Born in Horwich, Lancashire, Brian was educated at Leigh grammar school and, in 1945, entered Manchester University where he obtained MSc and PhD degrees. Academic posts followed in Aberdeen - where Brian met his wife, Catherine - Bristol and then Birmingham, where Peter Hilton and he ran classes for teachers explaining how classical mathematics was being re-thought in universities and discussed how such changes might affect school mathematics. This led to a successful book by the pair, A Comprehensive Textbook of Classical Mathematics.
In 1964, he was appointed professor of pure mathematics at Southampton University - a post he occupied for 28 years. There he played a major role not only in expanding and revitalising the pure mathematics group but also in bringing statistics, computing and operations research teams into what remained a unified mathematics department. Accordingly, new options were introduced for third-year students. One was on the history of mathematics; another allowed students to select a topic they wished to study and, supervised by a tutor, write a dissertation on; in a third, students investigated and solved problems with no pre-set mathematics syllabus; the fourth led to pioneering work on the relationship between mathematics and society. The resulting book, Mathematics: Society and Curricula (co-authored with myself), is still considered of importance.
Brian was also driven by his belief that the conventional timed exam failed to test those qualities he wished mathematics graduates to possess. As a result, lecturers were allowed to use coursework as part or all of their assessment and even to permit students to bring notes or textbooks into examinations. Refusing to allow their use in examinations, he argued, rewarded memory at the expense of problem-solving capability. Ron McLone and he then carried out sponsored research into what qualities appeared to be promoted by the mathematics examinations set in a sample of universities.
His concentration on mathematics education and departmental administration took a toll on Griffiths' research work. Yet when Max Newman, his old Manchester supervisor, urged him to spend less time on education and more on research, Griffiths, with his different priorities, could not accept this advice. Indeed, more initiatives followed. With Heine Halberstam he established the annual Nottingham conference on the teaching of mathematics to undergraduates - just one of several national and international commitments. He also spent time at the Institute for Advanced Study, Princeton, New Jersey (1956-58), the Courant Institute, New York (1963-64), and the Institute des Hautes Études Scientifiques, France (1972-73).
During much of this time, Catherine and Brian faced difficult problems at home, for both their sons suffered from cystic fibrosis and required extensive care. The death of the younger son, Joe, prevented Brian from giving an invited talk on mathematics education to the 1970 International Congress of Mathematicians, and the elder, Adam, died when studying for a DPhil at Oxford.
Nonetheless, the Griffiths were always generous hosts and took great care to see that newcomers to the department were comfortably settled in Southampton. Their house was always one of music. Catherine was a piano teacher and their daughter, Hannah, a cellist. However, only after retirement in 1992, could Brian find time to practise his violin and play in a local string orchestra and two string quartets.
He is survived by Catherine, Hannah and three grandchildren.
Wednesday July 16 2008 © Guardian Newspapers Limited