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In seven houses there are seven cats. Each cat catches seven mice. If each mouse were to eat seven ears of corn and each ear of corn, if sown, were to produce seven gallons of grain, how many things are mentioned in total?

This is just one of dozens of similar problems, all equally complicated, all carefully written out – with the answers and showing the working in best schoolbook manner – that are recorded in the Rhind Mathematical Papyrus. This object is the most famous mathematical papyrus to have survived from ancient Egypt, and the major source for our understanding of how the Egyptians thought about numbers.

The Rhind Papyrus gives us no sense of maths as an abstract discipline through which the world can be conceived and contemplated anew. But it does let us glimpse – and share – the daily headaches of an Egyptian administrator. Like all civil servants, he seems to be looking anxiously over his shoulder at the National Audit Office, eager to ensure that he is getting value for money. So there are calculations about how many gallons of beer, or how many loaves of bread, you should be able to get from a given amount of grain, and how to calculate whether the beer or the bread that you’re paying for has been adulterated.

The papyrus contains eighty-four mathematical problems. Red ink indicates the name of or answer to a problem

The whole Rhind Papyrus contains eighty-four different problems – calculations that would have been used in different scenarios to solve the practical difficulties of administrative life, for instance how to calculate the slope of a pyramid, or the amount of food necessary for different kinds of domesticated birds. It’s mostly written in black, but red is used for each problem’s title and solution. And, interestingly, it is written not in hieroglyphs but in a particular kind of scribbly administrative shorthand that’s much quicker, much simpler, to write.

The papyrus owes its name to an Aberdeen lawyer, Alexander Rhind, who took to wintering in Egypt in the 1850s because the dry heat helped his tuberculosis. There, in Luxor, he bought this papyrus, which turned out to be the largest ancient mathematical text we know, not just from Egypt but from anywhere in the ancient world.

Because it is extremely sensitive to humidity and to light, we keep it in the Papyrus Room of the British Museum. It’s pretty dry and stuffy there, and above all it’s dark, all of which suits the papyrus, which rots in the damp and fades in bright light. It’s the nearest we can get in Bloomsbury to conditions in an ancient Egyptian tomb, where the papyrus presumably spent most of its existence. The whole papyrus would originally have been about 5 metres (17 feet) long and would normally have been rolled up in a scroll. Today it’s in three pieces. The two largest ones are in the British Museum, framed under glass to protect them (the third is in the Brooklyn Museum, New York). The papyrus is about 30 centimetres (roughly a foot) high, and if you look closely you can see the fibres of the papyrus plant.

Making papyrus is laborious but quite straightforward. The plant itself – a kind of reed which can grow to about 4.5 metres (15 feet) high – was plentiful in the Nile Delta. The pith of the plant is sliced into strips, which are soaked and pressed together to form sheets, and the sheets are then dried and rubbed smooth with a stone. Conveniently, the organic fibres of papyrus mesh together without the need for glue. The result is a wonderful surface for writing on – papyrus went on being used across the Mediterranean until about a thousand years ago, and indeed gave most European languages their very word for paper.

But papyrus was expensive – a 5-metre roll like the Rhind Papyrus would have cost two copper deben, about the same as a small goat. So this is an object for the well off.

Why would you spend so much money on a book of mathematical puzzles? I think because to own this scroll would have been a good career move. If you wanted to play any serious part in the Egyptian state, you had to be numerate. A