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Articles on the history of mathematics can be written from many dierent perspectives. Some aim to survey a more or less wide landscape, and require the observer to watch from afar as theories develop and movements are born or become obsolete. At the other extreme, there are those that try to shed light on the history of particular theorems and on the people who created them. This article belongs to this second category. It is an attempt to explain Goldie’s theorems on quotient rings in the context of the life and times of the man who discovered them. 1. Fractions Fractions are at least as old as civilisation. The Egyptian scribes of 3,000 years ago were very skilful in their manipulation as attested by many ancient papyri. To the Egyptians and Mesopotamians, fractions were just tools to find the correct answer to practical problems in land surveying and accounting. However, the situation changed dramatically in Ancient Greece. To the Greek philosophers, number meant positive integer, and 1 was ‘the unity’, and as such, had to be indivisible. So how could ‘half’ be a number, since ‘half the unity’ did not make sense? Possibly as a consequence of that, the Greek mathematicians thought of fractions in terms of ratios of integers, rather than numbers. After the demise of Greek civilisation, mathematicians reverted to the more prosaic view that fractions were numbers. Indeed, for the next thousand years everyone seemed happy to compute with all sorts of ‘numbers’ without worrying much about what a number was really supposed to be. It was the need for a sound foundation for the infinitesimal calculus that put mathematicians face to face with the nature of numbers. The movement began in the 18th century, but its first fruits were only reaped in the 19th century in the movement that became known as the arithmetization of analysis. In short, mathematicians felt quite sure that they knew their integers very well; so they thought that by constructing the real numbers in terms of positive integers they would place the latter in a sure foundation. The most extreme version of this credo