The Ikhwān al-Ṣafāʾ (Brethren of Purity), the anonymous adepts of a tenth-century esoteric fraternity based in Basra and Baghdad, hold an eminent position in the history of science and philosophy in Islam due to the wide reception and assimilation of their monumental encyclopaedia, the Rasāʾil Ikhwān al-Ṣafāʾ (Epistles of the Brethren of Purity). This compendium contains fifty-two epistles offering synoptic accounts of the classical sciences and philosophies of the age; divided into four classificatory parts, it treats themes in mathematics, logic, natural philosophy, psychology, metaphysics, and theology, and also includes didactic fables.

Epistles 1 and 2 present technical and epistemic analyses of mathematical concepts, and of their metaphysical underpinnings, investigating the properties of numbers and of geometric magnitudes, based primarily on the traditions of Nicomachus of Gerasa and of Euclid. The Ikhwān view arithmetic and geometry through a monotheistic spiritual lens, with a Pythagorean construal of the ultimate principles of mathematics within the symbolic order of mysticism, which is inspired by their ontological outlook on the articles of faith in Islam. The content of this volume also offers enlightening perspectives regarding the canonization and popularization of the mathematical sciences within the greater Islamic intellectual milieu.