From the origins of Christian architecture there was a strong interest in incorporating sacred geometry and number symbolism into places of worship. From the beginning this was expressed in its simplest terms by the adoption of a tripartite apse, often lit by three windows in the central apse, signifying the mystery of the Trinity. This interest in number symbolism extended to the shape of buildings, especially octagonal buildings, including such centrally planned monuments as Qal‘at Seman in Syria, where a central octagon surrounds the stylite’s pillar and an octagonal baptistery stands at the ancient entrance to the complex. The significance of octagonal baptisteries is explained in a 4th-century inscription on the baptistery at Milan (CIL V, p. 617, 2 = ILCV 1841), attributed to S. Ambrose but probably earlier. The inscription links the number eight to baptism and the Christian hope of salvation, drawing on a common Christian cosmological association between eight and the General Resurrection which will occur once the seven Great Days of world history have been completed by the Last Judgement.

The most famous example of mathematical virtuosity in architecture, praised by Procopius (Aed. I, 1, 29) and much discussed by scholars, is the Church of the Holy Wisdom in Constantinople. Historians have particularly examined the mathematical calculations that enabled Isidore of Miletus and Anthemius of Tralles to build upon a rectangular base a curved (if irregular) dome with a diameter of 30.9 m (101 feet 6 inches) to 31.8 m (104 feet 4 inches).

However mathematics was employed by Late Antique architects for purposes which went far beyond the symbolic and mechanical calculations necessary for the construction of large buildings. Detailed knowledge of astronomy and optics could be combined with geometry and number symbolism to ensure that buildings such as the Holy Wisdom were aligned to be well lit whatever the season of the year, and to enhance the sensation of entering a hallowed space, a microcosm, so Procopius claims of the Holy Wisdom, created from the composition of number, nature, and light (Aed. I, 1, 27–65).