People think that mathematics is a human invention. To this way of thinking, mathematics is not a language but a way of thinking, and it doesn't exist outside the minds of people who use it.
The Pythagorean school of thought held a different view. Proponents believed reality is mathematical.
Philosophers and physicists are starting to take this idea seriously.
In a new paper, I argue that mathematics is an essential component of nature and gives structure to the physical world.
There are bees and hexagons.
Hives produce hexagonal honeycomb. Why?
According to the honeycomb conjecture in mathematics, the most efficient shape for tiling the plane is hexagons. hexagons are the shape to use if you want to cover a surface with tiles of a uniform shape and size while keeping the total length of the perimeter to a minimum.
Charles Darwin believed that bees have evolved to use this shape because it produces the largest cells to store honey for the smallest input of energy.
The honeycomb conjecture was first proposed in ancient times, but was only proved in 1999 by mathematician Thomas Hales.
Prime numbers and cisadas.
This is another example. Most of the time, the North American periodical cicadas live in the ground. The cicadas emerge in great swarms for a period of around two weeks after 13 or 17 years.
Why is it 17 years? Why not 12 and 14? Or 16 and 18?
There is an explanation that 13 and 17 are prime numbers.
The cicadas spend most of their lives in the ground, and they have a range of predator that also spend most of their lives in the ground. The cicadas need to come out of the ground when they're not being attacked.
There are life cycles of 2, 3, 4, 5, 6, 7, 8 and 9 years. What is the best way to avoid them all?
The P1–P9 represent cyclists. The years are represented by the number-line. The highlighted gaps show how 13- and 17-year cicadas are able to survive.
A 13-year life cycle and a 12-year life cycle can be compared. The 2-year, 3-year and 4-year predator will be out of the ground when a 12-year life cycle comes out of the ground.
None of the cicada's predators will be out of the ground when it comes out of the ground, because they all divide into 13 in a 13-year life cycle. The same thing is true for 17
The basic facts about numbers seem to have been exploited by these cicadas.
It is easy to find other examples once we start looking. The shape of soap films, the size of the gaps in the rings of Saturn, and the design of engines are all mathematics.
It is unlikely that mathematics is something we've created if it explains so many things around us. The alternative is that mathematical facts can be discovered by insects, soap bubbles, and planets.
What did Plato think?
What is it that we are discovering?
Plato had an answer. He thought mathematics describes things that are not true.
The objects included numbers and shapes. More complicated mathematical objects such as groups, categories, functions, fields, and rings could be added to the list.
Plato believed that mathematical objects exist outside of time and space. It only deepens the mystery of how mathematics works.
Explanation shows how one thing in the world is dependent on another. If mathematical objects exist in a realm other than the world we live in, they don't seem to have much in common with physical objects.
Plato and the ancient Pythagoreans agreed that mathematics describes a world of objects. They didn't think mathematical objects existed beyond space and time.
They believed that physical reality is made of mathematical objects in the same way matter is made of atoms.
It's easy to see how mathematics might play a role in explaining the world around us if reality is made of mathematical objects.
The Pythagorean position has been defended by two physicists in the past decade.
Tegmark says reality is a big mathematical object. Think about the idea that reality is a simulation. A computer program is a kind of mathematical object.
The view of McDonnell is more radical. She believes reality is made of mathematical objects. The Universe is conscious and comes to know itself through mathematics.
The world has two parts, mathematics and matter. Matter gives mathematics its substance.
There is a structural framework for the physical world.
The future of mathematics.
Pythagoreanism is being rediscovered in physics.
In the past century physics has become more and more mathematical, using fields of inquiry such as group theory and differential geometry to explain the physical world.
It is hard to say which parts of the world are mathematical and which are physical.
Pythagoreanism has been neglected by philosophers for a long time.
I think that is about to change. The time has arrived for a Pythagorean revolution that will change our understanding of reality.
Sam Baron is an associate professor.
The Conversation's article is a Creative Commons licensed one. The original article can be found here.