Mathematics stopped being defined by reality – and started to invent new ones
nature.com
nature.com
https://en.m.wikipedia.org/wiki/Non-Euclidean_geometry#Disco... :
"Bolyai ends his work (from 1830) by mentioning that it is not possible to decide through mathematical reasoning alone if the geometry of the physical universe is Euclidean or non-Euclidean; this is a task for the physical sciences."