**Archibald Macintyre**'s parents were William Ewart G Archibald Macintyre and Mary Beatrice Askew. William Macintyre, who used his middle name of Archibald, was born in 1878 in Long Eaton, Derbyshire, and was a schoolmaster at a public elementary school in Sheffield. Mary Askew was born in 1877 in Sheffield, Yorkshire and, before her marriage, she had also been a school teacher. They were married in Sheffield in June 1905 and their first child, Kathleen Mary Macintyre, was born the following year in Ecclesall Bierlow, in Sheffield. She was two years older than Archibald, the subject of this biography.

Archibald Macintyre was educated at the Central Secondary School, Sheffield. The school opened on 10 March 1880 as the Central Higher Grade School in the centre of Sheffield, and re-located to its present site at High Storrs (and renamed High Storrs Grammar School) in 1933, a few year Macintyre had completed his studies there. He graduated in 1926 and, in October of that year, he matriculated as a scholar at Magdalene College, Cambridge. There he took the Mathematical Tripos with great success, tutored by Arthur Stanley Ramsey, the father of Frank Ramsey. He was ranked as First Class in Part I of the Mathematical Tripos in June 1928 and awarded the Davidson Prize for Mathematics after taking the Mathematics Preliminary Examination in June 1928. Again he was ranked First Class in these examinations and was a Wrangler in Part II of the Mathematical Tripos in June 1929, being awarded distinction in Schedule B. Fellow students at Cambridge included Donald Coxeter, Harold Davenport, Raymond Paley, S Verblunsky and James Cossar. Macintyre spent the academic year 1929-30 undertaking research at Cambridge advised by Edward Collingwood. In fact Collingwood, although seven years older than Macintyre, had a rather unusual route to teaching at Cambridge. He had been awarded a Ph.D. in 1929 after a short career in the navy and only gave advanced courses, doing no undergraduate teaching.

After one year of research at Cambridge, Macintyre was appointed as a temporary Assistant Lecturer attached to the Mathematics Department of Swansea University College. He taught courses in applied mathematics and theoretical physics during the academic year 1930-31. Archibald Read Richardson had been appointed as professor of mathematics at Swansea in 1920 and was head of department at this time. During this year he became friendly with R Wilson, and the two undertook some research projects together. Macintyre moved to Sheffield in 1931 where he was appointed as an Assistant Lecturer in the Mathematics Department. He had continued to undertake research, advised by Collingwood, and was awarded a Ph.D. in 1933 for his thesis *Some Properties of Integral and Meromorphic Functions*. In 1935 he was promoted to Lecturer in Mathematics at Sheffield but he did not hold this position for very long for, on 1 October 1936, he took up the position of Lecturer in Mathematics at King's College in the University of Aberdeen in Scotland.

Macintyre's research contributions are discussed in detail in [3] and [4]. The following overview is from [3]:-

His first papers were:As a classical analyst, Macintyre considered a diversity of problems, throughout many of which, however, runs a strong thread, viz., his keen interest in overconvergence. Amongst his43papers, often grown from seed sown in his Ph.D. thesis, one finds such topics as asymptotic paths, the flat regions of meromorphic functions, interpolation problems based on the Laplace transform and other formulae for regular functions, Tauberian theorems in connection with certain canonical products, and numerous problems, many published jointly with R Wilson, in the theory of the singularities off(z) = ∑c_{n}z^{n}on the circle of convergence.

*Un théorème sur l'ultraconvergence*(1934); (with R Wilson)

*On the order of interpolated integral functions and of meromorphic functions with given poles*(1934);

*On the asymptotic paths of integral functions of finite order*(1934);

*Elementary proof of theorems of Cauchy and Mayer*(1935); and

*A theorem concerning meromorphic functions of finite order*(1935). Macintyre acknowledged the contribution from his thesis advisor in the last of the papers we have just listed:-

Through an introduction by Edmund Whittaker, Macintyre met the mathematician Sheila Scott. After studying at Cambridge, Sheila Scott had taught mathematics at St Leonard's School, St Andrews, for four years, followed by short spells teaching at Allen's School for Girls in Dulwich, South London, and Stowe School in Buckingham. Macintyre and Scott were married on 27 December 1940 and, in the following year, Sheila Macintyre was appointed as an assistant lecturer in the same department as her husband in the University of Aberdeen. At this time World War II was taking place and several of the mathematics staff at Aberdeen had been called up for war service. She taught courses at the university filling in for the men who were fighting and also undertook research for a Ph.D. thesis. The Macintyres had two children, Alister William Macintyre (born 8 February 1944) and Susan Elizabeth Macintyre (born March 1950). A third child, a boy named Douglas Scott Macintyre, died from enteritis in March 1949 at the age of two years.The author is considerably indebted to Dr E F Collingwood for assistance in the preparation of the manuscript and for improvements in the argument ...

Archibald and Sheila Macintyre undertook some joint mathematical work. In volume 23 of the *Journal* of the London Mathematical Society (1948) there are two papers by the Macintyres. The first, by Sheila Scott Macintyre, is an 8-page entitled *A functional inequality* while the next paper, by Archibald Macintyre, is a 3-page paper entitled *Note on the preceding paper*. These two papers investigate a problem posed by E M Wright and give conditions on a real function *f* (*x*) and its derivatives to ensure that *f* (*x*) ≤ sin *x* in a certain interval. Sheila Macintyre proved two new theorems attacking Wright's question while Archibald Macintyre used one the lemmas in Sheila Macintyre's paper to generalise a theorem proved by Wright in an earlier paper. A few years later, in 1952, the two Macintyres published a more conventional type of joint paper, namely the 2-author work *Theorems on the convergence and asymptotic validity of Abel's series* which was published in the *Proceedings* of the Royal Society of Edinburgh.

Archibald Macintyre was elected a fellow of the Royal Society of Edinburgh on 3 March 1947. He had been proposed for the fellowship by E M Wright, Ivor Etherington, Edward Copson, Edmund Whittaker, and James Cossar.

At Aberdeen, Macintyre was thesis advisor to James Clunie. In 1952 Clunie was awarded his Ph.D. by the University of Aberdeen for his thesis *On Certain Topics Concerning the External Behaviour of Functions*. In a paper Clunie published in 1953 he expressed his thanks to his advisor:-

N A Bowen, who collaborated with Macintyre on many research articles, gives this appreciation of his colleague [3]:-I wish to express my gratitude to Dr A J Macintyre for suggesting the problems treated in this paper, and for his advice and criticism throughout the work.

In 1958 Macintyre and his wife accepted visiting research professorships at the University of Cincinnati in the United States. They returned to Aberdeen in 1959 but, on 30 September of that year, Archibald Macintyre resigned his Senior Lectureship at Aberdeen so that he could take up a permanent post as Research Professor in Mathematics at Cincinnati. Sheila Macintyre resigned her Lectureship at the same time and was also appointed as a professor in the Mathematics Department at Cincinnati where she taught until her early death from breast cancer in March 1960. In 1963 Macintyre was named Charles Phelps Taft Professor of Mathematics at the University of Cincinnati. He held this position until his death, after a brief illness, in 1967 at the age of 59. Although he had only worked at the University of Cincinnati for nine years (less in a permanent position), nevertheless he advised at least twelve Ph.D. students during these years with seven graduating with their doctorates in 1963 or 1964.During my thirteen-year association with him at King's College, Aberdeen, Scotland, I naturally came to know him well, and to admire his many fine attributes. His good nature and kindness, his subtle but delightful sense of humour, the patience with which he explained mathematical problems to those less quick than he to see the point, the facility with which he was able to imbue his students with the feeling that mathematics was a living and growing subject and not a defunct language of invariable symbols, his encyclopaedic knowledge of mathematical research papers especially in the various branches of mathematical analysis - all these were highly impressive and go some way towards explaining not only the high esteem and popularity accorded to him, by both staff and students wherever he went, but also his power of attracting research students to work under his inspiring supervision. Another aspect of his character that impinged itself early on his mathematical friends, especially on his research collaborators, was his high standard - he simply would not countenance publication unless, and until, the proposed article was of first-class quality as regards both content and exposition. However, what impressed me most of all about him as a mathematician was his humility. He told me once that he did not regard himself as an original thinker, but merely as one who could sometimes push further ahead with the ideas and methods of others. All who have worked in the field of analysis will surely agree that such an opinion of his work does him less than justice, and I have no doubt that many of us would be only too happy to produce work of his quality.

Although Macintyre is best known for his work in pure mathematics, he did have interests in applied mathematics and physics. In fact some of his ideas, such as those on the design of aircraft, were unconventional [3]:-

Finally, let us record that Macintyre was a member of the Cambridge Philosophical Society, the London Mathematical Society and the Edinburgh Mathematical Society.He was also deeply interested in aerodynamics, fluid mechanics and related fields. He believed, for example, that aeroplanes should have their control surfaces - rudder and elevator - located at the front and not at the back. He conducted with great enthusiasm his experiments with model planes, and corresponded widely with experts on these matters, steadfastly refusing to accept their views unless soundly backed by evidence, at the same time being himself able to answer their objections to his revolutionary ideas. He was awarded a Caird Senior Scholarship in Aeronautics for1943-44, and a D.S.I.R. grant from1946-49for special research on the Lanchester Vortex.

**Article by:** *J J O'Connor* and *E F Robertson*

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