>For the sake of the public good, abelian groups can wait.
Amazing. I can't wait to put that on a plaque. "Abelian groups can wait for the sake of public good." Holy cow! Dude, Niels Abel was 17 when he invented most of the machinery that goes by the name Group Theory. By the age of 19, he had proved quintics don't have a general solution by simply cranking up his machinery. And today we have 17 and 19 year olds who not only don't know what a group is, but don't particularly want to know. Because, like you say, they'd rather be real world accountants & repairmen, not ivory tower mathematicians. Wouldn't you rather have just 1 Abel and a whole generation of pissed off accountants than the other way around ? I would. You know, when we do eventually get the hell out of this planet and conquer other dimensions and populate new worlds, get beyond this ethereal realm so to speak, it would be purely due to the ideas of an Abel or a Gauss or a Riemann. Even an army of real-life accountants wouldn't get you off this planet - they'd be busy calculating the price of the spacecraft with their fancy spreadsheets.
I guess we have different views of what's important. There are maybe 2-3 Abel's per century. Gauss completed some of his greatest work in his early twenties, but that doesn't mean that everyone else did as well as he did. I'd love for everyone to be Gausses and Abels, but the truth is, they aren't. Neither do they want to be. Neither are they unhappy "pissed off accountants" because they aren't, like you describe. Neither are they idiots because they aren't math-savvy, like you imply.
I'd rather human development and quality of life come before space travel. If there are junior Abels among us, they are going to stand out regardless of whether you teach them subject X in highschool or not. Furthermore, they are going to pursue a specialized education (college) in said subject anyway. I don't think not recognizing geniuses is a problem we have since geniuses tend to be fairly resourceful. Thus, we can focus on improving the standard of education for everyone else. I'm not suggesting a ban on the study of mathematics altogether.
There is no causation link as you imagine. No amount of increased math in highschool is going to breed geniuses like Abels. Increased general skills like logic and problem solving is going to result in higher ability and better education for almost everyone.
Amazing. I can't wait to put that on a plaque. "Abelian groups can wait for the sake of public good." Holy cow! Dude, Niels Abel was 17 when he invented most of the machinery that goes by the name Group Theory. By the age of 19, he had proved quintics don't have a general solution by simply cranking up his machinery. And today we have 17 and 19 year olds who not only don't know what a group is, but don't particularly want to know. Because, like you say, they'd rather be real world accountants & repairmen, not ivory tower mathematicians. Wouldn't you rather have just 1 Abel and a whole generation of pissed off accountants than the other way around ? I would. You know, when we do eventually get the hell out of this planet and conquer other dimensions and populate new worlds, get beyond this ethereal realm so to speak, it would be purely due to the ideas of an Abel or a Gauss or a Riemann. Even an army of real-life accountants wouldn't get you off this planet - they'd be busy calculating the price of the spacecraft with their fancy spreadsheets.