In the early 1800s, the mathematician Gauss dispatched observers to the tops of three mountains to determine whether the sum of the angles in a real triangle was truly 180°. Gauss was not certain that mathematics really matched reality perfectly. (His experiment was inconclusive.) Today, in most scientific edu-cation and practice, it is customary to assume that mathematics is not only a faithful mirror of the real world but that it can actually lead us to new insights into reality.

Unfortunately, two facts mar this idealistic picture.

Mathematics itself contains contradictions and does not have a solid foundation; that is, it is "impure."

Some portions of reality seem to confound mathematics; for example, Einstein found Riemannian geometry and tensor analysis imperfect for formulating the Theory of Relativity. Despite this disappointment, Einstein maintained his belief that God does not play dice with the universe. Some more recent scientists suggest that God not only plays dice but throws them where they cannot be seen!

Despite the acknowledged deficiencies, it is clearly more than a stroke of luck that mathematics describes so much of reality so accurately. And here is the spooky part of the whole business. In formulating their web of logic, mathematicians make many more or less "artistic" decisions that are colored by reality and their expectations of reality. To illustrate, "symmetry" is a human passion that reality may disdain. In other words, because mathematicians are prejudiced by their experience in the real world and are an integral part of that world, it is not surprising that their artistic renditions mirror reality to some extent.

(Little, John; "The Uncertain Craft of Mathematics," New Scientist, 88:626, 1980.)

Comment. It might also be that mathematics predicts unknown realities because of the human mind's subconscious knowledge or appreciation of them -- a sort of innate appreciation of that portion of the universe still unknown to the conscious mind.