Proof in history: The intertwined relationship between maths and art

The relationship between maths and art seem polar opposites by nature, with one typically perceived as being devoted to logic and reasoning with the other devoted to expression, passion and aesthetic. The common belief is that maths merely works closely with science to define and prove the laws that dictate our natural world, whereas art depicts human senses and provokes emotional responses.

Although the two disciplines seem vastly different on paper, in reality maths and art are for the most part, intertwined. Have you ever considered that maths and art essentially make the invisible visible, and typically use patterns to rationalise thoughts and concepts?

In a practical sense, painting a line on a canvas or carving a surface from a sculpture relies on a realisation of the underlying geometry of a subject. Equally, maths strongly influences the architectural aesthetic of our cities, and is key to engineering structures that stand tall and strong.

In his article Why Math is an Art, Not a Science, Peter Flom argues that maths is less like science and more like art due to its subject matter, goals and history. Science is the study of real, concrete things. By contrast, maths invents and proves abstract ideas conceived purely by theorising in the mind – a process comparable to the creation of abstract art stemming from an artist’s imagination. Scientists seek to explain observations using hypotheses that don’t need to be proven true, whereas mathematicians work to solve conjectures and theorems in an absolute sense by seeking new proofs – just like artists seek new forms of beauty and expression. The history of science is littered with theories disproven over the ages and hence disregarded. However, many mathematical concepts (dating from ancient Greece or even earlier) have endured centuries of scrutiny to become the foundation of modern maths, a process comparable to the evolution of modern art which is often inspired by past masters.

The intertwined relationship between maths and art is evident throughout history, spanning back to ancient civilisations around the world. Many ancient artefacts (such as pots and vases), sculptures and architectures are rich in intricate geometric designs, reflecting a strong relationship between maths and art. Historic Islamic art contains detailed symmetries that continue to be studied today. On a grander scale, one might even say the execution of ancient wonders like the Egyptian Pyramid, or the giant Columbian Nazca Lines etched landscapes demonstrate how closely maths and art coincide to create objects both functional and aesthetic.

One of the oldest known artists to consciously incorporate maths into his works was Ancient Greek High Classical Sculptor Polykleitos (Polyclitus) of Argos during the 5^th Century BCE. Considered one of the greatest sculptors of classical antiquity, Polykleitos formulated new methods and principles, known as the Canon (or “rule”) of Polykleitos, for designing aesthetic human sculptures with ideal proportions and balance. Based on a simple mathematical formula in which the human body is divided into measured parts relating to one another, his Canon suggests the shoulders and hips of sculptures are positioned in a way that counterbalances tension and relaxation known as the chiastic balance. Polykleitos’ Canon is the perfect expression of what the Greeks called symmetria, or symmetry, which encompasses balance, proportion and contrast in artistic works.

Beginning in the 14^th Century, The Renaissance was a period of artistic “rebirth” following the Middle Ages in Europe, which saw more artists recognise the close relationship between maths and art. Several Renaissance artists realised that basic notions of mathematics such as perspective and symmetry would make artworks more realistic and alluring. Leonardo da Vinci famously incorporated mathematics into some of his artworks (“Let no one read me who is not a mathematician”), one of which being the iconic Mona Lisa (painted sometime between 1503 and 1519) – although it is up for speculation. Many scholars believe he consciously utilised The Golden Ratio (or the Divine Proportion, the “most beautiful number in the universe”) – an irrational number approximately equal to 1.618 – to create the Mona Lisa’s appealing proportions, but others suggest the contrary. Nonetheless, Leonardo da Vinci was responsible for drawing the iconic Vitruvian Man, or Proportion Man, in a collaborative three-volume treatise on the ‘Golden Ratio’ in 1509 entitled De Divina Proportione (On Divine Proportion). Combining maths and art, the Vitruvian Man shows a man fitting inside a circle and square to demonstrate the different ratios of the human body and teach the importance of proportions.

The beauty of maths embedded in art is often subtle, unrecognised and taken for granted, yet their intertwined relationship is evident throughout history – this blog only scratches the surface! Beyond sculptures, paintings and drawings, maths underlies the forms, patterns and frameworks of several famous historical poems, plays and novels. In the music world, Pythagoras famously discovered that the notes humans respond to as harmonic has a mathematical underpinning and that maths informs musical compositions. As German philosopher Gottfried Wilhelm Leibniz once famously declared: “Music is the pleasure the human mind experiences from counting without being aware that it is counting”.

You may ask ‘…so how does this all affect me?’.

Well, there are many well known benefits to mixing maths and art education, children demonstrate improved comprehension, concept visualisation, increased inspiration, technological inspiration, and of course it is simply – a great way to multiply your children’s fun! After all, ORIGO Education is focused on making learning mathematics meaningful, enjoyable, and accessible for all.