Tayler was born and bred in Birmingham, went up to Clare College, Cambridge, as a scholar, graduating in 1950 and winning a share in the Mayhew Prize, for performance in Part III of the Mathematics Tripos. He worked for his PhD in theoretical astrophysics with (Sir) Hermann Bondi as his supervisor. By then, after the work of Sir Arthur Eddington and others, the structure of chemically homogeneous stars was thought to be reasonably well understood, and descriptive of "main sequence" stars of different mass, such as the Sun and the bright white stars like Sirius and blue stars like Vega.
Attention began to be focused on stellar evolution, in the hope of explaining the origin of "red giants" such as the enormously extended star Betelgeuse. Such a programme of work requires the use of the powerful electronic computers which we now take for granted. Tayler said he was about the last person to tackle the equations of stellar structure with the aid just of a mechanical desk calculator.
After a postdoctoral year at the California Institute of Technology and Princeton, Tayler returned to England to work as Scientific Officer in the Atomic Energy Research Establishment at Harwell in 1955. There he wrote - parallel to but independently of Marshall Rosenbluth in the United States and V. Shafranov in the Soviet Union - fundamental mathematical papers on the problem of the "stabilised pinch", in which a perfectly conducting cylindrical current has its gross instabilities removed by an axial magnetic field within conducting walls.
The hope was that the hot plasma in the current would be magnetically confined long enough for energy generation by the same hydrogen-to-helium fusion process to occur on Earth as in the Sun and stars. In the slow progress over the decades towards this long-term aim, Tayler's work on this and on cognate problems remains highly relevant: one hears reports of its being rediscovered by young workers unfamiliar with the literature.
In 1961, Tayler returned to Cambridge to work with (Sir) Fred Hoyle on nuclear astrophysics. Following Hoyle's pioneering paper of 1946, there appeared in 1957 the masterly paper by "B2FH" (i.e. Hoyle, the late Willy Fowler and Geoffrey and Margaret Burbidge) on the build-up of carbon, oxygen and the heavier elements in the hot dense cores of highly evolved stars, to be distributed subsequently into the interstellar medium, e.g. during explosion of the star as a supernova. Tayler's contribution to this problem was a careful calculation of the relative abundances of the elements near the "iron peak".
The importance of heavy element build-up as part of normal stellar evolution is manifest from studies on "primordial" nucleosynthesis, which show that only helium and other light elements can form from hydrogen during the hot dense early phases of the standard "Big Bang" cosmology.
Belief in the Big Bang was revived by the discovery of microwave background radiation, announced in 1965. Shortly before this, Hoyle and Tayler had published a landmark paper, pointing out the importance for cosmology of observations of the helium abundance in different objects. Both earlier calculations and their own in fact yielded a theoretical abundance somewhat higher than that inferred from observation. However, Tayler in particular stressed that the computations were sensitive both to the number of neutrino types and to the lifetime attributed to the neutron.
His words were prophetic: over the years, new measurements have steadily reduced the neutron lifetime to a value that appears to remove the discrepancy; and the realisation that the helium abundance could tell us the number of neutrino types has become a major link between particle physics and cosmology.
In 1967, Tayler left Cambridge to join (Sir) William McCrea in the build- up of the Astronomy Centre at Sussex, in collaboration with colleagues at the Royal Greenwich Observatory, then located in Herstmonceux Castle. Not surprisingly, he proved a very able administrator; but despite the heavy calls on his time - including a five-year stint as dean and the ongoing supervision of many MSc and DPhil students - he maintained his research momentum, working in particular on stellar magnetism and on the chemical evolution of galaxies.
Tayler was a superb teacher, admirably clear without being prolix. This is apparent from the reading of his papers and review articles, and in his monographs which have a world-wide readership both among students and faculty: The Stars: their structure and evolution (1970); The Origin of the Chemical Elements (1972); Galaxies: structure and evolution (1978); and most recently The Hidden Universe (1991) and The Sun as a Star (1996), the last two being written in the period of remission during his last illness.
He was also very generous with his time, especially to students. And on top of all his research activity, his service to Sussex University, his membership of Science and Engineering Research Council Committees, and his work for his local church and the parochial church council, he shouldered an immense burden on behalf of the astronomical community.
Over 20 years he served first as Secretary, then as Treasurer and finally as President of the Royal Astronomical Society (RAS). For about the same period he was managing editor of the society's Monthly Notices. Recognition of his services to astronomy came with his appointment as OBE in 1990, and recognition of his research with election to the Royal Society in 1995.
In 1989 Tayler was diagnosed as suffering from myeloma, forcing him to retire a year early from the presidency of the RAS. The technical expertise and dedication of the staff at the Royal Marsden Hospital, and the devoted support of his wife Moya, gave him a six-and-a-half-year period of remission. With characteristically quiet courage and dignity he carried on teaching and research, even giving a lecture course after his official retirement.
Roger John Tayler, applied mathematician and astrophysicist: born Birmingham 25 October 1929; Scientific Officer/Senior Scientific Officer, AERE, Harwell 1955-61; Fellow, Corpus Christi College, Cambridge 1961-67; University Lecturer in Mathematics, Cambridge 1963-67; Professor of Astronomy, Sussex University 1967-94 (Emeritus); Gresham Professor of Astronomy 1969-75; Secretary, Royal Astronomical Society 1971-79, Treasurer 1979-87, President 1989-90; OBE 1990; FRS 1995; married 1955 Moya Fry; died London 23 January 1997.