What if math is an essential part of nature and not something people invented? What if the world of mathematics is the foundation of the world?

Nature is an unstoppable force, and it is beautiful. Everywhere you look, the world of nature is permeated with astonishing patterns that mathematics can describe. Mathematics can explain how such beauty is created from bees to blood vessels, from ferns to fangs.

Mathematics is often described as a language or tool created by people to describe the world around them accurately.

But another school of thought believes that mathematics is actually what the world is made of. That nature follows the same simple rules over and over again because mathematics supports the fundamental laws of the physical world.

That would mean that mathematics existed in nature long before people invented it, says philosopher Sam Baron from the Australian Catholic University.

“If mathematics explains so many things we see around us, then it is unlikely that mathematics is something we created,” Baron writes.

Instead, let’s think of mathematics as an essential component of nature that gives structure to the physical world, as Baron and others suggest. It might prompt us to reconsider our place in it instead of enjoying our own creativity.

Such thoughts date back to the Greek philosopher Pythagoras (~ 575 – 475 BC), who first defined mathematics as one of the two languages that can explain the architecture of nature. The other is music.

# The World of Mathematics

According to Professor Baron, Pythagoras believed that all things were made of numbers and that the Universe was “created” by mathematics.

More than two millennia later, scientists are still trying to figure out where and how mathematical patterns appear in nature to answer some big questions – for example, why cauliflower looks perfect.

“We spent many hours frantically disassembling cauliflower flowers, counting them, measuring the angles between them,” wrote Etienne Farcott, a mathematician at the University of Nottingham who studied cauliflower growth in an attempt to understand this “mysterious variety of wild cabbage.”

Fractals are exceptional, self-repeating patterns that, in addition to some cauliflower, are also found in fern leaves, branched blood vessels, and Saturn’s rings. Fractals are geometric shapes composed of ever-smaller copies of themselves, creating an enchanting “self-image” that is infinitely deep.

Although only mathematically or computer-generated fractals are truly perfect fractals, nature is pretty close.

“These repetitive patterns are everywhere in nature,” says mathematician Thomas Britz of the University of New South Wales in Sydney. “In snowflakes, river nets, flowers, trees, lightning strikes – even in our blood vessels.”

Part of the charm of fractals is that they help explain how complexity is born of simplicity. As Benoit Mandelbrot, a French mathematician of Polish descent who coined the term fractal, said in 2010, “Bottomless miracles spring from simple, endless rules.”

Branched river systems also create almost perfect fractal patterns in the landscape.

These patterns are so persistent that, in one case, archaeologists searched for missing fractals to conclude that the ancient Egyptians may have modified river canals when building pyramids nearby.

## Insects Also Seem to Follow Mathematical Principles

Know it or not, bees build hexagonal honeycombs in a way that produces the most storage space using the least amount of material – a theory known as the ‘honeycomb assumption’ that American mathematician Thomas Hales finally demonstrated in 1999.

Some species of cicadas also have a life cycle directed toward prime numbers. Swarms of two North American species emerge from their underground lairs every 13 or 17 years; a trick scientists think helps cicadas avoid predators at a more regular pace.

In early 2021, researchers discovered a hitherto unknown law of nature: A growth pattern that describes how pointed shapes are formed over and over again in nature – from shark teeth and spider fangs to bird beaks and dinosaur horns.

“The diversity of animals, and even plants, that follow this rule is astounding,” said evolutionist biologist Alistair Evans of Monash University in Australia at the time they discovered a mathematical formula called the “power cascade.”