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.
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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.
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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. 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.
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.
Physicists are discovering that imaginary numbers 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.
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 paintings of coloured squares.
But some go still further. They think maths is 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.
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<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".
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
The Mandelbrot set: An aesthetic marvel created with imaginary numbers. 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”.
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.