According to Simone Weil, for the Pythagoreans, elucidating the elegant mathematical “laws” of the physical world was a way of imitating their causal God. In contrast, the Babylonians were willing to play “mathematical games” via problems that were construct entirely by virtue of their solutions.
Quote @2024weil, “Four Letters.”
[Geometry’s] purpose was the same as the purpose of their art, namely to make perceptible a kinship between the human mind and the universe, to make the world appear as ‘the city of all rational beings.’ And it was really made of solid matter, matter that existed, like that of all the arts without exception, in the physical sense of the word; this matter was space actually given, imposed as a de facto condition to all of man’s actions. Their geometry was a science of nature; their physics (I’m thinking of the Pythagoreans’ music, and especially of Archimedes’ mechanics and his study of floating bodies) was a geometry in which the hypotheses were presented as postulates.
I fear that today it is rather toward the Babylonian conception that we’re moving, in other words playing games rather than making art. I wonder how many mathematicians today see mathematics as a process aimed at purifying the soul and “imitating God”? What’s more, it seems to me that the matter is lacking. There is a lot of axiomatics, which seems to be closer to the Greeks, but aren’t the axioms largely chosen at will? You speak of “solid matter,” but isn’t this matter essentially formed by the entirety of mathematical work accomplished to this day? In that case, current mathematics would be a screen between man and the universe (and consequently between man and God, as understood by the Greeks) instead of putting them in contact. But perhaps I’m disparaging it.