Maths theory holds the key to nature’s beauty

Colour by numbers: There’s mathematical order to patterns in the natural world.

Is maths the secret of beauty? Scientists have discovered that the world’s most famous codebreaker was right when he proposed that natural shapes and patterns were ruled by a hidden formula.

Alan Turing is famous as the mathematician who helped shorten World War Two by two years, with his work cracking Germany’s Enigma code.

But he made another remarkable contribution to science: a mathematical theory that explains all of nature’s patterns.

In the natural world, some shapes and patterns happen time and time again — from the huge spirals of galaxies, right down to the circles of dividing cells in an embryo.

In 1952, Turing came up with a theory suggesting that what look like random designs are actually controlled by two chemicals. Different reactions between these chemicals produce patterns like spots, stripes and spirals.

Turing even worked out that these patterns can be predicted by two mathematical equations.

“There’s an elegant simplicity and beauty in nature revealed by mathematical patterns and shapes,” says physicist Max Tegmark, author of Our Mathematical Universe. The beauty of the natural world, he says, is ordered by the laws of maths.

For thousands of years, humans have tried to understand how maths shapes the world around us. The “golden ratio” (first described by the Greek mathematician Euclid, in the 4th century BC) has been seen by artists throughout history as the perfect, most beautiful proportion.

The eye of the beholder?

Is beauty really down to maths or creativity? Isn’t beauty about looking at something and being overwhelmed by its wonder? It can’t be explained by rules or laws. There aren’t any right or wrong answers. Creative beauty is the opposite of maths.

But is beauty ever random? Doesn’t all art obey rules? The paintings of Jackson Pollock may look like chaos, but there is also order to them. Why else have artists and architects bothered to study the golden ratio? Beauty depends on patterns of order beneath the surface.

You Decide

  1. How can maths be beautiful?


  1. Write your own definition of “beauty”. Is there anything that all beautiful things have in common? Then, discuss your answers as a class.

Some People Say...

“The study of mathematics, like the Nile, begins in minuteness but ends in magnificence.”

Charles Caleb Colton, English cleric and writer (1780-1832)

What do you think?

Q & A

What do we know?
Recently, scientists have proven that patterns in hair follicles and chicken feathers are — as Turing believed in 1952 — caused by two chemicals reacting to each other.
What do we not know?
Why some patterns happen so often in the natural world. Scientists think it might be the most effective way for plants to grow.

Word Watch

Enigma code
The Enigma was a type of machine used by the Germans to send secret messages during the war. Turing helped to build a machine called the Bombe to make it quicker to crack a code that the Germans were changing every day.
A fertilised egg that is developing into a fetus.
The same year that Turing was convicted of being gay. As a punishment, he was chemically castrated and died by suicide two years later. In 2013, he was given a royal pardon.
Jackson Pollock
Modern abstract American artist (1912-1956), famed for pouring or splashing paint onto canvases as art.
Golden ratio
Also known by the Greek number “phi”, which stands for 1.618.

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