A Short History of Algebra Brought to You by Professor Marcus Du Sautoy

As a leading game-based learning platform, one of our games Jabara helps children to develop a deeper understanding of algebra. Marcus Du Sautoy has kindly written us a two-part blog on algebra, from its beginnings to its use in the present day. And allowed us to share his fantastic BBC documentary on the subject. Read Part I below!

 

When I’m at a party and someone asks me what I do, a look of horror generally descends on their faces when they discover I’m a mathematician. I get the impression that as a research mathematician they think I must be doing long division to a lot of decimal places and surely I’ve been put out of job by my computer.

 

But before they flee to the other side of the party I try to explain to them that mathematics is not about doing calculations. It’s all about looking for patterns. We are all pattern searchers at heart. Our brains are programmed to be sensitive to spotting patterns because it gave us an evolutionary advantage. If you’re in the jungle and you spot something with symmetry then it’s likely to be animal. And chances are, one of you is on the menu!

 

As kids learn their multiplication tables they might start to spot some curious patterns that are hiding underneath these calculations. For example, ask your students what 5×5 is. Then ask them 4×6. What’s the connection between the two answers? Now ask them 6×6 followed by 5×7. Then 7×7 followed by 6×8. Hopefully they spot that the second answer is always 1 less than the first

 

It’s spotting these sort of patterns that can turn the tedium of learning tables into something slightly more interesting. But does this pattern always persist? If I take a number and square it will it always be one more than taking the numbers either side and multiplying them together.

 

I’ve used words to try to describe this pattern but in the 9th century in Iraq a new mathematical language called algebra was created that could describe this pattern. Let x be any number. Then if you square x it will be 1 more than (x-1) times (x+1). Or written as an algebraic formula:

 

x2=(x-1)(x+1)+1

 

But this algebraic language also allowed mathematicians to show why this pattern will always persist whatever numbers you choose. Expand (x-1)(x+1) and you get x2-x+x-1=x2-1. Add 1 to this and you’ve just got x2.

 

Algebra is the grammar that underlies the way that numbers work. This new language of algebra provided a syntax to explain the patterns that lie behind the behaviour of numbers. A bit like a code for running a programme, it will work whatever the numbers you feed into the programme.

 

It was developed by the director of the House of Wisdom in Baghdad, a man called Mohammed ibn-Musa al-Khawarizmi. Founded in 810 the House of Wisdom was the foremost intellectual centre of its time and attracted scholars from around the world to study astronomy, medicine, chemistry, zoology, geography, alchemy, astrology and mathematics. The Muslim scholars collected and translated many ancient texts, effectively saving them for posterity and without their intervention, we may never have known about the ancient cultures of Greece, Egypt, Babylonia and India. However, the scholars at the House of Wisdom weren’t content with translating other people’s mathematics as they wanted to create a mathematics of their own and push the subject forward.

 

It was this desire for new knowledge that led to the creation of algebra…

 

 

Words by Marcus Du Sautoy

Simonyi Professor for the Public Understanding of Science at the University of Oxford.

www.simonyi.ox.ac.uk

@MarcusduSautoy

 

 

Click here to have a go at playing our algebra game Jabara!