Did humans invent maths, or did we discover it? Does nature conform to maths or maths to nature? Debates over these complex and contrasting questions continue to rage today. Both sides of the debate have compelling evidence and arguments to support, but perhaps the true reality lies in the middle-ground?
Fuelling the fire to this debate, famous German theoretical physicist Albert Einstein once remarked: “How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?”. Simply put, this cleverly ambiguous remark questions whether it is merely a coincidence that mathematics so incredibly conforms to and explains the workings of nature.
In his 2013 article Is Mathematics Invented or Discovered?, physicist and electronic engineer Derek Abbott writes that Einstein’s conundrum typically attracts various responses. Let’s explore the two most common, which are that maths is innate (naturally occurring) and that maths is a human construct.
Maths is innate
Nature exists and functions due to an underlying rule of mathematics, which humans have discovered during our endeavour to understand our natural world, and hence mathematics provides predictive power (that is, it generates testable predictions).
Interestingly, the Ancient Greek philosophers and mathematicians Pythagoras, Plato and Euclid (the ‘father of geometry’) believed, to varying degrees, mathematics to be the architecture of nature – that nature is a physical manifestation of mathematical laws.
There are several notable examples that support the idea of maths being intrinsic to nature.
Shapes that can be seen repeatedly in themselves (never-ending patterns) are called Fractals. They exist in nature ranging from macroscopic to microscopic observations as rivers, coastlines, mountains, clouds, plants, snowflakes, lightning strikes, seashells and even blood vessels.
Another example of mathematics innate character is seen in the insect world. Whether by intellect or pure instinct, bees build honeycombs as hexagonal structures to produce the most efficient storage space and using minimal materials – a theory known as ‘honeycomb conjecture‘.
In 1202 Leonardo Fibonacci in Pisa discovered and published the theory of Fibonacci numbers, where each number in a sequence is the sum of the previous two. They are evident in the formation of sunflower seeds, flower petals, pinecones, pineapples and countless more occurrences in nature.
Some spiral galaxies and nautilus shells even mimic golden spirals – which are based on the Fibonacci derived golden ratio, an ‘ideal’ number approximately equal to 1.618. Even Leonardo da Vinci was said to have likely used the golden ratio in painting the Mona Lisa’s appealing facial features by employing Fibonacci spirals.
Maths is a human construct
Of course, the counter argument to all of the above is that nature exists and operates purely due to coincidences, and that humans have invented mathematics to rationalise nature. Maths is a product of the conscious mind: both a tool and a language used to make sense of the designs and functions of our universe – quenching humans’ instinctual thirst for rationalisation.
The debate over whether mathematics is man-made or intrinsic to nature is reminiscent of the chicken and an egg conundrum – ‘which came first?’ – an ambiguous conundrum with no definitive answer. By simply asking whether maths is invented or discovered, the possibility that it is an intricate combination of both becomes overshadowed.
Perhaps all the designs and functions of nature are created as random coincidences, yet still conform to an abstract universal order which humans decipher and build concepts to comprehend thus creating mathematics?
ORIGO Education’s Core program Stepping Stones, is an Australian Curriculum approved program and brings conceptual understanding of mathematics to the forefront of teaching and learning through digital tools and print supplements.