Don't turn the page. Do not, under any circumstances, think, "Algebra... ugh... what is the point?" Algebra is to me, a goddess. Algebra is the universal language that allows us to question the mysteries of life, explosions, patterns, the brain, the oceans, evolution. Take it away, and the world falls apart. And yet this mystical, beautiful discipline is misunderstood by so many, its beauty is hidden in the salt mines of school mathematics. On the right are the sort of algebraic problems that put off students for life. No wonder their answers are so literal.
Most of us were introduced to algebra at school where we substituted letters for mystery numbers (variables), letters which would normally earn great scores on a Scrabble board like x, y and z. Then we would juggle them around to solve the equation. But algebra is so very much more than that.
The story begins in AD830. The place: The House of Wisdom, Baghdad, Persia in the Islamic Golden Age. Works from around the world were brought to Baghdad for translation. Scholars of Babylonian astronomy, Indian numbers and Greek mathematics all came to the richest city in the world to embrace its powerful intellectual culture. A paper mill had been built in the city, and due to this minor industrial revolution, there was a proliferation of books and libraries.
Mohammad Bin Musa Al-Khwarizmi was the father of algebra. He introduced the idea of the zero (brought from India) as a place-holder in arithmetic, which give our calculations their columns of hundreds, tens and units. He also wrote the book that probably changed our world as much as any other: Hisab al-jabr wa al-muqabala, which translates as "The Compendious Book on Calculation by Completion and Balancing". From al-jabr came the word "algebra".
The study of al-jabr progressed in the East, but it took hundreds of years for the scholars of western Europe to advance. Most notable of those who took the Lady Algebra to her next incarnation was Leonardo of Pisa, more commonly known as Fibonacci (c1170-1250).
Fibonacci, the most talented western mathematician of the Middle Ages, spread throughout Europe the use of the Hindu-Arabic numeral system, the system we use today. He also showed that new methods could be used to find solutions of some cubic equations, something that many students still learn, but which, at the time, was a stupendous advance.
The essence of algebra is solving or "reducing" equations to their simplest form. Taking away the confusion and the noise, and making sense of it all. To do that, we have to find specific methods. These methods are known as algorithms – the Latin and English corruption of al-Khwarizmi's name. You can try to solve algebraic equations in different ways. Guessing at solutions, for instance, is one way. It is possible, if you try for long enough, to guess the exact solution of a simple equation. Another way to find a solution is by means of geometric construction. The Greeks favoured this. But it is the invention of further algorithms that has driven, and will continue to drive forward, the language of algebra.
This development of algebra continued through the High Middle Ages, and into the Renaissance. In 1545, we meet one of "the bad boys of maths" – Girolamo Cardano. We may associate mathematicians and scientists with nerdiness and cardigans but, believe me, artists do not have an exclusive hold on drinking, gambling and generally behaving badly (although some nights I wish they did).
Cardano was an illegitimate child whose mother had tried to abort him. His father was a mathematically gifted lawyer and friend of Leonardo da Vinci. Cardano studied medicine at the University of Pavia, but his eccentricity and low birth earned him few friends. Eventually, he became the first to describe typhoid fever, a not inconsiderable achievement in itself, but today, he is best known for his love affair with algebra. He published the solutions to the cubic and quartic equations in his 1545 book Ars Magna, but Cardano was notoriously short of money, and had to keep himself solvent by gambling and playing chess. His book Liber de ludo aleae ("Book on Games of Chance") written in 1526, but not published until 1663, contains the first systematic treatment of probability, as well as a section on cheating methods. I told you he was bad.
Cardano's eldest son was executed in 1560, after he confessed to having poisoned his unfaithful wife. Another son was a gambler, who stole money from him. Cardano allegedly cropped the ears of yet another son. He may have been a genius, but his financial and family life wasn't exactly stable. I wish I'd known him.
After Cardano, we tumble through the "greats". René Descartes (1596-1650) was not merely "the father of modern philosophy"; one of his most enduring legacies was his development of Cartesian geometry. His work allowed geometric shapes to be described in algebraic form. Remember the x and y axes at school? Thank Descartes. How useful was his invention? Probably one of the greatest progressions in our global history, no matter what the subject. Without it, we could not describe music, electronics, wave motion, computing, the movements of the oceans, volcanoes... the list is endless. Descartes gave the goddess her physical form and us, the eyes with which to see her.
Euler, the pre-eminent mathematician of the 18th century, continued with the introduction of function and number theory and infinitesimal calculus. He worked at the St Petersburg Academy founded by Peter the Great, and returned there when Catherine the Great succeeded to the throne. Euler was not a bad boy. He was Swiss. And so to Lagrange, and Galois, who took Milady Algebra to greater and more complex levels, and who enabled us to unlock codes and keys to so much of the natural world around us.
I fell in love with the goddess Algebra when I was very young. I may not have been her greatest child prodigy (we talked less after fifth order partial differentiation at Cambridge, although I blame Newton for that), but I still love her.
She has mystery, she is not stern but, like any goddess, she has her rules. I have an online maths school for children to the age of 13. It is a kind and friendly school, and we have thousands of children who learn with us. Between them, they complete half a million sums a week.
Last week, we launched our School of Mighty Algebra. Set in an animated Ancient Greece, we take our children from the concept of mysterious numbers through to the solution of simple simultaneous equations, where two things can exist at once, but there may be only one circumstance in which that can happen. Now that's magic.
I hope that, at the school, we can introduce many to the goddess Algebra and show them her mystery and beauty. She needs to be released from the darkness, to be appreciated by more. It's time to explain her ways to children in a more engaging manner. After all, it is never good for a goddess to be misunderstood.
Mighty Algebra has videos, games, printables and skill checks: www.themathsfactor.com/algebra
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