Maths can be hard, but numbers are easy. You can count the apples on a tree, or fingers on your hand. Even some intelligent animals can count. Can maths really be so complex, we ask, if it is based on such simple foundations?

But it turns the numbers we can "see" in the real world - known as "natural numbersNumbers used for counting and ordering. When used for counting, they are called "cardinal numbers", and when used for ordering, "ordinal numbers"." - are only part of the story. In fact, many other kinds of number exist.

For example, it is much harder to visualise negative numbers: no-one has ever had negative three fingers.

And so-called irrational numbersNumbers that do exist, but are not natural numbers. They are defined as those numbers that cannot be expressed as the ratio of two integers. They include almost all square roots. - usually the square rootA number derived from dividing another number by itself. of a natural number - play an important part in our everyday lives. One of the most famous irrational numbers, piA number equal to the ratio of a circle's circumference to its diameter. In every circle, this number comes out at approximately 3.14159, although its decimals technically never end., is essential for building anything with circles. We could not have invented the wheel without understanding irrational numbers.

One of the most important types of unnatural numbers today is imaginary numbersA natural number multiplied by the imaginary unit i, which is the square root of negative one. They were discovered in the 16th century.: square roots of negative numbers. They are particularly important when it comes to quantum physics. At this level, natural numbers all but disappear. If an electron could count, it would count in imaginary numbers.

It took some time for quantum physicists to embrace imaginary numbers. But now, they are discovering that imaginary numbers are more present in nature than we thought.

All this talk of imagination and tiny worlds has some asking if we need to rethink maths. They argue maths is an art.

Leonardo da VinciAn Italian artist and inventor (1452 - 1519), considered to be one of the world's greatest geniuses. He painted the Mona Lisa and designed an early flying machine. made use of the mathematical concept of the golden ratioIf a line is divided into two unequal parts, the larger part will be bigger than the smaller part by a particular proportion, or ratio. If the ratio of the larger part to the smaller part is the same as the ratio of the total line to the larger part, that ratio is then known as 'golden'. The golden ratio is about 1.618 to 1. in many of his works, including the Mona Lisa.

The alliance between maths and art grew stronger in the 20th Century. Russian abstract artist Wassily KandinskyA Russian painter and art theorist who was a pioneer of abstract art. made grand paintings using straight lines, concentric circles and triangles.

Dutch painter Piet MondrianA Dutch painter famous for his abstract grids of primary colours. became known for his minimalist, geometric paintings, composed of coloured squares. He thought this very abstract kind of painting was the truest form of art, because it emphasised art's distance from ordinary reality.

But some think maths is a kind of art.

One idea that has become more prominent in recent times is the idea of art as a practice. According to this idea, 'art' is a process by which we apply a consistent set of principles to produce something beautiful. 

And maths, some argue, is the same: applying rules to create patterns from nature.

Yes: Although we think of maths as analytical and stuffy, in reality mathematicians have access to a whole wonderful world of imaginary things. They are closer to artists than scientists. 

No: Maths might be more impressionistic than we first thought, but it is still a rigorous process of discovery. Art is about invention and creativity. The two have completely different aims.

Or... Whether or not we consider maths a kind of art, the most important lesson to draw is that we can find art and beauty in everything, be it an abstract painting or a mathematical equation.

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