ABSTRACT
The Euclidean method of demonstration has spawned its own most fitting parody and caricature in the famous controversy over the theory of parallels, and through the attempts, repeated every year, to prove the eleventh axiom. The only immediate utility that is granted to mathematics is that it can accustom unstable and fickle minds to a focusing of their attention. Even Descartes, who was himself famous as a mathematician, passed just the same judgment on mathematics. The alleged inscription over the Platonic lecture-hall, No one is admitted, who has not studied geometry: inscription above the entrance to Plato's Academy of which the mathematicians are so proud, was without doubt inspired by the fact that Plato regarded geometrical figures as entities intermediate between the eternal Ideas and individual things, as Aristotle frequently mentions in his Metaphysics. Furthermore, the contrast between those eternal forms or Ideas, existing for themselves, and transitory individual things could be most easily grasped through geometrical figures.
