I think the issue was that they are representing a real as a product of a rational and that more complicated type, so without a symbolic representation for 1, when representing and rational, they would have to multiply it by a RRA representation of 1 which brings in all the decision problem issues.
It was discovered that the procedure mechanism of Algol 60 was effectively equivalent to the lambda calulus. This insight was written out in a famous paper by Peter Landin, "Correspondence between ALGOL 60 and Church's Lambda-notation: part I"
A mathematics degree will have some kind of 'transition to higher mathematics' course that you take your freshman or sophomore year. You meticulously work with sets, definitions/theorem/proofs in a simple setting, and especially adding 'structure' to sets with axioms.
In regards to the article, the course of this type that i took had frequent quizzes that required nothing but reproducing precise definitions or proofs we had learned. Of course the ideal would be for the student to be able to reproduce these from understanding. But in practice i was doing a lot of brute force memorization of definitions - i just hadn't internalized the language of mathematical logic well enough to reconstruct a concept's definition yet. however, it got my foot in the door and having those definitions in my head made the next courses easier, so if i retook that transition course a few years later on, i would not have needed to do so much memorization. i got better at learning those kinds of basic definitions.
So my answer to your question is yes to some extent - the memorization aspect of learning described in the article is useful for learning the first step to Math B as well. Also if you want to make another learning attempt, be sure and go back and start at that freshman/sophomore level transition course i was describing!
It's amazing how far we've come in a few centuries. From sketching a few visible features with the help of a telescope, to mapping out the microscopic variations in the moons gravitational field[1] with robot satellites!
I agree with you that academic summary works are probably the best way for a non-researcher to learn what exists, what's known (and what isn't). Since i've never seen them discussed or referenced on this website, let me also point out the existence of academic encyclopedias, such as the Springer encyclopedia of algoriths[1] (each entry is essentially a slightly more pedagogical review article about a subfield or important problem in CS, along with loads of references to the literature for digging deeper), and the delightful encyclopedia of distances [2](800 pages long!). A couple others i've seen that may be of interest to this audience are the encyclopedia of systems and control[3], and the encyclopedia of unconventional computing[4]
Unfortunately some of these are absurdly expensive, so if you don't want to go the piracy route the cheapest way to access them is to get a membership to your local public university's library system, which in the US typically costs like $100 a year or something.
"Python's predecessor, ABC, was inspired by
SETL -- Lambert Meertens spent a year with the SETL group at NYU
before coming up with the final ABC design!"
--Guido van Rossum
Here [1] is a great (short, readable) paper from 2015 that explains Timsort and similar stack-merge sorting algorithms. It also gives a runtime analysis, and a simplified version of the algorithm that they call 'alpha-sort'.
My vulnerability is that I take immunosuppresants, which makes the vaccines significantly less effective (last I heard a few months ago, fully half of the breakthrough infections of the vaccinated were in the small population of immunosuppressed people).
OK, I get your point. It's an ideological dilemma then - you'd prefer as many people around you to be vaccinated and boosted to lessen your chance of getting infected (although, even those boosted could transmit). On the other hand, those younger cohorts getting vaccines mostly to protect the others are subjecting themselves to low, but still tangible risk of getting vaccine complications. So there is some altruism at play and this is something which shouldn't definitely be mandated by the governments.
(PS: It's good that very effective pills are now coming to help immunosuppressed).
TD;DL: we discovered Higgs, but we don't know much about it because LHC doesn't give us enough resolution, and its exact properties are crucial for the future of the whole of theoretical physics. Therefore, even if we do not hope to discover new particles, there's motivation enough to build bigger colliders.
