Math is the code of space/time that tells how it works, much like zeros and ones are computed as on/off in computers to make computer environments work. Yet the environment of space and time is such that it requires no represented numerical computation -- there is no crunching of zeros and ones -- instead the environment, the context that some call "nature," is such that the system works on its own accord and syncopation.
Geometry, a sub-set of math, is special because it is a means of translating our understanding of the math code to space/time, and from space/time to the code of math. Trigonometry, calculus, basic arithmetic, and other forms of math, are all means of reading and writing the code. Math is logical because our understanding of the code must be computed by reason; people have still much to discover in the logic of math. Math can also become illogical and it is in this capacity that people also have much to discover. The majesty of our computational ability is to construct mathematics -- as well as translate them into space/time -- that utilize the code and model algorithms observed in space/time but might not exist in space/time without human-assisted computation and construction.
(c) M. Waxman 2007