From Geometry to Cosmology: The Relationship of Shape, Ratio, and Order in the Ottoman Scientific World

​​Mathematical thought in the history of Islamic science underwent significant development during the Ottoman period, evolving into a conceptual framework aimed at understanding the order of the universe, beyond mere numbers and shapes. In the Ottoman scientific tradition, this perspective demonstrates how mathematical reasoning became integrated with the concepts of form, ratio, and order. Within this context, geometry in the Ottoman Empire was not viewed merely as a computational tool but also as a symbol of mathematical reasoning. This philosophical approach formed the foundation for Ottoman scholars’ contributions to both practical and theoretical sciences, establishing a clear link between mathematical knowledge and the endeavor to comprehend cosmic order.

​The Euclidean Tradition and Geometrical Reasoning in the Ottoman Empire

The foundations of geometrical thought in the Islamic world were laid with the translation of Euclid’s Elements into Arabic. This work established a logical mathematical system composed of definitions, postulates, and proofs. The emergence of mathematical reasoning in Ottoman scientific history was built upon this system. The Elements not only ensured the precise determination of geometric figures but also made it possible to reflect on the scientific principles underlying mathematical reasoning.

Ali Kuşçu and Education-Based Mathematics

One of the most important representatives of this tradition in the Ottoman Empire was Ali Kuşçu. His work Risâletü’l-Muḥammediyye occupied a central position in the development of mathematical education during the Ottoman period. Kuşçu defined arithmetic operations and ratio systems, transforming mathematics into a discipline grounded in educational practice rather than purely theoretical inquiry. In this way, he pioneered the popularization of scientific knowledge and established a solid mathematical foundation for the Ottoman educational system.

Representation of Ali Kuşçu and His Students (Generated by Artificial Intelligence)

Philosophical Interpretation of Postulates

Pre-Ottoman Islamic mathematicians interpreted Euclid’s postulates not merely as tools for geometric analysis but as modes of thought concerning the order of the universe. Statements such as “A straight line can be drawn between any two points” were not merely mathematical terms but mental representations of the concepts of order and harmony. This interpretive tradition influenced the reasoning patterns of Ottoman scholars and added philosophical depth to mathematical thought.

Algebraic Thought and the Contribution of Taşköprizade

For Islamic scholars, the concept of algebra was a crucial element in the field of mathematical reasoning. When examining how Ottoman scholars employed algebra in mathematical reasoning, Taşköprizade emerges as one of the most significant figures in this domain.

Taşköprizade and the Systematization of Algebra

In the Islamic scientific tradition, algebra was defined by al-Khwarizmi as a means of solving practical problems and by Ibn Khaldun as “the derivation of an unknown quantity from known quantities.” The Ottoman scholar Taşköprizade advanced this understanding further by presenting algebra as the fundamental instrument of mathematical thought. By systematizing algebra, he established a logical coherence between methods of solving equations. This transformed abstract reasoning into concrete mathematical expression.

Geometry, Cosmology, and Applications in the Ottoman Empire

Representative Image of Geometry, Cosmology, and Their Applications in the Ottoman Empire (Generated by Artificial Intelligence)

Takiyüddin b. Ma’ruf and Astronomical Observations

The development of mathematical thought in the Islamic world progressed alongside astronomical observations aimed at understanding the movements of celestial bodies. In observatories such as the Maragha Observatory, geometry was employed extensively, and Nasir al-Din al-Tusi’s trigonometric system enabled the integration of geometric principles into astronomical calculations.

Observation and Measurement in the Ottoman Empire

By the 16th century, the work of Takiyüddin b. Ma’ruf represented one of the most brilliant examples of this tradition in the Ottoman Empire. Takiyüddin’s writings reveal that in Ottoman scientific thought, mathematics was not regarded merely as a tool for calculation but also as an instrument of observation and measurement. This scientific outlook is the most concrete evidence of a strong connection established between geometry and cosmology in the Ottoman context. The precise measuring instruments used by Takiyüddin in his observatory in Istanbul—for example, the zâtü’ş-şubet—stand as testament to this approach.

Explaining Cosmic Order

The tradition of interpreting the cosmological order of the universe through geometrical and algebraic thought, initiated by scholars such as Jawhari and Ibn al-Haytham, continued within Ottoman intellectual circles. Mathematical ratios and geometric principles played a vital role in understanding and explaining celestial bodies.

This perspective transformed mathematics from a mere calculating tool into a conceptual system capable of explaining universal order. Thus, the concepts of form, ratio, and order in Ottoman science reveal a profound relationship between mathematical thought and cosmology.