Blueprints by Marcus Du Sautoy (Fourth Estate £22, 304pp)
The pairing of art and mathematics, as Marcus Du Sautoy writes on the first page of his absorbing new book, would seem for many ‘synonymous with chalk and cheese. A contradiction in terms.’
Maths inhabits a realm of cold logic; the arts, one of emotional expression. Yet Du Sautoy will have none of this. Maths has its own aesthetic. He quotes approvingly the mathematician
G.H. Hardy, who once wrote that, ‘Beauty is the first test: there is no permanent place in this world for ugly mathematics.’
Recent research has shown that, when mathematicians encounter maths they consider beautiful, a part of their brain lights up. It’s the same part activated in non-mathematicians looking at art or listening to music that they appreciate.
Du Sautoy contends that the fundamental structures underpinning artistic creativity are mathematical. He calls them blueprints. Artists may not always know it but they are ‘secret mathematicians’.
The strong connections between music and maths have frequently been acknowledged. Two of the greatest classical composers were obsessed by numbers. According to Du Sautoy, Mozart’s opera The Magic Flute is ‘dripping with maths’. The repeated use of groups of three in the story is only the most obvious of many numerical patterns the composer employed. J.S. Bach had his own obsession – with the number 14 – and wove it everywhere into his music.
However, it is not just music that is shaped by mathematics. So too are other arts. In architecture, the villas designed in the 16th century by Andrea Palladio have been described as ‘frozen music’. They could equally be called ‘frozen mathematics’, since they make ingenious use of geometric theory.
In the 20th century, the tower block known as L’Unite d’Habitation, designed by the Swiss-French architect Le Corbusier, has measurements based on a sequence of numbers he devised. Each number in the sequence is the sum of the two previous numbers. This is familiar to mathematicians, who know it as the Fibonacci sequence.
Mozart’s opera The Magic Flute is ‘dripping with maths’
Du Sautoy finds his blueprints wherever he looks in creative endeavour. In the visual arts, he notes that the abstract works of Jackson Pollock were examples of an important mathematical structure only identified properly in the 20th century.
Pollock was painting ‘fractals’, a word describing a geometric pattern that arbitrarily repeats – it was not coined until two decades after the artist’s death. Recently, a group of supposed Pollock canvases were shown to be fakes because they were not fractals.
In literature, Du Sautoy explores the hidden games Shakespeare played with numbers.
Blueprints is not always an easy read for non-mathematicians. But it’s a constantly surprising one in its determination to show us that works of art we love are ‘often pieces of mathematics in disguise’.