24/01/2024

Folha: Mathematics is much more than a language.

Reproduction of Marcelo Viana's column in Folha de S. Paulo.

Galileo Galilei (1564–1642), one of the giants of the Renaissance, wrote that "Mathematics is the language in which God wrote the universe." And the British physicist Stephen Hawking (1942–2018) reinforced this: " Mathematics is the only language we have in common with nature." I agree with both, of course, but I think it's important to clarify: mathematics is not a language, it is much more.

My colleague Artur Avila , winner of the Fields Medal in 2014, explains it very well. Just as Brazilian literature uses a language—Portuguese—to express the experiences, feelings, and worldview of a people, mathematics uses its own language to express ideas and facts about the Universe. It is the ideas and facts that form mathematics, not the language, emphasizes Artur.

One important point, which is rarely highlighted as it deserves, is the incredible capacity of mathematics to help us discover the world around us. A spectacular example is the work of the British mathematician and physicist Paul Dirac (1902–1984).

The son of a French-speaking Swiss immigrant, Dirac was born and raised in the English city of Bristol. His father, strict and authoritarian, forbade his children from speaking any language other than French at home. Unable to express himself well in French, Paul chose to remain silent, and thus became a taciturn adult. His colleagues at Cambridge University joked that "a dirac" is a physical unit meaning one word per hour.

The physics of his time was dominated by the two great advances of the 20th century: on the one hand, quantum mechanics, focused on the infinitesimal world, below the atomic scale; on the other, the theories of relativity, both special and general, formulated by Einstein . The problem is that these two advances have very different natures and seemed incompatible: one of them had to be wrong!

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