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I see from the answers that some immediately confused numbers with measures, which are completely different things (although you usually use numbers to convey results of measurements). The knowledge meaning ascribed to numbers must depend on a study of literary sources, and whatever we have left of traditions - maybe even "archetypes" in the Jungian sense.

About the current query - "why" - I tend to apply a rather functional view, of mathematics as a tool, but a tool that can be played with in a kind of game.

As an example I'm working on: A group of 12th C churches in the S.E. part of Norway with quite uniform plan disposition are clearly modelled on the plans of the now ruined Oslo and Hamar Cathedrals.

We may suppose that a master builder, by training and experience, would have acquired command of a repertoire of models for planning churches of various sizes and complexity. As a help to setting out the plan on the site, these may have been based on geometrical diagrams and/or simple numerical ratios. The choice of model depended on the client’s needs, while the chosen model could be scaled to accord with his budget. In theory, a suitable measure unit could then be chosen more or less arbitrarily for the necessary calculations, dependent on the wanted size of the building.

It seems to me that, if the builders used a preconceived diagram to determine the dimensions of a church, it was more in the manner of a guiding framework that could be handled with flexibility, than a fixed ideal they felt forced to stick to. There is little or no evidence in the contemporary sources to Mediaeval church building to support speculations that geometrical diagrams or numerical relationships in the design of churches were required for expressing symbolic or religious meanings. As there in Christianity is no physical dimension directly corresponding to the spiritual, no specific architectural norm can ”truly” represent the theological contents. If particular numbers, or combinations of numbers were infused with some symbolic value, or wanted as an emulation of a significant sanctuary taken as a model, the clients seem to have been quite content with approximations.

Anyway, mathematically based methods of design, to the extent they are likely to have been used, seem to have been part of the builders’ planning tools, and not something the clients were bothered with. A church can resemble another in so many aspects that they by a superficial glance seem identical, but there will always be more or less subtle differences in proportions. When analyzed geometrically, similar diagrams and patterns can be found, but not fitting in exactly the same way. If the client wanted a “copy” of an existing church, it is as if the master builder deliberately made it different from the model by varying his procedure by the ”rules of play” in what may be called a ”mathematical game”.

My own view is that the use of mathematics is the differentia that distinguishes architecture proper from mere building. Building (an art widely practised by many species) is the larger, natural genus which includes the important subset of mathematical building (also practised by some non-humans). Perhaps the simplest form of mathematical building is that which involves the use of prcise canons or measures - hence achitecture might also be defined as 'rational building' - especially when the use of a regular canon or measure enables the introduction of symmetry (or common measures) and hence, of modules.

The role of mathematics in architecture wold make an excellent conference topic (I mean the general theory or philosophy of mathematics and architecture, as opposed to particular examples of their interrelations).

It makes sense because the people who are more mathematically inclined,therefore left brained, are less likely to think in the abstract. As a result they do not stray from the norm or what is generally accepted. Most scientist believe that everything is a result of science and nature. Most don't specifically believe that there is a God, or conscious mind behind creation. "Why" is the question of those who believe that a conscious mind is behind creation in all of it's forms, whether in architecture or nature. "How" is the question of those who know that everything follows a pattern and want to understand it better.

Perhaps it is best to think about what we are trying to do with architecture. What should it be ideally? Math is of course needed as a practical tool for engineering and measurement, but when we talk of aesthetics we are of course talking about a different use of math.

There are actually many other uses for math and the readers will probably respond according to their goals. Those obsessed with the "sacred," and the romance of the past will perhaps answer that math is needed and used to achieve sacred principles and relationships: the importance of 3, the fact that 8 stands for the resurrection, 12 as a divine number, etc, golden mean, etc, etc.

Those who approach things from a more intellectual or mathematical point of view may focus on the order of composition and rationality that mathematics brings. These minds probably favor the rational Renaissance as the highest point possible.

Probably each viewpoint or approach has its own truth. For me I ask myself the question again, what should architecture be? And, I answer this with a single word: beautiful. Then I ask myself, what is beautiful - what is beauty? And, beauty is hard to define; so, I search for examples...I think of music and the way that it reaches to my core; I think of sunsets; I think of walking through a forest and the peace I sense; I think of flowers and the way that each pedal fits together; I think of vibrant paintings; I think of all these things and many other things, and then I ask myself, what makes them so beautiful?

All of these things have in common elements of composition, and these elements combine to create the sensation of beauty. There is unity, proportion, rhythm, harmony, nuances, etc. It is not so easy to break apart the composition, because when something is truly beautiful each part is less itself and more of the whole. But, if you did, you would find that one part is proportion, and proportion is of course related to math.

The notes of the musical scale, the leaves of a tree, the division of a face and body, the field of colors in a painting, all of these things have a structure and proportion - they have much more also, but proportion is one necessity.

So why is math important for architecture? Or better yet, why is it important for beautiful architecture? Because, beauty is composed, a part of composition is proportion, and proportion relates to mathematics. It doesn't have to be about symbolism, theory, or philosophy. It can simply be about creating beauty in and of itself. Mathematics and proportion do not create beauty by themselves, but they are a necessary part of the compositional whole.

What will architecture be without mathematics?

• 1.it is needed for the aspect of structural design.

• 2.cost analysis, etc.

the list could go on and on