The relationship between philosophy and mathematics in the context of the treatises of the Ikhwān al-Safā'

Ikhwān al-Ṣafā' documented their thought system, established in 10th-century Basra, under the title "Resā'il of the Ikhwān al-Ṣafā'". In grounding their thought system in their treatises, Ikhwān al-Ṣafā' accepted mathematics as a constant. They constructed their epistemological, ontological, and cosmological systems upon this foundation. Drawing inspiration from ancient Greek philosophers and the Hellenistic tradition, Ikhwān al-Ṣafā' endeavored to comprehend and expound upon philosophical matters while evaluating the accumulation of tradition. They progressed in mathematics and geometry, incorporating influences from Pythagoras and Euclid and from Ptolemy in geography. It can be said that the translation of their treatises into our language has contributed to an increase in studies on the thought of Ikhwān al-Ṣafā'. Among these studies, we have encountered few that delve into the relationship between philosophy and mathematics in the context of Ikhwān al-Ṣafā'. Our aim with this study is to elucidate how the mathematical language, recognized by the mind as a universal language, forms the foundation of the philosophical and mathematical relationship established by Ikhwān al-Ṣafā', grounded in their understanding of unity and diversity. In composing our work, we initially explore the science of numbers, which forms the basis of the group's ontology, occasionally referring to Pythagoras, Plato, and Aristotle's texts to address the issue of unity and diversity. Within this framework, we examine the relationship between philosophy and mathematics and elucidate how Ikhwān al-Ṣafā''s understanding of mathematics influences physics, metaphysics, and ethics while providing insight into how their foundations are rooted in mathematics. Ultimately, we will integrate information related to astronomy, the golden ratio, and numerical calculations / abjad within the context of ethics, concepts that are frequently utilized in contemporary discourse.