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Comment by har777 | Hacker News Reader

I have to shout out MathAcademy(the same platform the author is using). It's pretty darn good. I did like 2 hours a day for 90 days and went from Math Foundations I(70% completed) to Math Foundations III(74% completed). The pace of improvement was very fast.

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I have not detected anything wrong with mathacademy, it does what it says on the tin. With that said, I stopped using it myself as I felt that my ability to "find the slope intercept form of blankety blank" did not actually translate to any deeper understanding of math than I had before.

I think mathacademy is excellent for developing the skills necessary for solving the problems on mathacademy (which largely are the problems on math exams).

But if your goal is understanding rather than application, then mathacademy is more similar to duolingo than it is to language immersion. You can go quite far in mathacademy (and much of performative mathematics) without really having thought about anything. It is procedure learning rather than understanding.

I'm sorry if this is a not a good question but as some one who never really had a good relationship with maths.

How do I get to a stage where I can just do math for the sake of understanding it.. to enjoy working on it.

I'm happy to "just do it" but is there some branch of match that might feel familiar and less removed from the real world?

I have a 2 tier-ed personal response to this question.

For "basic math" up to high school algebra and such, having an intuitive understanding of this lets me quickly do back of the envelope math anytime I hear something that sounds off, or something matches a "pattern" of a type of math I've done before.

Two concrete examples of this are:

  - doing drop rate calculations in games (probability)..i.e. I've killed 500 of these, and it is interesting to note that I should've gotten this drop 93% of the time. I'm mathematically unlucky. 

  - trying to calculate how much it is worth to me to drive at 80mph vs 55mph to get to work, and the relationship between gas prices and my willingness to drive fast (algebra, physics, etc)

For more advanced math, I personally find my high level understanding of the topics enough to appreciate how much goes into everyday things. The algorithms that govern our understanding of radio signals, information theory to pack bits into a given bandwidth and frequency, algorithms and math to ensure what was transitted is what is received, and how hundreds people can be using it at once and still get their data where it needs to go. The amount of math that goes into this all makes me appreciate the beauty of it all.

Thanks for this

I have no real answer to this.

People who I know who are actually really good at math (and are paid for it) say that there is no shortcut to interest and wrestling/thinking about the problems. You have to mule over things. You have to pack and unpack it over and over in your head.

If I had to put it in a phrase, it would be, "there is no shortcut to understanding without thinking".

Maybe the trick is taking the question and writing lecture notes / delivering the explanation as a teacher. Surely explaining it is much better than just solving the question and tap tap tap.

I disagree with this take though I've seen the same criticism online a lot before I signed up. I found myself understanding stuff the more I did it. And MathAcademy makes you do a lot of problems on repeat. I also used gpt for stuff MathAcademy didn't explain well.

But the platform does have its issues. I should probably do a writeup someday.

Isn't this more or less true of the whole undergraduate college calc syllabus? Like, I had the same thought grinding on trig integrals: "these problems seem super artificial", and I gather they basically are, and I guess closed-form solutions to arbitrary random integrals all sort of are? But that's not Math Academy's doing, or any kind of "teach to the test"; I went through these same problems with both my kids as they did STEM degrees at Illinois, and that's the actual material.

Mathacademy is meeting a market demand, which mostly seems to be being good enough to solve problems in several standardized math courses. In that regard, I think it is a thing that I would prescribe to any student (along with tutoring and study groups) in order to do well in that course.

But I am just not convinced it can ever (especially, in isolation, which you never claimed) lead to you being a good mathematician in the sense of having internalized the material. I can't quite put my finger on it, but I think it is similar to the feeling you get when you are some high level in duolingo and realize you still can't follow daytime soaps. You have the rigid intelligence, but not the fluid (internalized?) one.

Oh, I have no idea if it can help make someone a mathematician. But that's not why engineers study math, right? It's still extremely valuable to be able to do, and to an operational extent understand, advanced math.

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