Many people think that mathematics is a human invention. It has been thought mathematics is like a language. It may describe real things in world but it does not exist outside minds of people who use it.
Pythagorean school in ancient Greece held a different view. They said reality is fundamentally mathematical. More then 2,000 years philosophers and physicists started taking this idea seriously. Mathematics is an essential component of nature that gives structure to the physical world. The nature and physical world is made of mathematics.
Honeybees and hexagons
Honeybee hives are made of hexagon. If you want to fully cover a surface using tiles of uniform shapes keeping the total length of perimeter to a minimum, hexagons are the shapes to use. Thus bee hives are made of hexagons.
Cicadas and Prime Numbers
Here is another example. The two subspecies of North American cicadas live mostly in the ground. In every 13 or 17 years the cicadas swarm for a period of around two weeks.
Why is it 13 and 17 years? Why not 12 and 14 or 16 or 18? It is because 13 and 17 are prime numbers. When a cicada with a 13-year life cycle comes out of the ground, none of its predators will be out of the ground, because none of 2, 3, 4, 5, 6, 7, 8 or 9 divides evenly into 13. The same is true for 17.
Mathematics is not a discovery but a creation. From shape of soap films to gear designs, to location and size of gaps in the rings of Saturn mathematics is everywhere. The ancient philosopher Plato thought mathematics describes objects that really exist. Plato also maintained mathematical object exist outside time and space. But such a view deeps the mystery explains everything. The ancient Pythagoreans agreed with plato but they did not think mathematical objects exist beyond time and space. Tegmark argues reality is a mathematical object and reality is a simulation.
The future of Mathematics
It makes sense that pythagoreanism is being rediscovered in physics. As the boundary between physics and mathematical blurs it is harder to say which parts of world are physical and which and mathematical. it is strange that Pythagoreanism has been neglected by philosophers for so long. The time is about change. The time has arrived for a Pythagorean revolution to radically alter the understanding of reality.
