People Australia

Alwyn Horadam, n.d.

image provided by family

Alwyn Francis (‘Horrie’) Horadam, mathematician, was born on 22 March 1923, to parents who were dairy farmers in the rural settlement of Scotts Flat near Singleton in the Hunter River Valley, NSW, Australia. He died at 93, on 22 July 2016, in Armidale, after several years of serious physical incapacity but with his mind undimmed and ever interested, keeping to his ideal of ‘a kind heart and a tranquil mind’. 

His primary school education began at the outpost of Roughit, in a one-room school taught by his grandfather, and continued in Singleton. For high school, he travelled 110 km daily by train (milking the cows before and after) from Singleton to Maitland Boys High School, where he became School Captain and Dux. He won numerous school prizes, chief of which was the Waddy-Portus plaque for outstanding scholarship, sporting ability and citizenship. He was a talented and proud cricketer. For the Combined High Schools Cricket team, he was selected as a reserve, and later at the University of New England (UNE) he was Cricket Captain, Club President, and a ‘blue’. 

A Teacher’s College bursary allowed him to enrol at the New England University College (NEUC, which became UNE in 1954) in 1940, where his life-long passions for English, Classics, History and Mathematics flourished. As a student in a reserved occupation course, he undertook basic army training and dug trenches on campus. On graduation in 1944 with BA (First Class Hons) in Mathematics and Dip Ed from the University of Sydney (SU), Alwyn was sent to country high schools to serve out his bond for three happy and busy years. 

Teaching gave Alwyn great joy all his life; he was deeply committed to his craft and to the transforming and enriching power of mathematics in uncounted outreach courses to secondary students and teachers, and in lectures to the public. He wrote a series of high school text books and served on the NSW Junior School Mathematics Committee for 25 years continuously, as well as writing articles such as [4] for teachers, combining history and mathematics. Even when he was Head of Department and Dean of Science at UNE, his door was always open, with a notice ‘Students may see me at any time’. 

Appointed to NEUC as Lecturer in Mathematics in 1947, Alwyn progressed to Senior Lecturer (1959) then Associate Professor of Mathematics (1963). Along the way, he earned a BEd from the University of Melbourne and an MA (Hons) from SU. In 1957 he obtained his PhD from SU for the thesis ‘Clifford geometry in complex projective spaces of two, five and eight dimensions’, taken under the supervision of Professor T.G. Room. Projective geometry was his initial field and the substance of his second book [3]; the first was an encyclopaedic pure mathematics first year text [2] which remains a treasure house for any young lecturer searching for inspiration and example. 

In 1950, Alwyn married Mollie Spedding, a fellow mathematics lecturer at UNE, who had degrees from Cambridge and London Universities. They had a half-century of happy life together, having three daughters; Kathy, a mathematician, Kerry and Alanna, both medical practitioners, and six grandchildren. Further aspects of Mollie’s life and career appear in this Dictionary. 

Alwyn’s earliest publications (of which there are about 180 refereed, mostly in overseas journals and many co-authored) were in algebra and geometry. The two seminal, most cited papers were in number theory, and that is likely to be where his mathematical legacy holds strongest. The second of these papers [1] generalised the Fibonacci and other sequences. These generalisations, familiar now but novel then, were known as Horadam numbers and sequences by 1999. A survey to 2013 appears in [5] and Google Scholar shows they live and flourish today (2023). For more on this mathematics, see [5] and the tributes [7] and [6, 8]. In creating mathematics, he liked to quote the poet Browning: ‘A man’s reach should exceed his grasp.’ 

Allied with this research, Alwyn contributed strongly to the international community as a foundation and sustaining member of the Fibonacci Association, on the editorial board of the Fibonacci Quarterly, and as co-editor of the Proceedings of the Biennial International Conferences on Fibonacci Numbers and Their Applications. 

In service to UNE over his 40-year career, he was variously Foundation President of the Alumni Association, President of the Union, Council member elected by Convocation for six three-year terms, Governor of Wright, Robb and Duval residential colleges, University Ombudsman and Esquire Bedell. The longest serving member in mathematics, he was Head of the Department of Mathematics, Statistics and Computer Science (by election) on two separate occasions (the position he held on retirement in 1987) and Dean of the Faculty of Science. 

As a supervisor, he guided over fifty postgraduate students through LittBs and MA Hons and five through PhDs. Alwyn continued to work from his office at UNE for ten years after retirement, and then from home, with his final papers appearing in 2006. He was an enthusiastic traveller, and Mollie and he were overseas several times a year. He had an abiding interest in the polar explorers, and cruised to the Antarctic and Arctic several times, once being icebound for a week. The regret of his last trip was that he was too frail to walk to Mawson’s hut at Cape Denison. 

Alwyn always tried to put everyone he met at ease and to leave them with a joke and a smile. He is remembered as someone of great integrity with a deep commitment to treating people fairly; a civil and gentlemanly scholar. 

References
[1] Horadam, A.F. (1965). Basic properties of a certain generalized sequence of numbers. The Fibonacci Quarterly 3, 161–176.

[2] Horadam, A.F. (1968). Outline Course of Pure Mathematics. Pergamon Press, Oxford.

[3] Horadam, A.F. (1970). A Guide to Undergraduate Projective Geometry. Pergamon Press, Oxford.

[4] Horadam, A.F. (1975). Eight hundred years young. The Australian Mathematics Teacher 31, 123–134.

[5] Larcombe, P.J., Bagdasar, O.D. and Fennessey, E.J. (2013). Horadam sequences: a survey. Bulletin of the Institute of Combinatorics and its Applications 67, 49–72.

[6] Larcombe, P.J. (2016). Alwyn Francis Horadam, 1923–2016: A personal tribute to the man and his sequence. Bulletin of the Institute of Combinatorics and its Applications 78, 93–107.

[7] Shannon, A.G. (1987). A.F. Horadam – ad multos annos. The Fibonacci Quarterly 25, 100–104.

[8] Shannon, A.G. (2016). Alwyn Horadam: The man and his mathematics. Notes on Number Theory and Discrete Mathematics 22(3), 1–4.