Where does mathematics come from? This is an issue that some of the most prominent mathematical minds are discussing.
Some believe that we are discovering them, others that we invent them; some think they are partially discovered and partially invented, and some admit they do not know.
The jury is very divided.
But there is something that all sides had to consider before taking the position: the ideas of Plato, one of the most important figures of ancient Greece.
What the famous philosopher has said remains to this day the basis of what many scientists think about the origin of mathematics.
Basic, but separate
There was no doubt in ancient Greece, because everything seems to indicate that mathematics is something that we have discovered.
For Pythagoras and his followers, they were a window to the world of gods.
But there is something more: although they are a basic part of the world in which we live, they are somehow strangely separated from it.
Attempting to understand this apparent paradox is a key point dilemma about the origin of mathematics.
And that's what Plato did.
In another kingdom
The philosopher was fascinated with geometrical shapes that could be produced in accordance with the principles of mathematics, which he believed were derived from deities.
To understand what he said, let's use a flat, closed curve in which all points are an equal distance from the center.
It's better to say the circuit.
Most likely you had to draw one one day that you tried to look good and that it certainly worked, although not entirely perfect.
You had access to the most accurate computer in the world, the circuit you draw would not be perfect either.
Approach enough and each physical circuit, as well as the circle that defines it, will have bumps and imperfections.
According to Plato, because circuits and pristine circles do not exist in the real world; the perfect circle lives in the divine world of perfect forms, a kind of sky in which you can find all maths, but only if you are a true believer.
The philosopher was also convinced that everything in the cosmos can be represented by 5 permanent objects known as Platonic solids.
So the Earth was a solid rock cube. The fire was a very pointy tetrahedron. The air was an octahedron, and the icosahedron with 20 triangular sides represented water.
The last Platonic solid, the dodecahedron, closed the entire Universe.
There is something special in platonic solids. These are the only objects in which all pages have the same shapeand there are only five.
No matter how hard you try, you'll never find another object with these unique mathematical features.
All these forms, as Plato believed, existed in a world of perfect forms beyond our reach – ordinary mortals – a place we call platonic world.
Although these ideas may seem a bit crazy, there are many people who believe in them, and these people seem to be in their right senses.
"Platonic solids are for me a great example that math is discovered instead of coming up"says Max Tegmark, professor of physics and mathematics at the Massachusetts Institute of Technology (MIT).
"When the ancient Greeks discovered that they existed, they were able to come up with their names." The twelve-year-old was called a dodecahedron. But the pure dodecahedron was already there to discover, "says Tegmark.
"I have a Platonic vision that there are triangles, numbers, circles" – says the philosopher of physics Eleanor Knox. they are part of this mathematical landscape I discover. "
But not everyone believes in this Platonic world of mathematical truths.
"I think so The Platonic world is in human head", says astrophysicist Hiranya Peiris," It's a product of our imagination, "he adds.
"I understand people who really believe in this other realm of reality, and especially if they spend days and nights thinking and researching this kingdom," says Brian Green, professor of physics and mathematics at Columbia University.
"It does not mean it is real", decrees.
Plato would not agree.
He encouraged us to believe in this other world where all mathematics can be found, and do not be fooled and think that the world around us is all that exists.
What we perceive as reality is warned, it is nothing but shadows.
Two thousand years later …
Over 2,000 years ago, Plato took the geometry of forms as proof of God's influence, ideas limited to the senses and imagination.
Today Geometry is at the forefront of science.
New technologies have allowed us to look at the world beyond our senses and once again it seems that the natural world is really written in the language of mathematics.
This is the virus model.
You will immediately notice its geometric shape: it is one of the Platonic solids.
Reidun Twarock, a professor of mathematics at the University of York, her colleagues designed a computer simulation that puts mathematics at the center of the virus.
"We are trying to understand how this virus is made and we create the illusion of being inside a virus, in a position where genetic material is usually found," explains BBC Reidun.
So they discovered it the virus uses the power of mathematics to build its outer wall in the fastest and most efficient way.
Armed with this knowledge, Reidun tries to find a way to prevent the spread of viruses such as hepatitis B and even a cold.
This is what makes these tests so exciting.
Revealing the mathematics that allows the virus to form its envelope can give us a way to stop it. There is no virus without the external wall; no virus, no infection.
Discovered or invented?
Beyond the reach of human senses, it seems that the Universe knows somehow mathematics.
Really it's amazing how often these patterns seem to appearThey are in plants, they are in marine life, even in viruses.
And each time we add more things that we can discover and use with the mathematics we have.
All this gives weight to the idea that there is a natural order that sustains the world around us and that we do not just discover mathematics.
But maybe we were looking for patterns in the wrong places.
If everything is in our heads, the brain can be a good place to look.