mathematics are a bridge between the natural and eternal (or between humans and God).

 The Pythagorean Doctrine”, she argues that mathematics are a bridge between the natural and eternal (or between humans and God). That is, the Pythagoreans held an intellectual solution to apparent natural contradictions. Inspired by Pythagoras, she claimed that the very study of mathematics can be a means of purification if light of the principles of proportion and the necessary balancing of contraries—especially in geometry. She saw in the Pythagorean legacy and spirit a link between their mathematical insights and their distinctly religious project to penetrate the mysteries of the cosmos.

the criterion of the real” and correspond with the orientation of detachment (GG 98). For example, Christ’s imperative to “love your enemies” contains a contradiction in value: love those who are detestable and who threaten the vulnerability of loving. For Weil, submitting to this union of contraries loosens one’s attachments to particular, ego-driven perspectives and enables a “well-developed intellectual pluralism” (Springsted 2010: 97). She writes, “An attachment to a particular thing can only be destroyed by an attachment which is incompatible with it” (GG 10