Math
Balderdash?
When presented with any mathematics most people are humbled, or frustrated, or ______ (you fill in the blank). It probably has a lot to do with the way mathematics is taught in school which used to be “shut and memorize this” but now is some woke post-colonialism philosophy about one and one being two. This does not give students an understanding about what the difference is between 2/3’s and 3/5’s whereas a drunk can tell you right away he would rather share three bottles between two people than three between five.
Formulas seem to scare. Mathematics is nothing more than the Generalization of geometry and algebra with one technical tool added in, namely Proofs. Here is an equation that says (sorta) the same thing. M=G(g+a) +P. This math statement seems scarier than the English statement. Maybe math should be words not equations. It is just another language, just like French is in France, or English is in England. The country of mathematics is science.
In mathematics one starts with a hypothesis but instead of testing it using evidence like in experimental science, one tests it using logic. This is a problem. Einstein’s friend, Kurt Gödel showed that any mathematics system is either incomplete or inconsistent. He did this by mathematizing the sentence, “This statement is not provable.”. Note that this sentence refers to itself. It is self-referential. It is inconsistent if you think it can be proven and it is incomplete if you think it can’t be proven. So broaden that thought a bit and math is either inconsistent harboring contradictory theorems or it is incomplete harboring unprovable theorems. He basically said that mathematics depends on assumptions about what is true.
“Is math discovered (Platonic, in the mind’s eye) or invented (non-platonic, in the real world)” is a question that math-y philosophers go on about. This is just another typical dualism that is all related to evolutionary biology. Evolution should not have favored math skills in the Paleolithic as there was little use for it when we were cavemen. However as language evolved one can see how math came directly out of this. Linguists will say that if you strip down the principles that give you basic linguistic structure to the bare minimum you get something like called the successor function which is basically the start of addition.
Individual human psychology is crazy. Each society of humans is crazy. This cannot be turned into mathematics but economists keep trying.