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Where exactly do mathematics come from? It is a question with which some of the most eminent mathematical minds have been discussed.
Some people think that we discover them, others that we invent them; some think they are both discovered and invented, while others confess that they do not know it.
The jury is very divided
But there is something that all parties had to take into account before taking sides: 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 of the origin of mathematics.
Fundamental but separate.
In ancient Greece, there was no doubt because everything seemed to indicate that mathematics was something we discovered.
For Pythagoras and his disciples, they were a window on the world of the gods.
But there is more: although they are a fundamental part of the world in which we live, they are, in a way, strangely separated.
It is crucial to try to understand this apparent paradox in . the dilemma on the origin of mathematics .
And that's what Plato did
In another kingdom
The philosopher was fascinated by the geometric shapes that could be produced according to the rules of mathematics, which he believed they came from the deities.
To understand what he said, let's use a flat, closed curve whose all points are equidistant from the center.
Better said, a circumference.
It is likely that you already had to draw one, that you tried to make yourself and that it went well, but not quite perfect. [19659018] Get close enough and any physical circumference, as well as the circle that it determines, will have protuberances and imperfections.
According to Plato, it is because circumferences and impeccable circles do not exist in the real world; The perfect circle lives in a perfect-form divine world a kind of paradise where all mathematics can be found, but only if you are a true believer.
5 objects
The philosopher was also convinced that everything in the cosmos could be represented by 5 solid objects called solid platonic .
So, Earth was the solid rock cube. The fire was the very pointed tetrahedron. The air was the octahedron, while the icosahedron, with its 20 triangular sides, represented the water.
The last Platonic solid, the dodecahedron, encapsulated the entire universe.
Platonic solids have something special. These are the only objects in which all faces have the same shape and there are only 5.
As difficult as you can try, you will never find another object presenting these unique mathematical qualities.
Plato believed that forms existed in a world of perfect forms beyond our reach – mortal simulations – a place we call the Platonic world .
Although these ideas may seem a little crazy, they are numerous. people who believe in it, and who look like strings.
"Platonic solids, for me, are a excellent example of discovering mathematics instead of inventing ," explains Professor Max Tegmark. Physics and Mathematics at the Mbadachusetts Institute of Technology (MIT).
"When the ancient Greeks discovered that they existed, they were able to invent their names.The twelve-sided one called it the dodecahedron." But the pure dodecahedron itself already I was there to discover, "says Tegmark.
" I have Platonic vision that there are triangles, numbers, circles around there, "says Physics philosopher Eleanor Knox All of them are all part of this mathematical landscape that I'm exploring."
But all the world does not believe in this Platonic world of mathematical truths.
"I believe that the Platonic world is in the human head ," adds astrophysicist Hiranya Peiris, "it's a product of our imagination," he adds. he.
"I understand people who really believe in this other realm of reality and, in particular, they spend their days Brian Green, professor of physics and mathematics at Columbia University. 19659033] "That's not to say that it's real" Decree.
Plato would have disagreed. 19659036] He encouraged us to believe in this other world where we could find all mathematics, and not to be fooled and to think that the world around us is all that there is.
What we perceive as reality, has he warned, is only in the shadow
Two millennia ios later …
More than 2,000 years ago, Plato took the geometry of forms as proof of the influence of God, ideas that were limited to the senses and to the imagination
Today, geometry is at the forefront of science. [19659039Newtechnologieshaveallowedustoobservetheworldbeyondoursensesandagainitseemsthatthenaturalworldisactuallywritteninmathematicallanguage19659042] This is a virus model.
You will immediately notice its geometric shape: it is one of the platonic solids.
Reidun Twarock, professor of mathematics at York University, his colleagues designed a computer-based simulation that places the mathematician at the center of the virus.
"What we are trying to understand is how this virus is formed and we create for it the illusion of being in the virus, where the genetic material is normally located," Exp
They thus discovered that the virus exploited the power of mathematics to build its outer wall in the fastest and most efficient way possible.
Armed with this knowledge, Reidun was trying to find a way to prevent the spread of viruses such as hepatitis B and even the common cold.
That's what makes this research so interesting.
Reveal the mathematical foundations that allow the virus to form an envelope. This can give us a way to interrupt it. Without an outside wall, there is no virus; no virus, no infection
Discovered or invented?
Beyond the realm of the human senses, it seems that the Universe knows mathematics one way or another.
It's really surprising to see how many times these patterns seem to occur. They are in plants, they are in marine life, even in viruses.
Mathematics … do we invent them or discover them? A millennial debate without solution
And each time we add more things that we can explore and exploit with the help of the mathematics we have,
All this reinforces the idea that there is a natural order that supports the world around us. and that we are only discovering mathematics.
But maybe we looked for models in the wrong places.
If everything is in our head, the brain could be a good place to look.
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