In one of the chapters of the book “Mathematics: Frontiers and Perspectives”, published in 2000 by the International Mathematical Union and the American Mathematical Society, the Belgian-French mathematical physicist David Ruelle (b. 1935) receives a visit from the beautiful alien Pallas, who is writing a thesis on the mathematics of Earth, for a discussion of how it compares to the mathematics of other planets.
Pallas is peremptory: “Logical truth is absolute and equal everywhere. It is not determined by social circumstances, nor by the particular structure of the mind of the galactic species with mathematical abilities. But the style of mathematical knowledge depends enormously on the structure of the mind. that produces it.”
She explains that the most advanced civilizations in the galaxy study mathematics through gigantic computer programs, which deal very efficiently with the most difficult problems. One example was presented by Douglas Adams in his “The Hitchhiker’s Guide to the Galaxy”: an entire planet runs a program to discover “the ultimate question about life, the universe and everything”, after a slightly less beefy computer concluded that the answer to such a question is “42”.
Terrestrials, on the other hand, study mathematics with their own heads, Pallas points out in amazement. Therefore, the nature of Terran mathematics depends on the peculiar structure of the human brain and the way in which it is organized. “One day you will evolve — assuming you survive — and Earth’s math will be comparable to that of the great galactic civilizations, for example the slimy superoctopus of Ix,” he says, with ambiguous optimism.
Based on this discussion, Ruelle would delve into the topic a few years later in the book “O Cérebro Matemático” (translated into Portuguese in 2011), where he discusses in more detail the relationship between mathematical knowledge, as we know it, and the functioning of our brain. In the absence of reliable information about Ix’s slimy superoctopi, he appeals to terrestrial computers as a comparative term. Worth checking out.
However, a fundamental aspect of this peculiar relationship had already been clearly understood by the Hungarian mathematician Alfréd Rényi (1921–1970) when he formulated his famous definition “A mathematician is an apparatus for transforming coffee into theorems”. This important discovery will be the subject of next week.
