Mathematics and the Architecture: The Problem and the Theory in Pre-Modern Cultures Zafer Sagdic Architecture Department Yildiz Technical University 80630 Besiktas Istanbul, Turkiye zafersagdic@hotmail.com Abstract: There is always a mystery on pre-modern architecture practice on the relation between dimensions and ratios. The reasons of using certain proportions used on the design of religious buildings/ spaces are the result of the application of numerical symbolism and Pythagorean triangle. Thus, the paper will be focused on the unity of theory in pre- modern architecture practice via giving some special examples of pre-modern architecture through the human history, such as Antique Egyptian and Antique Greek temples, Roman churches, Gothic cathedrals, and so on. 1.The Problem and The Theory In modern architectural practice, it is known that, the formation of spaces are the result of diverse needs and requirements, such as; being suitable for certain activities, offering enough space to accommodate needed number of users, giving answer to technical regulations and parallel to reality resisting the influence of climate, earthquakes, storms, etc. Also, in modern thought, scientific thinkers interpreted the nature has an inherent order beyond that which man brings to his observations. In pre-modern cultures, theologians transformed nature to mean god, and through this they were able to give architecture a formalised higher purpose. This way of thinking allowed them to interpret nature through the use of power of algorithms- mathematics. The artist- form makers- usually found himself somewhere between the two positions, making the best use of each for the purposes determined by his culture. At certain times in history the artist relied heavily on religious scholasticism for interpretations of natural phenomena. It is seen on the pre-modern cultures that some certain numerical values are used to serve a religious purpose, especially on the design of religious buildings, such as mosques and churches. It should not be forgotten that the mathematics is a kind of language used through the mystery of existence. According to Galileo, “the big book of nature only can be read by the one who knows the language of it; the language of mathematics”. If we are using mathematics to the formation of result of “real” needs and requirements, it should be zoomed on the nucleus of designing purpose of the religious buildings in the pre-modern world. Parts of the main religious building may be grouped to symbolise religious beliefs, and some symbolic numbers have been utilised for centuries in these spaces. “The form of a building is its internal physical structure, as described under some appropriate conceptualisation”. This definition is in the spirit of the general usage of the term aesthetics. According to Clive Bell (1914), all of the relations and combinations of line, spaces and even the colours are build up the “significant form”. So, what architects did in pre-modern space formulation, is that, they always use the organisations and completion of their formal experiences are mixing with the mathematical and geometrical rules of architecture, the rules such as proportion, balance, line recession and so on. Architects are the coordinators and organisers of these experiences and finally the ones who definite form in a 269