The illusion of certainty in mathematics

It is frequently stated that mathematics is the language of nature, that the laws of mathematics must, necessarily, apply everywhere in the universe, because they are absolute. Why exactly? What makes them so absolute? How do we know they cannot change, or that their meaning is perpetually fixed in nature somehow? Well, first of all, it's necessary to define precisely what mathematics is, and what it is not. While mathematics sometimes is described as "The Queen of the Sciences", mathematicians themselves -- who tend to be rather charming and reasonable people, in general -- are rather more likely to describe what they do as a kind of "art". Why is this? The reason mathematicians tend to describe what they do as more of an art than a science, is that it is a highly subjective, introverted, rather aesthetic kind of activity. What do mathematicians do exactly? Well, they try to come up with concepts that appeal to other mathematicians, basically. Ideas that are interesting, and somehow meaningful, in an intuitive way. And -- this is the really unique thing about mathematics that distinguishes it from the other so-called "sciences" -- mathematics really isn't mathematics unless it acquires at least temporary universal agreement amongst mathematicians that it is in fact mathematics. In a way, then, mathematics is, in fact, the ultimate, and most essential principle, or principles of human social conformity! And, it is this aspect of extreme social conformity that does indeed explain why we hear of the "essential universality" of mathematics, of the inevitability of mathematics, of the consummate power of mathematics. Because, my friends, mathematics is, quite frequently anyway, nothing more, nor less, than a social control strategy! When we hear about the "cult of Pythagoras", they really do mean "cult", you know. Pythagoras had his own little empire and army, and was by no means above abusing his acolytes in any way you can possibly imagine! Really! So, when we hear of non-euclidean geometries, almost no one says that non-euclidean geometry "disproves" Euclid. After all, this is mathematics, mathematics is the ultimate reality it cannot possibly be disproven, right? Right?? No, no, no, non-euclidean geometry merely extends or provides, perhaps a "new perspective" on euclidean geometry. One that illustrates that all the assumptions and conclusions of euclidean geometry are wrong, of course, or usually wrong anyway, but, no matter! No matter at all! After all, this is mathematics! So, basically, mathematics is just stuff that some people with some good publicity agreed on sometime. Nothing more than that. Nothing. Nevertheless, because it is stuff that was widely agreed on and understood, mathematics does provide a pretty good basis for communication, particularly in areas where good communication and understanding are essential, like important engineering projects. Mathematics provides a well understood common language for these engineering projects, and, no doubt, that does help somewhat. Sometimes, anyway. Problem is, when we get into the notion that mathematics is "truth", absolute and total, and anything done mathematically must necessarily be true and useful, and that mathematics combined with some purely fictional "scientific method" can do anything we want, by some kind of magic only understood by PhD's. Then we get into the total drivel and nonsense of Einstein's Special Theory of Relativity, and endless absolutely pointless research in "controlled nuclear fusion", and, then, God help us all! #mathematics #geometry #noneuclideangeometry #euclid #science #philosophyofscience #metaphysics #philosophy #physics #engineering #sociology #conformity #institutions #institutionalization #historyofphilosophy #philosophyofhistory #pythagoras #conformity #socialconformity #publicity #publicrelations #relativity #einstein #fusion #controlledfusion