My former colleague and father-in-law, Alan Carling, who has died aged 75, was an acclaimed sociologist; he taught for many years at the University of Bradford.

Former students remember his sense of humour and ferocious intellect. He was widely respected, known for his generosity and feared by some for his boyish delight in shredding weak arguments.

Born in Ipswich, Suffolk, Alan was the son of Freda (nee Williams) and David Carling, a hospital administrator for Bupa. He won a scholarship to Brentwood school, Essex, going on to study maths at Emmanuel College, Cambridge, in the late 1960s, graduating with a double first.

He changed to sociology for his PhD at Essex, where he met his first wife, Chris (nee Fisher), then started a career as a manager in the charity sector. They divorced in 1992. Alan’s doctoral thesis was an interpretation of Marx’s Das Kapital based on mathematical principles more commonly associated with econometrics than Marxist critical theory.

Through the pages of New Left Review, Alan rose to prominence in the 80s as the leading British exponent of a reformulated Marx that combined the rigour of mathematical modelling with a trenchant restatement of the latter’s concern with social justice. When Verso published his book Social Division (1991), he became the sociologist of analytical Marxism.

In 1977 Alan became a lecturer in the department of interdisciplinary human studies at Bradford; he inspired many to take up academic work because of his infectious spirit of curiosity. Alan lit up the grey Bradford winters with his personality and an impressive collection of Hawaiian shirts, which, combined with his large red beard, made him a highly recognisable figure on campus in the 80s and 90s.

After he retired as professor of sociology, he continued to publish studies of religion and globalisation. His final work, Galileo’s Revenge, which is in the course of being published, uses a broad range of historical examples to explore the idea of testing as a deeply ingrained feature of modern societies. The book is a return to social theory on the grandest of scales and represents the culmination of a lifetime’s advocacy of the power of sociological reason to explain complex phenomena.

A keen football fan, Alan was an active member and former chair of Bradford City Supporters Trust (now the Bantams ST), reflecting his belief that the game should be democratised; with his second wife, Beryl (nee Spink), a college lecturer whom he married in 2017, he was also an active member of his local Labour party.

He is survived by Beryl, his children from his first marriage, Sarah and David, and two stepsons, Jonathan and Iain.