I think it's a bit like PG Wodehouse. The world of Bertie Wooster or Clarence Threepwood, 9th Earl of Emsworth is certainly an idyll; at the same time no one would pretend it is a classless idyll.
Tolkien would not refer to that class structure as "economic exploitation" - that is part of his politics. That does not mean he did not understand that society very well, and seek to portray it in an idealized form.
Neither Poincare nor Lorentz are relevant to the genesis of General Relativity.
The only relevant priority dispute is whether Einstein or Hilbert wrote down the correct field equations first. This was after a long correspondence between the two, in which Einstein explained his ideas -- there is no dispute that Einstein "invented" General Relativity. See https://en.wikipedia.org/wiki/General_relativity_priority_di...
> Neither Poincare nor Lorentz are relevant to the genesis of General Relativity
Well, that's just plain wrong. From the horse's mouth:
> As we know, this is connected with the relativity of the concepts of "simultaneity" and "shape of moving bodies." To fill this gap, I introduced the principle of the constancy of the velocity of light, which I borrowed from H. A. Lorentz's theory of the stationary luminiferous ether, and which, like the principle of relativity, contains a physical assumption that seemed to be justified only by the relevant experiments
Yes, everybody agrees, but you specifically responded to the statement that Poincaré and Lorentz had nothing to do with GR. You said that statement was wrong, but it looks more like you confused SR and GR, which are two entirely different beasts.
Well the comment by pnin made it about GR, when the parent by boringuser2 was about the general contributions to relativity, both SR and GR. I believe "general theory of relativity" to be different than "general relativity" here, the former encompassing both SR and GR. Maybe that's where our misunderstanding comes from. Also, if you believe that GR has absolutely nothing to do with SR, then no Lorentz has no relevance to the genesis of General Relativity.
Anyway I don't believe we're having a discussion worth having here.
Since you provide a zoological metaphor, let me offer an alternative. Category theory is much more like Goethe's work on the /Urpflanze/ (primeval plant). Linné had developed a way of systematically naming species of plants, but Goethe was not satisfied by this approach.
Goethe wanted to find an underlying pattern common to all plants which would explain how plants grow and develop. Something like a "universal grammar" (to draw an anachronistic parallel to Chomsky) of plants. Goethe called this his "morphological" method and wrote about it in "On the metamorphosis of plants".
One caveat: this paints a slightly too esoteric picture of category theory. Goethe was very idiosyncratic as a scientist, whereas category theory, far from being esoteric, is a common language for all of modern mathematics.
I have some sympathy for this sentiment, and there is no doubt that the producers of mathematics could and probably should spend more time making life easier for the users and consumers of mathematics. This is true even /within/ the discipline, for very theoretical stuff. In the end this takes vastly more work than people expect. That's not an excuse, but it's true.
However, I also have a fundamental objection. I don't see how you can be an intelligent tool user without at least a little curiosity about how your tool functions. Maybe you can apply your tool, even be highly effective, in certain instances. But this is inherently brittle knowledge. When the parameters of your problem change and you don't understand your tool well enough to adapt, you're lost.
"Math for people who just want to use it" is very broad. What do you want to use it for? Physics, biology, chemistry, computer science? Sociology? Economics? There might be some shared stuff, but for all of these disciplines there is a vast space of mathematics that might be relevant.
I think Eliezer Yudkowsky's idea of a book (series) covering "The Simple Math of Everything" is fantastic. I would love to read that book.
I do not have the right background to be an authority on this, but from going through school myself and paying a fair amount of attention to math reformers over the years, it seems like they usually believe:
1) The problem with math in school is that there's not enough "real math".
2) Relatedly, insufficient exposure to "real math" in compulsory schooling is also (a major part of) why people think they don't like math.
My suspicion (again, without the actual background to make this claim with any authority) is that they are dead wrong on point 2—the "real math" parts probably contribute strongly to most folks' dislike of the subject, and the parts the mathematicians didn't like are probably relatively popular among people who don't go on to become mathematicians. This puts point 1 on some shaky ground (though it could still be true and well-justified, for other reasons).
I think it's a kind of rope that frays on both ends for systemic reasons:
1. Students in math courses and their parents grow to prefer(through the overall institutional constraints) to have a simple exercise that guarantees them credit - while actually doing math is a matter of crossing the Rubicon into tough puzzle-solving, and it needs some guidance for unexceptionable students to start enjoying.
2. Math teachers, particularly in the lower grades where qualifications are lower, have a harder time teaching concepts than they do exercises. And they are also incentivized to hand out a grade, preferably one that satisfies the parents.
So no matter how the high level is set up, everything converges into giving the kids a worksheet to "plug 'n chug." Which is just a confusing, badly paced grind, and therefore an easy reason to hate math. Either you get it completely and are just sitting there chugging through the problem set, or you have no idea what's going on and it's due tomorrow so your grade rests on something you feel defeated by.
I actually think that for the parts that are currently treated as rote memorization work, the curriculum should lean into it and treat it like learning the alphabet, with worksheets where you literally fill in the dotted lines repetitively; hand them out to everyone as a portion of the homework. And then the logic and critical thinking aspects need to proceed like a philosophy course, with interaction through a step by step process, not "get the answer in the back of the book". This element is something I've long thought could be automated in some degree with computer systems that let you play with the concepts, and therefore correct your thinking.
My suspicion (again, without the actual background to make this claim with any authority) is that they are dead wrong on point 2—the "real math" parts probably contribute strongly to most folks' dislike of the subject, and the parts the mathematicians didn't like are probably relatively popular among people who don't go on to become mathematicians. This puts point 1 on some shaky ground (though it could still be true and well-justified, for other reasons).
So you're saying you know nothing yet are sure "experts" are wrong, based on no evidence. OK.
No expert either, but I can speak as a non-traditional student (didn't go to college right out of high school join the Navy and started a family first) about to graduate with a degree in engineering. I was decent in math in grade school but did not like it. I didn't learn to actually enjoy math until my college calculus classes. And it goes back to the real math you are referring to. Looking back, Algebra in highschool just felt like, "memorize this type of problem and the steps," but didn't do anything to build intuition in actually understanding the why. Then calculus comes and I felt like that gave me the 'why.'
Its like how people use tools, like gears, knowing when to use what type of gears without needing to understand the microscopic material structure that provides its strength, or the mathematical definition of it's kinematics.
I think if you use gears, it would be well to know some Newtonian mechanics. The material structure might not be relevant, but in mathematics you also don't need to go down to the foundational level for every problem. You don't need to go deep into set theory to understand the proofs in calculus (though it is true that Cantor's investigations into set theory started from the question of convergence of certain infinite series, which is a calculus problem).
Hayek himself used the term "neo-liberal" to describe the "movement" of liberalism to which he belonged [0]. The historian Quinn Slobodian [1] advocates using the term "neoliberal" for the intellectual history surrounding the Mont Pelerin Society. In this context, it is sensible to distinguish between a Hayekian strand and, say, Wilhelm Röpke's version of neoliberalism.
