Mathematician, born at Bacup and brought up in Thorn Methodist church, with which the family were closely involved. He was educated at Bacup and Rawtenstall Grammar School and at Manchester University, where he graduated in mathematics and achieved a doctorate in 1954. After a short while at Aldermaston, in 1955 he became a lecturer in applied maths at Manchester University, then in 1963 began a long career as Professor of Applied Mathematics at the University of Leeds. The focus of his research was in fluid mechanics, and especially stellar evolution; but his wide-ranging interests included geographical models of cities and cattle movements in Botswana, where he established a link between the local church and his own church back in Ilkley.
He became a local preacher in 1952, serving many pulpits in Yorkshire and Lancashire, and in 1981 he was invited to give the University Sermon in Leeds. In 1992 he retired to Pickering, where he also became an Anglican lay reader.
His son, Andy Goldsworthy (1956- ), sculptor, photographer and environmentalist, received a honorary degree from Bradford University in 1993 and an OBE in 2000.