Comments by "Lepi Doptera" (@lepidoptera9337) on "projectMaria" channel.

You got it. When serious people talk about math they mean the latter. :-)
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That's not math. That's computation. Actual mathematics is about structure.
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@mage3690 I don't know what they are teaching in college algebra, but this is the algebra course description at Yale: "MATH 500a, Algebra Junliang Shen The course serves as an introduction to commutative algebra and category theory. Topics include commutative rings, their ideals and modules, Noetherian rings and modules, constructions with rings such as localization and integral extension, connections to algebraic geometry, categories, functors and functor morphisms, tensor product and Hom functors, and projective modules. " That is what a mathematician calls "introductory algebra". Okay?
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@mage3690 There is an entire subfield of math that deals with computation called numerical mathematics and if we want to talk about general computation, then it's computer science. What students need to learn to be successful in STEM today are STRUCTURAL insights. We should be teaching the beginnings of differential geometry (like the notion of tangent space - flat maps on a globe) in kindergarten today!
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I can't do math and if my life depended on it and I still have a PhD in physics. If you ask me about quantum mechanics I can explain it better to you than most theoretical physicists (even though I can't calculate a thing with it). That is not the problem. The problem is that hard sciences and engineering are very different from the simplistic ideas that people have about them in high school. I am quite good at EE in addition to experimental physics, but I would not have survived the sheer monotonicity of a EE university course. Being good at something in practice and actually being proficient at it at the university exam level are simply two pairs of boots and one is much, much heavier than the other. That liberal arts colleges let so many people pass is, by the way, just part of the business model. You can't tell a liberal arts student that he/she has absolutely no artistic talent and that they are wasting their time. If you did that, then almost nobody would graduate. It's an entirely different game in e.g. medicine (where it's important) and classical music (where nobody wants to hear you butcher Chopin for four years or more).
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Yes, that's approx. one in 30 million individuals. ;-)
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@ylvaseason Most mathematicians are rather normal people, they are just very specialized. I am a physicist but out of fun I went to a mathematical colloquium once. There were half a dozen mathematicians and half a dozen students there (in the physics colloquium at my university it was five to ten times as many). The speaker came from an entire different subfield of math then the people in the audience. He put up the basic definitions of his field on the first slide or two, then he began talking about his current work. After about ten minutes of total silence of the audience one of the professors raised his hand and asked "Would you mind putting the first slide up, again. I think you lost all of us at the definitions.". Big laughs because it was true. Absolutely nobody could follow what the speaker was talking about. I had a similar experience in a math seminar about quantum groups. After about an hour everybody in the seminar agreed that they had absolutely no idea what this stuff was about, not even the guy who was giving the seminar. I still don't know what a quantum group is... some 30 years later. ;-)
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Linear algebra is no more difficult than calculus. It gets a bit more tricky once we get into tensor algebras and it gets really tough once we are talking about algebras in general.
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And I am sure you also survived the university level practical organic chemistry class that required you to execute a 112 step reaction with a prescribed yield over the course of the semester? Oh, wait... you aren't talking about university level chemistry. You are talking about memorizing high school chemistry (H is for hydrogen and S is for sulfur). ;-)
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No, an average human being can not do math well. It takes rather special people to do real math. It's a rare gift. Everybody can memorize some simple results from mathematics, but that's not math. That is, at most, an algorithmic math toolbox.
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@fullfungo That's most likely because you have never been exposed to real mathematics and that is a consequence of the education system that screwed you up.
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Mathematicians don't consider high school calculus as serious mathematics. All you really have to do is to learn half a dozen rules for derivatives and integrals and that's pretty much it. Neither are they teaching you geometry in school. They are teaching basic trigonometry. That's not what geometry is to a mathematician.
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Why would you want to enter hell for minimum wage? :-)
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Calculus of a single variable WITHOUT all the necessary proofs. That's about as high as the average person can get in mathematics. If you are really interested in the subject you can learn linear algebra, multivariate calculus, some basic functional analysis and some very basic differential geometry. You won't make any inroads in number theory, graphs, geometry, topology or any of the algebraic disciplines like group theory. How do I know? I tried. Hard. ;-)
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No, not every human can learn math. Not every human can learn the piano, either. Nature didn't make us all the same. That would be a waste of the breadth of our talents.
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Sure. Let me see how you are solving non-linear and non-separable partial differential equations with that technique. :-)
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I would love to see you in a university level class on topological algebra. With or without a one on one teacher. ;-)
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@polblanes You can't teach a student who can't even deal with differentiation rules for functions of a single variable something like topological algebra. Neither can you teach everybody how to play Chopin. Humans don't work that way.
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@polblanes Dude, I consistently got As on all my math tests in high school. I consistently failed in mathematics in university. It's just not the same thing, OK? What we are teaching in K-12 is to real mathematics like painting walls is to Michelangelo and Picasso. No resemblance. So if all you want is to get K-12 students to remember a few calculus formulas for the next two hours while we are administering a test, then, yes, we can do better memory games with them by adapting to their pace, but that doesn't mean that they will actually learn math.
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@polblanes Yes, Dude. I had all the motivation in the world. I am a physics PhD. I can do experimental physics (and have) at the professional level all day long but I can, for the life of me, not prove a few trivial theorems from calculus and geometry. My brain just doesn't work that way. Guess what else I can't do? I will never be quarterback in an NFL game. I will never play Chopin in front of an audience at Royal Albert Hall. I will never compete in a Formula 1 race. I will never fly to the moon as the pilot of a spacecraft and I will never, ever, rescue someone from a burning building. And neither will you do any of these things and the next best kid won't, either. Some things can only be done by people who have the right brain structures for them. What about that offends you? ;-)
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