09/04/2020

In the 'Origins' series, concepts to define mathematics.

Foto: Reprodução NT Play

What's the first thing that comes to mind when we talk about mathematics? Some people shudder at the mere mention of the word: the concept seems completely abstract, distant from reality, and even incomprehensible. But there are also those who see beauty, perfection, and precision in it, allowing them to perceive, through this fascinating science, the reality that surrounds us.

To discuss this topic, the new season of the TV Novo Tempo series "Origins " features dozens of definitions of what mathematics is and talks about the science that, for many, can still be considered a real "monster ." Marcelo Viana, director-general of IMPA, and the winner of the 2014 Fields Medal, Artur Avila ( IMPA/Universität Zürich) , are among the mathematicians who share their personal and professional experiences to try to demystify the subject.

Although there is no consensus among experts, Viana defines mathematics as "the only thing that happens around us that we can describe using numbers or other concepts. It is the body of knowledge to manipulate these tools."

The director-general of IMPA further emphasizes that, within the field, they deal with many other notions, such as "shape, distance, and many others that cannot be reduced to numbers." The Rubik's Cube is a good example to illustrate this. "It's pure mathematics! And what lies behind the object is not a number: it's a group, which is another concept that gives rise to algebra, topology, and geometry. These are various notions that we develop to understand what is happening around us."

Foto: Reprodução NT Play

In an imaginary timeline, we can consider that the first contact with mathematics happens very early, during childhood, with concepts generally passed on by the family and continued in the first school years. “Young children are very curious and feel more comfortable with their own mathematics. Between the ages of 2, 3, or 4, we very quickly realize that mathematics is very useful for counting toys, knowing if their slice of pizza is bigger than their sibling's… So, concepts like volume and shape are very useful when the child is young,” she observes.

The mathematician warns that as children progress through school age, mathematics tends to become more abstract. This becomes a challenge for teachers who try to connect numbers, concepts, and definitions to reality. "It's not impossible, but it's an even greater challenge," he points out.

And when educational milestones are successfully completed, it's possible to develop a taste for each new achievement. "The pleasure you feel is different at each moment," points out Artur Avila. "In the beginning, I didn't have the mathematical knowledge I have now, and therefore I couldn't appreciate things in the same way I can now."

Experienced in competitions, Avila notes that problems without solutions provided by teachers can bring satisfaction and give impetus to the learning process, as they become challenges. "There is the pleasure of solving problems and making discoveries on your own, as happens during mathematics olympiads," emphasizes the researcher.

Click here to watch the episodes “ What is mathematics? ” and “ The math monster ” .