way viewed subjects geometers called lobachevsky copernicus geometry due revolutionary character work existence non euclidean geometries impacted intellectual life victorian england many ways particular one leading factors caused examination teaching geometry based euclid 's elements curriculum issue hotly debated time even subject book ''euclid modern rivals'' written charles lutwidge dodgson better known lewis carroll author ''alice wonderland'' planar algebras
Formal science Mathematics Pure mathematics Geometry Non-Euclidean geometry