane Ellen C Pairman (born 1942 in St Andrews) whose parents ran the tavern in Strathkinness and whose grandparents had run the Whey Pat Tavern in St Andrews. Jane was working as a Head Cook at the St Regulus Hall of residence in St Andrews and Tom was a subwarden there at the same time. They were married at the University Chapel in 1967 and moved into a house built by Jane's father, next to the Tavern in Strathkinness, where they spent their entire married life. On Saturday nights Tom would invariable be roped in to help out behind the busy tavern bar where he could pull a perfect pint.The Blyths spent the year 1968 in Canada where Tom Blyth was based at the University of London Ontario for a sabbatical year. Tom and Jane Blyth had one child, Abigail, born in 1970. Also in 1970, in September of that year, Blyth attended the International Congress of Mathematicians in Nice, France. He was very happy to be back in France and meeting up with Marie-Louise Dubreil-Jacotin, Paul Dubreil, and many of his French friends.

In 1972 Blyth was promoted to Senior Lecturer and, in the following year, to Reader. By 1972 he had 23 works in print including his first monograph

*Residuation theory*which he co-authored with Melvin F Janowitz from the University of Massachusetts. Blyth and Janowitz write in the Preface:-

This text has grown out of courses given by T.S.B. at the Universities of St Andrews, Western Australia and Western Ontario and by M.F.J. at the Universities of Massachusetts, New Mexico and Western Michigan. In this (hopefully happy) marriage of our efforts, the choice of text material has, quite frankly, been selfish and more or less motivated by our own research interests. It was never our intention to write an encyclopaedia on the subject (we leave that happy task to someone else!) but rather to produce a self-contained and unified introduction to the subject which may be used either as a textbook or as a reference book in this area.For more information about this book and other books by Tom Blyth, see THIS LINK.

The first time I [EFR] was asked to teach the first year mathematics course, I took over from Tom who had taught the course in the previous year. He offered me his lecture notes which I gratefully accepted. They were beautifully written notes in such a polished form that one felt they could be sent straight to a publisher. Although I gave the course a personal flavour, I relied heavily on Tom's notes which I found very helpful since they were so well thought out.

Blyth became Professor of Pure Mathematics in 1977 and was promoted to Senior Professor in 1979. Between 1982 and 1987 he was Chair of the Department of Pure Mathematics and in 1982-1987 he was Dean of the Faculty of Science [20]:-

A vital member of the University community, Tom undertook many different roles during his career at St Andrews. He was a member of the Library Committee, the University Printing Committee, and indeed the Senate's Advisory Committee on Committees! Perhaps one of his favourite roles was as convener of the Graduation Ceremonial Committee. He had a reputation in his administrative work for his down to earth, no-nonsense approach, with the promotion of academic excellence always the motivating force. As Senior Professor he played a major role at the installation ceremony of Dr Brian Lang as Principal in 2001.When his daughter Abigail was in her final year at school at Madras College in 1987/88, Tom decided to ensure she did well in the Sixth Year Studies Mathematics examinations [21]:-

Abigail remembers when she was studying mathematics in her final year at school she was having a bit of a struggle with algebra and calculus. To help her, Tom took down all the adolescent posters of pop stars and bands on one of the walls of her room and put up a plastic sheet to create a huge makeshift whiteboard. Every night he would put up a new algebra problem and a calculus problem on the whiteboard and Abigail would be expected to solve both before supper. When Abigail received her Sixth Year Studies results, she opened the envelope, turned to her Dad, and said, "We've got an A."In 2003 Blyth retired and was made Emeritus Professor. After retiring he presented his splendid Parisian doctoral robes to the University museum.

We gave details of his first monograph

*Residuation theory*(1972) above. He wrote four further monographs:

*Module theory. An approach to linear algebra*(1977);

*Categories*(1986); (with J C Varlet)

*Ockham algebras*(1994); and

*Lattices and Ordered Algebraic Structures*(2005). For information about these books, see THIS LINK.

I [EFR] co-authored quite a number of books with Tom. Both Tom and I had been teaching algebra courses at various undergraduate levels. I had produced tutorials with many questions attempting to improve student's understanding of concepts rather than testing their problem-solving skills. Tom liked the tutorials I was giving students and thought they complemented the style of questions he was setting. He had a notion to produce a series of small books on various algebra topics which he felt were more appropriate for students than large textbooks covering vast amounts of material. We collaborated on producing six problem-solver books,

*Essential Student Algebra.*The books were:

*Sets, relations and mappings*;

*Matrices and vector spaces*;

*Groups, rings and fields*;

*Linear algebra*;

*Groups*; and

*Rings, fields and modules*. They were published by Cambridge University Press in 1984 and, one year later, the Press published two larger books, putting Books 1, 2 and 3 in one volume and Books 4, 5 and 6 into a second volume. Tom and I then produced five companion texts:

*Sets and Mappings*;

*Matrices and Vector Spaces*;

*Abstract Algebra*; and

*Groups*which were published in 1986.

Springer then asked Tom and me to write a Linear Algebra text for SUMS (Springer Undergraduate Mathematics Series). We co-authored

*Basic Linear Algebra*which was published in 1998. It became, in Springer's own words, "one of SUMS' best-selling titles" and we were asked to produce a second edition and also to write a follow-on textbook suitable for a second course in linear algebra. For the Second Edition of

*Basic Linear Algebra*(2002) we added a chapter on computer applications to linear algebra and we published the second volume

*Further Linear Algebra*in the same year. Rabe von Randow writes in the review [29]:-

This text is a sequel to the authors' earlier Springer Undergraduate Mathematics series volume entitled 'Basic linear algebra', which is an introductory text for mathematics students. This book continues in a similar style and presents more advanced properties of vector spaces and linear mappings. As before, it embodies a beautiful, concise and precise treatment of the subject, with succinct numerical and algebraic worked examples at the right points, and many exercises.For further details on Blyth's career, we quote from [20]:-

This is an excellent textbook which, together with the earlier book, comprises a very nearly complete introduction to linear algebra which not only the undergraduate but also the advanced reader will enjoy studying.

Tom contributed in many ways to the wider mathematical community; he was Editor of the Royal Society of Edinburgh Mathematical Proceedings for 10 years, elected as a Corresponding Member of the Royal Society of Liège in 1973, made a Fellow of the Royal Society of Edinburgh in 1974, and was President of the Edinburgh Mathematical Society in 1979 and 1980. He organised the four-yearly St Andrews Colloquium and was Chair of the British Mathematical Colloquium when it came to St Andrews in 1987.Living locally in Strathkinness, Tom remained committed to his mathematical research long after his retirement, continuing his 30-year collaboration on semigroups with Maria Helena Almeida Santos from the New University of Lisbon; their last paper was published in 2021. Tom undertook research with Herberto J Silva, also from the New University of Lisbon, publishing research together covering a 20-year period dating from the late 1990s up to 2017.

Tom continued to be in good health during his retirement and his death was very sudden. Sitting at home in his favourite armchair, watching television and sipping gin and tonic, he suddenly passed away.

Let us end with looking at an example of Tom's mathematical humour. He sent the article "L-plate instructions" to

*The Mathematical Gazette*when still a research student. He notes that the Instructions for a person holding a Provisional Driving Licence displays a diagram of the L-plate to be attached to a car which it says is "half actual size". He wondered [3]:-

... what interpretation would [people] put on the word "size" - did it mean that the dimensions of the scale drawing were half those of the plate to be displayed, or that the area of the figure given was half that to be displayed? A simple mensuration exercise with a reliable ruler (at room temperature) proved the first of these to be wrong. As for the second, I found that most of my non-mathematical friends took this interpretation; I wonder if they know how to solve this problem.

He then considers the instructions "The corners of the white ground may be rounded off" showing that by following this instruction one could have an L-plate which resembles a red sausage on a white plate.

### References (show)

- M Abad, Review: Ockham algebras, by T S Blyth,
*Mathematical Reviews*MR1315526**(96b:06010)**. - J Abram, Review: Algebra through Practice, by T S Blyth and E F Robertson,
*The Mathematical Gazette***69**(448) (1985), 147. - T B Blyth, "L"-plate Instructions,
*The Mathematical Gazette***46**(355) (1962), 67. - T B Blyth,
*Contribution à la théorie de la résiduation dans les structures algébriques ordonnées*, Doctoral Thesis (Faculté des Sciences de l'Université de Paris, Paris, 1963). - T S Blyth, Marie-Louise Dubreil-Jacotin,
*Private Communication*(9 January 2003). - Editors, Review: Residuation theory, by T S Blyth and M F Janowitz,
*Mathematical Reviews*MR0396359**(53#226)**. - M J Ego, Review: Contribution à la théorie de la résiduation dans les structures algébriques ordonnées,
*Mathematical Review*s MR0156913**(28#156).** - K Falconer, Professor Tom Blyth,
*University of St Andrews*(21 May 2024). - F Gerrish, Review: Algebra through Practice, Books 4, 5 and 6, by T S Blyth and E F Robertson,
*The Mathematical Gazette***70**(452) (1986), 171-172. - F Hoffman, Review: Sets and Mappings, by T S Blyth and E F Robertson,
*Mathematical Reviews*MR0866311**(89b:00001a)**. - F Hoffman, Review: Matrices and vector spaces, by T S Blyth and E F Robertson,
*Mathematical Reviews*MR0866312**(89b:00001b)**. - F Hoffman, Review: Abstract algebra, by T S Blyth and E F Robertson,
*Mathematical Reviews*MR0866310**(89b:00001c)**. - F Hoffman, Review: Linear algebra, by T S Blyth and E F Robertson,
*Mathematical Reviews*MR0866309**(89b:00001d)**. - F Hoffman, Review: Groups, by T S Blyth and E F Robertson,
*Mathematical Reviews*MR0866141**(89b:00001e)**. - J M Howie, Review: Lattices and Ordered Algebraic Structures, by T S Blyth,
*SIAM Review***48**(1) (2006), 171-172. - J R Isbell, Review: Categories, by T S Blyth,
*Mathematical Reviews*MR0858127**(87j:18001)**. - G Leversha, Review: Basic Linear Algebra, by T S Blyth and E F Robertson,
*The Mathematical Gazette***87**(509) (2003), 390. - D Levine, Review: Algebra through Practice, Books 4, 5 and 6, by T S Blyth and E F Robertson,
*The Mathematics Teacher***79**(6) (1986), 479. - N Lord, Review: Essential Student Algebra, by T S Blyth and E F Robertson,
*The Mathematical Gazette***71**(455) (1987), 91. - S Mapstone, Emeritus Professor Tom Blyth,
*University of St Andrews*(28 May 2004). - B Millar, Tribute, A Celebration for the life of Thomas Scott Blyth. 3 July 1938 - 18 May 2024,
*Dundee Crematorium*(7 June 2024). - P Nemec, Review: Module theory. An approach to linear algebra, by T S Blyth,
*Mathematical Reviews*MR0491783. - Pure maths Professor hangs up his gown,
*University of St Andrews*(17 September 2003). - Review: Basic Linear Algebra, by T S Blyth and E F Robertson,
*Mathematical Reviews*MR1609579. - Review: Further Linear Algebra, by T S Blyth and E F Robertson,
*Mathematical Reviews*MR1864441. - B S W Schróder, Review: Lattices and Ordered Algebraic Structures, by T S Blyth,
*Mathematical Reviews*MR2126425**(2006h:06001)**. - P Shiu, Review: Basic Linear Algebra, by T S Blyth and E F Robertson,
*The Mathematical Gazette***83**(496), 175. - J Zemánek, Review: Module theory. An approach to linear algebra (2nd edition), by T S Blyth,
*Mathematical Reviews*MR1070710**(91i:16001)**. - R von Randow, Review: Further Linear Algebra, by T S Blyth and E F Robertson,
*zbMATH***Zbl 0986.15001**.

### Additional Resources (show)

Other pages about Tom Blyth:

Other websites about Tom Blyth:

### Honours (show)

Honours awarded to Tom Blyth

### Cross-references (show)

- Other: Colloquium photo 1968
- Other: Colloquium photo 1972
- Other: Colloquium photo 1976
- Other: Colloquium photo 1980
- Other: Colloquium photo 1984
- Other: Colloquium photo 1988
- Other: Colloquium photo 1992
- Other: EMS Presidents
- Other: Edinburgh Mathematical Society Lecturers 1883- 2023
- Other: Recent Changes — up to August 2024

Written by J J O'Connor and E F Robertson

Last Update August 2024

Last Update August 2024