If Palladio’s desire for an order based on mathematical proportions is expressed best in plan and if a similar desire in Le Corbusier’s work is expressed most prominently on the façade, then how can we think of a mathematical proportions as an ordering system in our contemporary (cultural and technological) context?

Both Palladio and Le Corbusier present structural reasons for a mathematical spatial order in their architecture: “Solid wall structures, Palladio declares, demand absolute symmetry; a frame building, Le Corbusier announces, requires a free arrangement” (6). Rowe rightly questions this as the only reason for applying mathematical proportions to architectural design.

He instead focuses on the respective structural systems’ ability to allow for and deny certain applications of a mathematical ordering system: “If Le Corbusier’s façades are for him the primary demonstrations of the virtues of a mathematical discipline, with Palladio it would seem that the ultimate proof of his theory lies in his plans” (9). Both structure and the need for using “‘customary’ materials” restrain Palladio’s most precise mathematical proportions to the plan but allow him to express variation in what Rowe calls a “free section” (11).

Rowe calls this a “freedom” that the horizontal floor planes and horizontal roof at Garches do not allow (11). I would question that and propose that each system (Palladio’s orderly plans and free section, and Le Corbusier’s orderly façade and free plan) comes with its own set of freedoms provided by structural constraints and cultural “customary” desires. In fact, Le Corbusier’s architecture is an advancement of the idea because his column grid does imply a mathematical order in plan as well as in the facade.

Given all this and considering OMA’s library project (shown above) where there are neither load-bearing walls nor horizontal floor plates, we have arrived at a new level of “freedom”. If mathematical order does represent a “natural beauty” (2) (and I believe it does) how do we employ mathematics to bring order to a complex system like OMA’s library?