Reflections on 1,000 Days of Math | Hacker News Reader

Reflections on 1,000 Days of Math

gmays.com

86 pointsgmays37 comments

I am quite sure that learning math has nothing to do at all with investments doing well. Would be a classic example of having made money, but getting the reason for why wrong.

The markets have been uponly since 2020 in general, so no surprise if one were invested, especially in technology, that one would have done well.

Well if you learn about financial engineering you can come up with a wider range of investing propositions but even that won’t necessarily translate to better portfolio returns.

OP is not aware of what he is not aware of (as we all are).

Surprised they spent 1000 days on math and still don’t understand correlation is not causation

I think the question to be asked about this post should be: "How many things can you solve by yourself outside the platform you are currently using?".

I have the feeling (though I could be wrong) that you might very well sort out the exercises and problems that are presented in the platform, but what about tackling for example Project Euler? How far can you go with the knowledge that you acquired from this platform after 3 years of daily usage?

Please note that I'm not trying to diminish the value of the mentioned platform but I believe that tackling problems that force you to hit your head on the wall and/or figuring out things by yourself with maybe some books, makes you learn in a completely different and richer way.

This is a view I strongly agree with. While the “worked example effect,” which is apparently a key part of the platform, does seem to accelerate learning compared with discovery based learning [0], I do not think the learning achieved by the regurgitation of another person’s ratiocination is nearly as useful or rich as learning acquired by discovery. In my view, the best way to fully and completely understand something is to come to it in your own mind.

[0]: https://en.wikipedia.org/wiki/Worked-example_effect

OK, as long as you're clear that this is an indictment of basically all ordinary undergraduate math instruction.

Yes the famous math curriculum everyone loves and instills an intrinsic love of mathematics forever

If you want to do this, there are at least two ways:

A) use the AoPS books, which present exercises before explanations, and expect students to attempt them first, or

B) Use Math Academy the way my son does: skip the explanation and worked example and immediately attempt the first problem. Only if stuck go back to the explanation and example.

(B) isn't what Math Academy recommended, presumably because you might be able to solve the problems in the current lesson, but still miss out on something else the lesson is supposed to teach you.

I remember your 500 days of math post! I'm curious if along the journey you took time to apply new concepts you learned in a larger project or lab? I've never used Math Academy, but does it just give articles/videos and then exercises? Congrats on the dedication, that's a lot of work especially with kids.

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.

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".

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.

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.

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 like his vibe. I guess it helps that I've been doing MA as well, although not daily. I'll get back to it soon though.

I'm a bit lacking intellectually, and I wonder if learning more math would make me a more intellectual person.

Reading would probably help the most. Read some classics, don't worry too much about the plot beforehand, dive in. Gives a ton of new ways to look at the world.

I'm a broken record on how valuable I found Math Academy to be; 22,000 XP in roughly a year, going from high school trig (and a grim confrontation with my intuitive ability to work with fractions) through multivariable calculus.

The most important thing to understand about Math Academy is that it's all problems, problems over and over again, with just enough pedagogy to get you from one kind of problem to the next. It's a form of spaced-repetition system (often with the repetition cleverly arranged through interleaved topics, so that solving problems in the "next" unit also depends on techniques from the previous) and a drilling tool.

I'd echo any other observation about that structure being limiting for deeper understanding. The thing about that is, though, we already have ample resources for deeper understanding! For my part, GPT4 and GPT5 were more than enough supplementation, to drill into topics, connect them to other topics, ask "why the fuck does this work", etc.

When I got to Calc II (in Math Foundations III), Herbert Gross MIT lectures were super handy too. If you're doing Linear Algebra, I'd pair Math Academy with Strang's lectures.

To me, the limitations of the approach aren't interesting. The problem Math Academy is solving is the limiting reagent for self-study: boundless exercises and worked examples, a clear syllabus, and a forcing function for actually doing the problems. If you're self-studying math, you probably don't need extra structure to get you to read about math; you need the structure to get you to do math.

Easily the most valuable learning resource I've ever spent money on. Highly recommend.

> Math Academy can give you the best learning system ever invented, but if you short-circuit the load-bearing parts you don’t build the prerequisites.

Why does this sound so familiar...?

I'm sorry but I can't help but be critical. This seems more like an advertisement for a duolingo-for-math than a serious personal undertaking. I am not sure if this level of proficiency is something you want to boast of at the end of 1000 days of self-directed study, regardless of what level you started at. Do you think you'd be better or worse off with just doing two days a week with a personal tutor?

Also I am fairly certain that not taking a day off has hindered your progress rather than improved it. This is not a productive attitude and ritualizes the study instead of encouraging self-reflection.

Your criticism is poorly informed. Math Academy is definitely not a "Duolingo-for-Math". As a platform it's far from perfect, but as a program it's a serious and complete secondary school to undergraduate university math program, with excellent explanations, reinforced by well-thought out exercises. It's definitely competitive with the top-rated math textbooks in each of the areas it covers.

As for the OP "not taking a day off"... for some of us ritualization is productive because it's what we need to stick with a difficult program. Maybe for you that's not the case. To each his own.

(I have my own criticisms of Math Academy: The platform should be more flexible in pacing and allow repeating sections. It should have built-in spaced-repetition features. And the company is uncommunicative and aloof. I'd be willing to overlook most of these faults at a lower price-tag, but for what they charge it really rubs me the wrong way.)

My criticism is about OP's attempt at getting better at math. I have no knowledge of or concern for the Math Academy curriculum. But reading this post obviously did not give me a favorable impression of it.

its clearly some kind of ad, not direct yet an ad

In what country do you live that a personal tutora two days a week is financial compareable ?!

I wrote it on the assumption that it would be something that OP could reasonably pay for, a possible alternate path for someone who wanted to improve at math and was willing to make an effort, specifically less of an effort than what they seem to have ended up doing in terms of time-commitment. Considering how much they value their time it may have even been more cost effective.

Do you actually have any concrete issues with Math Academy, or do just want to bitch?

So tired of posts vaguely criticizing instead of naming any tangible problems.

Math Academy is not the main subject of this post. The main subject of this post is OP's attempt at getting better at math through 1000 days of self study, in which that site is an instrument. My criticism is about how his approach may have been ineffective and may not be an ideal guide for others. It is the said ineffectiveness that made me question if his attempt was genuine.

I hope this has been clear enough for you. Let me know if you need more.

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