Our math has developed with our species and greatly enabled much. Without math humanity could not exist as it does today. And thankfully much of what is useful? Was developed long ago.
Was very hard for me in many ways when began absorbing that the mathematical field had gone astray in the late 1800's as seemed so impossible. And am thankful for over a decade now to consider, which allows me to easily explain the mathematics part at least.
However, I think it is natural to wonder how that could be possible in terms of the human side of a very advanced world we think, where mathematics is so important to just about everything technologically related. Where I found a problem arrived in the late 1800's, when MUCH of the math that is used in science and technology came long before.
Like modern calculus was developed by Sir Isaac Newton who died in 1727, and Gottfried Leibniz who died in 1716 just did a web search. And what they were doing is WAY beyond what most people learn today, if they even get to calculus. Where like if you THINK you are mathematically advanced, can you look at a cable hanging between two electrical poles and calculate the mathematical curve you see there?
Pondering was very humbling for me. And consider, you can hold a rope loosely between your two hands, yet calculating that curve so many know? Requires advanced mathematics, which pushed my limits to understand, as a teenager.
Turns out that curve is a catenary. Figured out back in, yup, the 1600's thanks to the Bernoulli brothers. Where here's a link to article about Jacob Bernoulli. Where came across the problem as a teenager and was humbled when I struggled with learning a solution to the problem with variational calculus, trying to work through to understand. Which only made sense to me many years later. Felt weird to struggle again with math.
We're lucky that so much in math got well developed long ago.
When we look at mathematics from the late 1800's turns out gets specialized in very specific ways while yes, there has been much relevant to technology but that is applied math which has no problems of which am aware. But you find that MUCH of the prestige in modern math field is attributed to pure mathematics and MOST of it goes to number theorists who primarily claim their research is useless in the real world.
Is very weird situation folks, as when you find out they are full of error, you start noticing things. Like who was one of the most acclaimed recent mathematicians who tragically died in a car accident with his wife? John Forbes Nash Jr.
An applied mathematician who gained quite a bit of celebrity including a movie made about him, check his mathematics only awards. Yes, he got the Nobel in Economics but famously there is no Nobel prize for mathematics things directly. (Some think maybe Nobel had something against mathematicians, I think. Where did I get that from? Regardless, he didn't set up any awards for them.)
Used to rip on mathematicians about not giving him ANY awards and then they gave him one.
Related to my criticisms? I'd think not. But yeah applied mathematicians are immune from the problem I found, as it cannot help them. It actually means number theorists can gain success with results which appear to be true, which actually are not. Such a thing could only be useful in exploiting your fellow humans, if you knew of it, with certain kinds of things. Applied mathematicians do not have option of using it, even if they wished.
Studying behavior towards applied mathematicians from others in mathematics is useful.
It does not take much to get a grasp of the actual situation, once you get suspicious.
There is a muddled picture I think for most people as to them is just mathematicians and what is with this pure versus applied and useful versus not or whatever? And there is how people can get away with mathematics which is NOT correct! Which I studied first over a decade ago.
So how do YOU know?
Well I get suspicious as soon as a mathematical result is emphasized as being worthless for anything practical, does not lead to any follow up results, and is incomprehensible supposedly except to a few leading mathematicians in the world. They've switched up the value of human knowledge.
Today many otherwise sensible people take it for granted that knowledge can be abstruse, useless and only understood by a select few, which those who know their human history know in the past was attributed to priesthoods. The Catholic Church at one point I think emphasized to people that reading the Bible could mess up their minds and they should only rely on Catholic priests for guidance. One of the things Martin Luther brought back I think, as going by memory, is the simple notion of reading the Bible again. Which was part of the Protestant revolution where was recently celebrated over a half a millennium since his famous Ninety-five theses.
But are distant from math now, now aren't we? If I got anything wrong above maybe will catch it with editing later. Main point though is the religious aspect to emphasizing trust from the people.
Reality is math developed for its usefulness. And continues to so develop so humanity is doing just fine. Esoteric reality of number theory means most people don't know and don't care about it, even though there has been a practical aspect with computer security.
Which is a very different subject and I tend to shy away from THAT subject lately.
So yeah, turns out is easy to explain how there can be this bizarre error that entered into mathematics in the late 1800's which did not derail science and technology, but did shift mathematical community, to focus on people who behave like a modern priesthood. With true believers trained to simply accept their proclamations, they can gain adulation, reward and continuing employment, when people who understand how things went wrong in late 1800's can reasonably suspect they have few if any correct mathematical results. Is so wild. But they are simply not needed for valid mathematics.
Good news is mathematical industry is doing just fine, regardless. Our species continues to progress and no reason to expect that will change from this particular problem I found.
When math is correct? It works for us. And vast amounts of useful mathematics is doing so much for our world, no worries.