David McWilliams: It’s a tragedy that so many people leave school hating maths

Belgians have a sense of humour, albeit a dark one. They house the stolen treasures of Africa in a majestic palace that was built by King Leopold with the very proceeds of the rape of Africa. The museum, in Tervuren just outside Brussels, is called (terrifyingly) the Royal Museum for Central Africa, though it is better known as AfricaMuseum. It devotes a modest, almost incidental footnote to the vicious colonial project that was the Congo Free State.

The stolen sculptures and artefacts of what is now the Democratic Republic of the Congo are intricate and beautiful, suggesting a rich artistic culture, plundered at gunpoint. By stealing and then trading the heritage of the Congo, the Belgians stole something more than the region’s art: they erased people’s memory, their legacy, their link to their forefathers.

Of course, Belgium was not alone in the cultural ransacking that forms the backbone of Europe’s great museums, bustling tourist attractions and revenue generators, from the British Museum to the Pergamon.

A few miles away, in the Royal Belgian Institute of Natural Sciences, lies another piece of African heritage which has intrigued me for years. The Ishango bone is the first known evidence of mathematics. A small, now shrunken bone with various notches, the artefact reveals that 20,000 years ago in an area of eastern Congo, not far from today’s Rwanda, people were counting using prime numbers.

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There’s lots of debate about whether the calculations were measuring a lunar calendar or whether the first mathematicians were women figuring out a menstrual cycle. What we do know is that these people were using computational records and division. The ancient civilisation was destroyed by a volcano and archaeologists uncovered the bone in the 1950s. A highly sophisticated civilisation existed in Congo using mathematics that predated the Egyptians or Sumerians by 15,000 years.

The evolution of maths is one of humanity’s most fascinating stories, yet it is rarely told. Its omission is even more bizarre when we reflect on just how important maths is to us and how our brains work.

One of the real tragedies is that so many people leave school hating maths, and never really make the link between maths and reason, precision, logic and truth. Maths moves us from superstition to proof, from conjecture to fact, from guesswork to certainty. Humans would simply not have evolved into the creatures we are without maths. And it shouldn’t surprise us that the story of maths, like the story of humans, begins in Africa.

It is most likely that maths evolved with sedentary agricultural societies, adjusting and adapting as we moved. Maths developed in the first agricultural societies of the Levant, from the civilisations of Sumer, Akkad and Assyria to Elba and Egypt. A simple numerical system was developed in Mesopotamia, using just two symbols. A vertical wedge (v) represented 1 and a horizontal wedge (<) represented 10; allowing us to write the number 23 as <<vvv. Without the concept of zero and the possibility opened up by using zero as a positional marker – such as 10, 100, 1,000 – these societies couldn’t have dealt with large numbers.

Egyptian hieroglyphs, by contrast, had a means of representing powers of 10, making it easier to make grand pharaonic proclamations of greatness.

Solving systems were developed in Babylon from 1900 to 1600 BC. Clay tablets, dating from around 1800 BC, read like ancient school textbooks, and a times table of sorts shows Pythagorean triples such as columns of integers a, b and c, with the property that a² + b² = c². The Egyptians solved quadratic equations in 1800 BC, providing evidence that they may have understood Pythagoras’s theorem before he did. The Greeks picked up the baton from the Babylonians and Egyptians, particularly in geometry, and, somewhere between 300 BC and AD 200, Euclid and his elements arrived on the scene.

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In Asia, the Chinese and Indians were making great leaps. We see that around 305 BC the Chinese were using the oldest-known decimal multiplication table deploying bamboo strips. In the golden age of Indian mathematics, from AD 500 onwards, we see the dexterous use of zero, something Indian mathematicians mastered. Arab invaders later adopted Indian ideas. While us Europeans were still counting on our fingers, in AD 820 the Persian polymath al-Khwarizmi wrote al-Jabr, birthing what we now know to be algebra.

Europe caught up through a process of intellectual osmosis, and by the 16th century we see Copernicus and Galileo and their mathematical study of the universe. The 17th century would later witness Descartes bridge the gap between algebra and geometry with his Cartesian co-ordinate system. All these innovations were the results of the “standing on the shoulders of giants” process, where ideas were passed down, tinkered with, improved and adopted. In a way, one of the saddest aspects of mathematical and scientific discovery is that it only comes about by being wrong. Progress means that many brilliant thinkers must conclude that they were wrong all the time, and off we go again. Science is humbling.

Maybe linking maths to the evolution of human thinking might spark a story in the minds of children, who could be attracted by the combination of anthropology, history and evolution, rather than the sterility of equations alone

We’ve been teaching maths for a long time too.

Thales was the founder of the earliest-known Greek school of mathematics and philosophy. In around 600 BC he was teaching, possibly for the first time, that a year was 365 days as opposed to 12 months of 30 days. The first-known abacus dates back to 300 BC and, in 1300, universities teaching maths were founded in France. The printing press accelerated mathematical education as the price of manuscripts and written books significantly declined (about 2.4 per cent a year for 100 years after Gutenberg). The printing press also shifted wages towards the scientific subjects. In the 17th and 18th centuries, pay rises for professors were highest among those who taught anatomy, astronomy, medicine and natural philosophy.

Our Leaving Cert is a flawed system – even the teachers acknowledge that – and it is a shame to see the furore over the latest maths exam. Teaching children to love maths should be a starting point for any syllabus. Maybe linking maths to the evolution of human thinking might spark a story in the minds of children, who could be attracted by the combination of anthropology, history and evolution, rather than the sterility of equations alone. There is so much beauty in maths, but it sometimes needs a bit of help to unravel.

What about starting with a story in Africa, 20,000 years ago in a lost civilisation, buried beneath a volcano, with ancient maths nerds scratching notches on a baboon’s femur? I’d sit up and listen – wouldn’t you?