Mathematics

by Sam Baron

Associate professor, Australian Catholic University

Many people think that mathematics is a human invention. To this way of thinking, mathematics is like a language: it may describe real things in the world, but it doesn’t “exist” outside the minds of the people who use it.

But the Pythagorean school of thought in ancient Greece held a different view ... its proponents believed reality is fundamentally mathematical.

More than 2,000 years later, philosophers and physicists are starting to take this idea seriously.

As I argue in a new paper, mathematics is an essential component of nature that gives structure to the physical world.

Honeybees and hexagons

Bees in hives produce hexagonal honeycomb. Why?

According to the “honeycomb conjecture” in mathematics, hexagons are the most efficient shape for tiling the plane. If you want to fully cover a surface using tiles of a uniform shape and size, while keeping the total length of the perimeter to a minimum, hexagons are the shape to use.

The hexagonal pattern of honeycomb is the most efficient way to cover a space in identical tiles.

Charles Darwin reasoned that bees have evolved to use this shape because it produces the largest cells to store honey for the smallest input of energy to produce wax.

The honeycomb conjecture was first proposed in ancient times, but was only proved in 1999 by mathematician Thomas Hales.