Mathematics is much more than a language – 01/23/2024 – Marcelo Viana

Galileo Galilei (1564–1642), one of the giants of the Renaissance, wrote that “Mathematics is the Language in which God wrote the Universe.” And British physicist Stephen Hawkings (1942–2018) reinforced: “Mathematics is the only language we have in common with nature.” I agree with both, of course, but I think it’s important to dot the i’s: mathematics is not a language, it is much more.

My colleague Artur Avila, winner of the Fields Medal in 2014, explains it very happily. 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 ideas and facts that form mathematics, not language, emphasizes Artur.

An important point, which is rarely highlighted as it deserves, is the incredible ability of mathematics to make us discover the world around us. A spectacular example is the work of 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. Severe and authoritarian, the father forbade his children to speak any language other than French at home. Unable to express himself well in this language, Paul chose to remain silent, and thus became a taciturn adult. His colleagues at Cambridge University joked that “a dirac” is a physical unit that means 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, restricted and general, formulated by Einstein. The problem is that these two advances have very different natures and seemed to be incompatible: one of the two had to be wrong!

Dirac focused on the search for compatibility between quantum mechanics and special relativity, which describes the properties of space and time in the absence of mass (making quantum mechanics compatible with general relativity is the holy grail of modern-day physics). This work earned him the 1933 Nobel Prize in Physics.

The most incredible thing is that Dirac’s mathematical formulas pointed to a surprising fact, which no one had predicted: every subatomic particle has an antiparticle, a kind of mirror image, with the same mass and opposite charge! The subsequent experimental confirmation of this prediction undoubtedly constituted a spectacular victory for mathematics. I will return to the topic.

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