... worked as a skilled fitter at Austin Motors, the car manufacturers. The factory employed 1 500 skilled workers serving 15 000 unskilled labourers. The former were responsible for preparing the brass templates used for the accurate positioning of the holes for the screws that held together the various parts of the car. Templates were prepared for new models every two years, and had to be accurate to one thousandth of an inch. The skilled workers often had little work to do, as the actual drilling was done by the unskilled employees.

[He] met G E H Reuter, who was at the time a research student working in Cambridge under Hardy and Littlewood. They discussed the possibility of Goldie's going back to Cambridge to finish his education by doing Part III of the Mathematical Tripos. However ... Reuter warned him that as a married man Goldie would not be able to afford another year as a student.

One of the most characteristic features of ring theory in the late 1940s and early 1950s was the search for a structure theory for general rings. The most successful approach to this problem was that of N Jacobson. Thus it is not really surprising that Goldie's early work in ring theory was influenced by Jacobson's papers and books.

After the war, whenever Brauer visited England he would go to Newcastle and stay with the Rogosinskis. On one of these occasions, Goldie showed Brauer his result on Noetherian domains. All Brauer said was: "Oh my God!" Goldie then explained that he now needed to "do the matrix case"; Brauer replied "my boy, you are on your own."

After five days they decided to give up, and returned to Newcastle on a Thursday. The break must have given Goldie's subconscious time to catch up, for between Friday and Monday he [made the breakthrough].

This result came as a huge surprise, since it had been unsuspected, and it was hailed as a most considerable advance. It led to invitations to work in other institutions, including Yale University, the Institut des Hautes Études Scientifiques in Paris and Tulane University in New Orleans. The developments since his discovery have only served to demonstrate just how seminal it was. It remains a major tool in the subject and in surrounding areas. It is pertinent to note that a 1987 graduate text which aimed to describe the result and to survey some of its consequences ("Noncommutative Noetherian Rings" by J C McConnell and J C Robson) uses about 50 pages to establish Goldie's Theorem and over 500 pages to outline consequences.

At Leeds he continued his work in algebra, building a "school" in ring theory, hosting many visitors, and organizing memorable conferences. Goldie visited the U.S. many times, with extended stays at Yale, Tulane, and the University of California at San Diego.

He was a vivid personality with an individual mind, full of opinions and strongly argued positions on mathematics but also on the wider world, including politics, where his views moved rightwards over the years - starting with Communism whilst a student at Cambridge, and ending well within traditional Conservatism. ... Alfred Goldie was a very practical man, particularly enjoying working with wood. He also had a love of the outdoors, which he shared with his first wife, Mary, a geographer. Despite somewhat incompatible personalities, they still managed to give their three children a stable and happy upbringing.

Alfred Goldie approached his work with optimism and with no fear of the really hard problems.