KEY WORDS

1. purity

"Mathematics is pure language--the language of science...unique among languages in its ability to provide precise expression for every thought or concept that can be formulated in its terms," writes Adler on the article's first page. He goes on to compare it to the game of chess, in which there is no room for subjective criticism regarding the genius of the player. In a mathematical problem, there exists just one solution and an infinite number of wrong answers.

2. creativity

The mathematical language, according to Adler, "is continually being altered to fit new results, to simplify new techniques." The spoken languages do not allow for the bending of words to denote refinement of their old images. Rather, human thought is bent by the accumulated meanings of words. Mathematics is not held bound by this constraint. Thus, mathematics is creative in nature. Mathematicians are always using their creativity in discovering new techniques and hypothesizing new possibilities; mathematics is always in a state of creative evolutionary flux. "The essential feature of mathematical creativity is the exploration, under the pressure of powerful implosive forces, or difficult problems for whose validity and importance the explorer is eventually held bound by. The reality is the physical world." Thus, like other creative areas of study, including architecture, mathematics allows a great deal of speculative freedom. But at the same time it must be relevant to physical reality.

DISCUSSION QUESTIONS

1. "What is more, mathematics generates a momentum, so that any significant result points automatically to another new result, or perhaps to two or three other new results," writes Adler in his concluding paragraph. Does architecture--a field of study akin to mathematics in many ways--also generate such a momentum? What exists that is evidence of such in the built environment?

2. Adler asserts that in mathematical creation, "an assertion, together with a proof" is required. Therefore, to state that the average speed at which an object travels is equal to its displacement divided by the time it takes to travel from point A to point B, a mathematician must prove it with a numerical formula. Does this translate also to architectural design? If so, does it apply in the same way? (Can we, in architecture, prove a design theory in such a simple quantitative way as mathematicians do with their formulas?)