19/03/2021

In an interview with Gazeta, Viana questions the 'decolonization of mathematics'.

Crédito: Tomás Rangel

In an interview with the newspaper Gazeta do Povo published this Wednesday (17), the general director of IMPA, Marcelo Viana, spoke about the “decolonization of mathematics”, a discussion that has been growing among researchers in the area. Recognizing that the discipline is used in different cultural contexts, Viana stated that mathematical knowledge is, by essence, “universal and abstract” and, therefore, “deconstructing mathematics is a completely meaningless expression.”

To illustrate the universal nature of the discipline, he cited the example of a mathematical theorem that determines that there are 24 types of symmetry in the world, present in art and nature. “If you analyze works of art excavated from Mesopotamia 5,000 years ago, you will find ceramics that contain these types of symmetry. If you stroll through Lisbon, you will notice that those beautiful Portuguese stone pavements use the same patterns, also present in Marajoara ceramics in Pará. Although the materials used and the symbols represented are diverse, the mathematics used is exactly the same.”

Despite this, the director-general of IMPA argues that mathematics, like other sciences, can also frequently be used to justify preconceived societal ideas. “The attempt to transform mathematics into ideological banners is everywhere and needs to be identified. Numbers have certainly been used to justify discrimination, just as physics was – and still is – used to build bombs, even before nuclear development.”

Read the full interview from Gazeta do Povo:

Marcelo Viana: "It makes no sense to talk about 'deconstructing' mathematics"

Hidden away in the vicinity of the Tijuca Forest in Rio de Janeiro is one of the most prestigious educational institutions in the country, currently closed due to the coronavirus pandemic. It is ironic that Brazil, with its very low PISA scores, is also home to a center of excellence like the Institute of Pure and Applied Mathematics (IMPA), as well as being a member of the elite group of the International Mathematical Union (IMU).

From IMPA (Institute for Pure and Applied Mathematics) came the mathematician Artur Ávila, winner of the Fields Medal – the Nobel Prize of the field – as well as some of the most important initiatives for the popularization of the discipline in the country, such as the Brazilian Mathematics Olympiad for Public Schools (OBMEP) and the Professional Master's Degree in Mathematics, aimed at primary and secondary school teachers.

Since 2016, this teaching, research, and outreach center has been led by the first Brazilian and first mathematician to receive the Louis D. Grand Scientific Prize, France's most prestigious scientific award, offered by the Institut de France. Marcelo Viana, 59, is from Rio de Janeiro, but retains traces of the Portuguese accent he acquired during his 23 years abroad; and he specializes in dynamical systems and chaos theory.

The subject of this interview with Gazeta do Povo, however, was the emergence of researchers who argue that mathematics should be "decolonized." Speaking by phone, Viana discussed the "deconstruction" of the discipline and its importance for a country immersed in inequalities.

Today, there is a movement advocating for the "decolonization of mathematics," in support of identity-based causes. There is talk of "decolonizing Pythagoras." Does "deconstructing" mathematics make any sense?

Mathematics, like any human activity, doesn't arise in a vacuum: it's used within a context. I think it's very important to study the ways mathematics has been applied throughout history. But a common misconception seems to be thinking that this is mathematics; or that doing this type of study is part of mathematics itself – and that's a fallacy. The content of mathematics is independent.

No one knows for sure who discovered the Pythagorean Theorem, but it was known in Mesopotamia around 1800 BC; and it was "rediscovered" and made famous by Pythagoras himself, who was Greek, a thousand years later. The theorem states that, in a triangle with a right angle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides (the legs).

This isn't Mesopotamian, it isn't Greek, it isn't French, it isn't African: this is mathematics. Mathematical knowledge, by its very nature, is universal and abstract, which doesn't mean it isn't used in a cultural context. The theorem worked in Mesopotamia the same way it works in Rio de Janeiro in 2021.

Another example I love: it's very common to see arguments, even in academic papers, that the mathematics that should be taught in a given culture is the one that is visible to its members. That in Africa we should teach starting from African art, etc.

There is a theorem in mathematics according to which there are 24 types of symmetry; a type of pattern that can be found in paintings, in nature, etc. If you analyze works of art excavated from Mesopotamia 5000 years ago, you will find ceramics that contain these types of symmetry. If you stroll through Lisbon, you will notice that those beautiful Portuguese stone sidewalks use the same patterns, also present in Marajoara ceramics in Pará.

Although the materials used and the symbols represented are different, the mathematics employed is exactly the same. Therefore, deconstructing mathematics is a completely meaningless expression.

In other words: it doesn't matter if the student learns from Marajoara ceramics or from Lisbon's sidewalks, as long as they learn the same thing.

Exactly. It's part of mathematics' DNA that it's universal. This makes it an exact, useful, and extremely flexible science. Consider that the calculations used to model reservoirs with dams are now being used to model the spread of Covid. When people try to hijack mathematics to serve causes – even meritorious ones, like the racial cause, for example – they do a disservice.

Furthermore, we cannot be naive: mathematics is accustomed to being used to justify people's preconceived ideas. It is very common to see numbers being used in isolation to prove things. The attempt to transform mathematics into ideological banners is everywhere and needs to be identified. Numbers have certainly been used to justify discrimination, just as physics was used – and still is – to build bombs, even before nuclear development.

There is an individual and collective responsibility in the use of knowledge. This investigation is the task of anthropology, history, and other disciplines. Not mathematics. The Pythagorean Theorem is agnostic.

The impression is that the humanities' yearning for "deconstruction" stems from a certain prejudice against the exact sciences, as if mathematicians were detached from reality, thinking only in "boxes."

That's the same feeling I have, and it's a bit pretentious. I could go around asking, for example, if people know the second law of thermodynamics, and saying that this law explains everything.

I can explain it in a way you won't forget: you know our house, the one we always have to tidy up because if we don't do anything it just gets messier? That's it. She basically says that as time passes, the universe becomes increasingly disorganized. If I want to impress my friends, I'll say that "the entropy of the universe is increasing."

The second law of thermodynamics influences social relations, the development of culture, and we are the ones who know about it. Similarly, I could say that the exact sciences possess the truth. The answer is that truth is multiple, complex, and includes all of that. Any attempt to say "my truth is more complex" is arrogant.

Why is it so important for a child to master mathematics? As a rule, young people leave school convinced that Bhaskara's formula is useless.

Bhaskara's formula isn't very useful anyway (laughs), but that's another argument. First, let's make it clear that no, mathematics should not be taught out of context. The generation that memorized multiplication tables without knowing what they meant is long gone. Contextualization is useful; it helps to value the child's repertoire and respect ancestral culture.

But it's essential to remember that the school's duty is to prepare the child for adult life. While the humanities and sciences are of paramount importance, having access only to these areas of knowledge leaves education incomplete. And why is it important to learn mathematics? Because we live in a world where it is increasingly responsible for wealth creation.

A 2012 study of developed countries – including the United Kingdom, France, Australia, and others – showed that, on average, mathematics contributes about 15% to their GDP. Here, I'm referring to mathematics applied in real life, in aircraft design, pharmaceutical production and development, information technology, engineering, etc. With advances in artificial intelligence, data science, and information technology, this is likely to grow.

So, can investing in real mathematics help reduce poverty?

Yes. First of all, it's worth remembering that it's not just university-level professions that require mathematics. Second, in addition to the job market growing ever larger, the average salary in this area tends to be double the national average. In the UK alone, 10% of the jobs created this year are highly mathematical, and these are responsible for a large part of the GDP. We are talking about wealth creation.

Given this, I ask: Brazil? Are we giving our young people the chance to have these kinds of professions? We are not. 46% of them don't even reach the first level of PISA – which means they don't know how to do the four basic arithmetic operations – while those who reach level 4, the proficiency necessary to practice these professions, don't even reach 4%. Level 2, you see, is considered the minimum to exercise citizenship. We are depriving generations of adults of basic access to social life, to elementary professions. Brazil has an obligation to give this to its citizens. Otherwise, yes, we are perpetuating inequalities.

When we dedicate ourselves to discussing whether mathematics contributes to racial discrimination, instead of teaching mathematics, we prevent our young people and children from the most disadvantaged classes from accessing this knowledge that can open the doors to social progress to which everyone is entitled.

So, going back to the initial topic of deconstructing mathematics: let's be serious? Let's give people what they need to be fully-fledged professionals? Our obligation is to create citizens whose horizons are not limited to technical aspects. But they have to learn to do math. And we keep insisting on this dichotomy of teaching sociology or mathematics. The best instrument to combat inequality is access to knowledge.

I doubt the answer is simple, but it doesn't hurt to try: how can we begin to improve this situation?

It's not simple at all, mainly because of the scale of our problem. We have some interesting initiatives, but little that encompasses public schools, which is where the biggest bottleneck lies. Teacher training is crucial, and this is a lengthy process; changes are hard work, require retraining, and provoke resistance. It's impossible to train 750,000 math teachers in the short term. This is without even mentioning the inertia of our institutions and the corporatism that became evident with the pandemic.

On the other hand, some time ago a statistic came out saying that our private schools are at the average level of European public schools, and it caused quite a shock; 'how can this be, our magnificent private schools?'. There's no surprise in that. We are immersed in a world where children don't have contact with mathematics on a daily basis.

It also involves us increasing the presence of knowledge in the culture. That's why I joke with people that it's time to have a soap opera heartthrob who's a mathematician. That's the purpose of the Brazilian Mathematics Olympiad, in fact: to make the discipline an event, a fun competition, that engages students and allows us to reach the entire country.

I'm not saying that the Olympiad replaces the classroom, but it shows that the teaching of mathematics – which, in Brazil, is very, very boring – doesn't have to be the way it is.