Math
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.
I can't begin to tell you the number of times that I've sat at a lecture being presented with some statistical analysis of some disease by some researcher and felt just like I was in Orwell's 1984 book. In statistics you have evidence but always with some uncertainty attached to whatever is being said. Statistics is simply a math statement about how surprised you are about some result.
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 a formula that says the same thing. M=G(g+a) +p. This math statement seems scarier than the English statement. But mathematics is just another language, just like French is in France, or Swahili is wherever Swahili is spoken. Mathematics’ country is science. Science finds regularities and those regularities are then described nicely by math that we then use to predict (or try to) things.
In mathematics one starts with a hypothesis but instead of testing it using evidence like in experimental science one tests it using logic. But mathematics is not foolproof. 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.
I don’t want to harp on Gödel but he showed that any finite axiomatization (sorry, assumptions) of mathematics that you make, that’s at least rich enough to account for arithmetic will have this weird property that there are truths that cannot be proven from that system. If you just add some more assumptions to take care of the truth that you just came upon that “can’t be proven” with your new assumption (axiom) then there will be other statements that come about that you can’t prove.
“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. IMHO, it is all evolutionary biology. True enough, evolution should not have developed math as there was little use for it when we where cavemen. There was not conceivable advantage. 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.
Human psychology and the crazy social world we live in cannot be turned into mathematical statements. The economists that seem to run the money world seem not to know this.