Is maths an art? For many, the idea of numbers that you cannot count seems bizarre. But now scientists are proving that we need imaginary numbers to understand the world we live in.
Imaginary numbers are real, say physicists
Is maths an art? For many, the idea of numbers that you cannot count seems bizarre. But now scientists are proving that we need imaginary numbers to understand the world we live in.
Maths can often be hard, but numbers, it seems to us, are easy. After all, we can see numbers in nature: you can count the number of apples on a tree, or fingers on your hand. Even some intelligent animals, like chimpanzees and dolphins, can count. Can maths really be so complex, we ask, if it is based on such simple foundations?
But it turns out this is too good to be true. The numbers that 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 in the world.
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 containing 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, the branch of physics that studies the behaviour of tiny particles, like electrons. 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 have, they are discovering that imaginary numbers are more present in nature than we might have thought. They are vital for many calculations in the real world: they can explain how electric currents work and guitar strings work, and why things swing back and forth.
All this talk of imagination and tiny worlds has some asking if we need to rethink maths. They argue that maths is really an art.
Maths has always been integral to 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 most famous works, including the Mona Lisa and the Vitruvian Man.
The alliance between maths and art grew ever stronger in the twentieth 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.
And Dutch painter Piet MondrianA Dutch painter famous for his abstract grids of primary colours. became known around the world for his minimalist, geometric paintings, composed of nothing but coloured squares. He thought that this very abstract kind of painting was the truest form of art, because it emphasised art's distance from and superiority to ordinary reality.
But some go still further. They think maths is actually a kind of art.
The definition of art has always been controversial. But 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 exactly the same: applying rules systematically to create beautiful patterns from nature.
<h5 class=" eplus-wrapper" id="question">Is maths an art?</h5>
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.
Natural numbers - Numbers used for counting and ordering. When used for counting, they are called "cardinal numbers", and when used for ordering, "ordinal numbers".
Irrational numbers - Numbers 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.
Square root - A number derived from dividing another number by itself.
Pi - A 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.
Imaginary numbers - A natural number multiplied by the imaginary unit i, which is the square root of negative one. They were discovered in the 16th century.
Leonardo da Vinci - An 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.
Golden ratio - If 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.
Wassily Kandinsky - A Russian painter and art theorist who was a pioneer of abstract art.
Piet Mondrian - A Dutch painter famous for his abstract grids of primary colours.
Imaginary numbers are real, say physicists

Glossary
Natural numbers - Numbers used for counting and ordering. When used for counting, they are called “cardinal numbers”, and when used for ordering, “ordinal numbers”.
Irrational numbers - Numbers 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.
Square root - A number derived from dividing another number by itself.
Pi - A 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.
Imaginary numbers - A natural number multiplied by the imaginary unit i, which is the square root of negative one. They were discovered in the 16th century.
Leonardo da Vinci - An 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.
Golden ratio - If 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.
Wassily Kandinsky - A Russian painter and art theorist who was a pioneer of abstract art.
Piet Mondrian - A Dutch painter famous for his abstract grids of primary colours.