Last year, on April 13, Paolo Soleri died. I believe he was an example of mathematical humanism. E.g. #1. to consider mathematics as a living entity (in particular, a super-organism); and #2. inheriting mathematical entities ~ trans-ferring them into human ones.

Soleri's models argue that it is necessary to infer mathematical models into human (social, organized) criteria: to achieve this goal, performing harmonic relations (in mathematical terms) during the construction of human vital places — social and organized ones — such as built artifacts and more broadly, cities.

Someone in the past [in Italy, for instance] used to consider Soleri's humanistic mathematics/architecture as a super-hypotetic act and creative gesture; I do not agree with these kind of critics, and prefer to consider Soleri's efforts, by the contrary, as hyper-realistic.

—g

http://www.google.it/search?q=paolo+solieri&newwindow=1&safe=off&client=safari&rls=en&source=lnms&tbm=isch&sa=X&ei=3e2hU7D5JObX0QWc7YCADw&ved=0CAgQ_AUoAQ&biw=1280&bih=683#newwindow=1&q=paolo+soleri+arcologies&rls=en&safe=off&tbm=isch

Pls, check out also Charlie Barnard's built superorganisms http://charliebarnard.wordpress.com

—g

In architecture today also modern mathematics is being used. They are designing buildings based on idea of fractals. In fact people always want to do something different and new . There comes mathematical ideas.

I think it is both- an injector of cultural meaning and a tool, not only to artifacts but other parts of culture such as food, and time value.We use mathematics to blend things quantitatively such as the design of jeepneys and water vehicles, food menu, religious symbols, illumination, and herbal medicine formulae. All of these designs or mathematical,blends vary from one culture to another.

A piece of mathematical art in the front of the new faculty building for mathematics and economical sciences of the University of Vienna: http://www.dodekaederstern.cc/index_en.html

Thank you Hermann Schichl for the image of the dodecahedral star at the University of Vienna. It's a mathematical beautiful shape, and the construction process is interesting. Does it carry any meaning for us as a culture? Or better, does it tell us anything about the culture/society that we live in?

Dear Kim Williams!

Well, I am a mathematician and not an architecture theorist or philosopher. So I was somewhat reluctant to answer your question, as I do not feel really competent to do so. However, since you asked for my opinion, it would be impolite not to give an answer.

For me "culture" stands for the collection of a society's history, its traditions, its tools, its art, its beliefs, its approach to life, among others. Abstraction is one of the most successful abilites of humans, and building models of reality is one of the most remarkable traits of abstraction. I guess that is why many cultures from the early ages on made use of models (images, sculptures, sound, or more abstract ones like relations between objects (e.g. stones whose gaps point towards the sun at sunset on the equinox), etc.) to communicate, preserve, and support their beliefs, their sense of aesthetics, etc. - lets call these models "cultural models" in the following.

In many cases these cultural models emerge from tools that have been developed to ensure survival or to facilitate everyday life. A successive refinement of these tools eventually yields a level of expertise that allows such abstract and often aesthetical modelling. Examples are: stonework for survival (stone axes, etc.) and, e.g., delicate stone figures (Woman of Willendorf, etc.), woodwork - carpentry - bowmaking and, e.g., carvings of figurines and symbols, signal tones and music, colors for markings, directions and paintings, building of shelters and modern architecture, etc. I guess that most of the tools developed in a society have been used in the construction of cultural models, and often they have developed an artistic and abstract branch that is used to construct especially aesthetic models, i.e., pieces of art. Sometimes - this is especially true for artifacts of ancient cultures - the method for interpreting those models has been forgotten, and then only the raw shape remains, which might look/sound appealing enough for us to acknowledge them as pieces of art - and, maybe, sometimes their only intention was to please people in the first place.

One of the tools humans have developed over the past millennia is mathematics. It started as a tool for solving various problems in economics and construction. Nowadays it is still used as a tool to solve problems from everyday life, it is used to communicate our knowledge and beliefs (as mathematical models in science, psychology, sociology, etc.), and it has developed an artistic branch - there are really beautiful mathematica theories around that, in my opinion, qualify as the most abstract form of art humans are capable of.

So, mathematics is a mere tool in some places, it carries/imbues meaning in other places, and it provides independent pieces of art in again other places. The dodecahedral star in my opinion is a piece of art in itself and it carries a meaning since it serves as a symbol for the beauty, versatility, and the central importance of mathematics in our science oriented culture. (That symbolic meaning, however, might be forgotten in centuries/years/months (who knows in our fast changing world) to come, and probably only the pleasing shape will remain.)

Now, since I have started writing, I will also try to give my opinion on the more architecture centered original question. I think that in architectural artefacts the cultural meaning is foremost encoded in the buildings themselves. However, the means by which that coding works, i.e., the code itself, in a number of cases is based on mathematics (pyramids, etc.). So if this is "injecting a meaning" in your opinion, then the answer is yes. In that case not much has changed over the past millennia.

E.g., in the area of constructivist architecture basic geometric shapes (cubes, spheres, cylinders, etc.) were mainly used, often the direction of forces was explicitly shown, the carrying structures were emphasised, transporting the beliefs of a "mechanical world" governed by predictable forces.

In the postmodern era deconstructivism takes place, the mechanical world is replaced by flowing and floating and softer (sometimes called "female") shapes, and again mathematics is used as the internal code - but now it is not basic geometric shapes but hyperbolic paraboloids, solitons, and NURBS (no way to produce a building like the Walt Disney Concert Hall without modern mathematical tools).

In buildings like this, mathematics is directly used for coding philosophical beliefs of our modern society: The shape shall resemble water waves, flows, etc., in contrast to beams, levers, pillars, framework, completely in agreement with postmodern philosophy. (I am referring here to the (IMHO absurd) idea (I believe it was Luce Irigaray's and/or Julia Kristeva's) that mechanics has been developed so well in the past since it describes the deterministic "male" part of nature, while hydrodynamics describing the indeterministic "female" part of nature has been grossly neglected.) So in these buildings modern beliefs are intrinsically coded by mathematical means. (But again, in future times this coding will likely be forgotten, and if the building survives only the aesthetic shape will remain to please the viewers, and mathematics will no longer inject meaning but will only serve as a tool ensuring that the building does not collapse...)

Math is built into ancient texts is is readable ... and not buildings ... modern decoders at first over use modern math that fails to decode math used to build monuments as ancients had considered ... one 4,000 year old text ,, the AWT is a case in point ... under read in 1906 as cubits ... misread in 1923 only by ro, 1/320th of a hekat remainders ... and misread by myself in 2002 .. was finally correctly read in 2006 ... as Egyptians scaled a hekat volume unit to 64/64 before exactly partitioning by multiplying by 1/3, 1/7, 1/10, 1/11 and 1/13 .. http://akhmimwoodentablet.blogspot.com/ such that

(64/64) x 1/n = Q/64 + (5R/n)ro

with Q = quotient and R remainder scaled by 5/5 as Peet did not see in 1923 so that ro - 1.320th of a hekat can always scale remainders

Thank you Hana Vymazalova for pointing out the 64/64 hekat unity, opening a door so that 5/5 scaled remainders could be decoded ...

 Designing with the golden ratio in mind...

http://en.wikipedia.org/wiki/List_of_works_designed_with_the_golden_ratio