500 days of math | Hacker News Reader

500 days of math

gmays.com

215 pointsgmays97 comments

FWIW my experiences with MathAcademy roughly overlap OP’s: it’s really hard work and adult life seriously interferes with making speedy progress (notice their own success stories are with teenagers who can devote hours upon hours on racing through the - very good - curriculum).

They say 1 point is equivalent to 1 minute of work and that you should earn at least 45 points a day. Well, for me 1 point is nowhere near 1 minute of work: I’m sloppy and sometimes downright stupid so it’s 1,5 minutes at best and often much, much more.

Banging your head against a wall every day for more than an hour (sometimes much more) just to get to what they consider to be the minimum of 45 points is no fun, and probably even counterproductive. I managed to keep it up for four months and made reasonable progress during that time (on getting back to where I was at the end of High School, 30 years ago) but it also burnt me out. I’ve now scaled it back to 30 minutes (not points!) a day. As a result my progress is now glacial.

Also, they’re very much of the “just do lots of problems and you’ll learn mathematic concepts and principles by osmosis” school of math instruction. For me I had to buy a textbook to get some extra explanation.

The good thing is that the problems seem well thought out and the spaced repetition system definitely works (for me, anyway).

I’m going to keep it up, because I have enough disposable income to afford it (though it is much too expensive for what it is) and I really want to bring my math skills up to a level where I can follow along the math in ML papers (and also because math, it turns out, is kind of elegant and interesting). I could go the self-study route, but then I’d have to spend time and effort guiding myself and figuring out what it is I needed to work on. If nothing else, MathAcademy is good at taking care of this for you so you can focus on the math itself.

Any pointers on useful textbooks in this space? I seem to have difficulties finding one that is at the right level (not too easy, not too hard) or that provides a way to gauge your level and start accordingly at a later chapter or whatever.

Depends on what you need, I suppose. This resource is said to be pretty good: https://www.susanrigetti.com/math

I decided start with Calculus I on MathAcademy because that was the last thing I did in High School. MathAcademy disagreed and told me to do PreCalculus and even bits of Algebra II first, but I knew better (MathAcademy was right and in hindsight I should’ve just started the Foundation courses to build up my pretty weak algebra skills again).

For Calculus I simply use the textbook that’s recommended at the link above. As far as I can tell, it’s good. I don’t do the problems, though - for that I use MathAcademy.

You lose math quickly if you don't use it.

I took college algebra three times - not because I failed, but because I had a couple multi-year breaks in my college career and didn't do much math during them. It was definitely worth it - each time I took the class I picked up on things I had missed previously.

If I went back for my master's, I'd probably take it again.

Not a textbook, but https://betterexplained.com is an awesome resource for gaining intuition, its author's approach is very unlike others I've encountered.

Just checking out a few of these will change your concept of what it means to understand something in math and cause you to seek out better explanations beyond the textbook one. You can also refresh yourself on a topic in a way that's fun.

https://betterexplained.com/articles/linear-algebra-guide/

This one really helped. Somehow realizing that matrixes are just equations with two or more unknowns was somehow mindblowing.

I'm biased, but very fond of the open-access introductory textbooks used where I studied. The department was very much pure maths, but the intro classes were accessible to general liberal arts students. I think the texts are relatively unique in that they're very proof oriented, yet with a pedagogical style that doesn't assume the reader is a future graduate student.

For calculus, three options to see if you like a particular author's style of explanation: http://people.reed.edu/~mayer/math111.html/math111.pdf - the most pedagogical http://people.reed.edu/~mayer/math111.html/math111.pdf - the most beautiful https://people.reed.edu/~jerry/111/calc.pdf - the most technical

For introduction to mathematical analysis and proof: http://people.reed.edu/~mayer/math112.html/math112.pdf

For multivariable calculus: https://www.stat.rice.edu/~dobelman/notes_papers/math/calcul... [1]

For linear algebra, we used the relatively standard Friedberg Insel and Spence [2], but I hear good things about https://hefferon.net/linearalgebra/.

[1] Link is off university domain, since apparently it was at some point turned into a bit more hardcore textbook oriented towards those going onto graduate studies in mathematics. If curious: https://www.amazon.com/Calculus-Analysis-Euclidean-Undergrad...

[2] https://www.amazon.com/Linear-Algebra-4th-Stephen-Friedberg/...

“The most pedagogical” and “the most beautiful” have the same link. I’d love to see the other one!

For proofs and introductory real analysis, I highly recommend Prof. Jay Cummings' books at the awesome price of about $20 on Amazon for freaking 400 page books. If anything, just buy it to support the guy.

I've been learning math from the ground up and I've gone to hell and back in terms of resources.

Art of Problem Solving is the best. I started with Prealgebra and it just flows. The best textbooks I have found.

Yeah, I only have a goal of 25 points a day, Monday through Saturday, and I still usually take more than half an hour (though usually less than an hour) per day.

I actually feel that 25 points may be a bad choice as it makes me spend too much energy picking lessons that will barely add up to 25 so I can be done with my daily. Probably causes me to review or whatever when maybe I don't need to?

You can do all of that without paying a monthly fee. You just need a library card (or know of a person called Anna and her archive ;) ) and a list of books. These are the ones I used:

Precalculus by Axler

Calculus (Ninth Edition) by Thomas

Linear Algebra by Lay

How To Prove It by Velleman

Understanding Analysis by Abbott <--- I'm currently here

Much, much, much cheaper than paying $50/month. What I've spent most on so far has been printer paper and fountain pen ink because I do exercises by hand instead of using a tablet/iPad but in total this expense has been waaaaay under $50.

The #1 resource needed for self-learning is motivation, and for many people it's a lot more difficult to come by than money. What you're paying $50 a month is not information, but a system that encourages you to keep doing it

Also, paying for something can increase your commitment to it.

On the other hand, when you invest your real money, you are more likely to continue.

That's not "the other hand", it's a rephrasing of my point. :)

My understanding is Math Academy is like combining anki with direct instruction.

It's a business premised on teaching people things faster by understanding research around learning.

If the math it teaches is the math you need or want to learn, its likely an efficient way to learn it.

So, you are paying for efficiency. Like using Pimsleur rather than spending a year in France.

You can do that manually. Say for example you learn integration by trig sub today and you do 30 problems from a book. Next week you do some more trig sub problems. Then 2-3 weeks after that you do some trig sub problems and then in a few months you do some. You can do spaced rep manually. Is mathacademy more efficient? I don't know. It's too early to say. But what I do know is millions of people have learned mathematics with books, pen and paper for hundreds of years.

> You can do that manually.

Absolutely. You can spend time on figuring out what to do next, and how, and how to do spaced repetition for the material and test yourself effectively. There are aspects you'll do better than a set curriculum because you understand yourself, and there are mistakes you'll make because misunderstandings and errors.

Or you can pay an expert to do that for you, and just use the time on learning.

$50 a month is just not that much money, though. It's maybe a percentage point or two of the average US person's take home pay. And if this even doubles the speed at which I learn what I need to, then I'm saving myself many hundreds of dollars of the equivalent of my time.

I've recently gotten back into math and I'm really struggling with your approach. I find it particularly difficult to get an accurate view of how well I'm doing and where I am. Most concepts I ingest easily, and I demolish any exercises in the books I read, find on the internet, ask AI for, or scribble down myself randomly. I repeat them a couple of times to make sure. All is well. Cute green checkmarks abound. Categories marked as mastered. Pride bordering on arrogance. I move on. A week later I'm handed new concepts. The house of cards collapses. I haven't mastered any of the things. There are gaping holes in the information I was given and I wasn't knowledgeable enough to notice.

The author doesn't seem to share my difficulties either. His are of motivation and those seem to maybe be addressed by the resource he used and specifically sharing his progress with other users. For $50 I expect more than polished KhanAcademy, promises like "accelerates the learning process at 4X the speed of a traditional math class" (if anything I want to slow down), and a progress tracker to post pictures of on X. If I wanted to be told I'm amazing, how long my streak is, and to learn nothing I'd use duolingo.

When do you do exercises, do you refer back to sections in the book or examples? If so, this is a bad habit. Try to do exercises without looking back. This will force you to use your memory. Also don't be too quick to check solutions for things you're stuck on.

Everyone who does mathematics feels the way you do when learning something new. It's a normal feeling. Don't get disheartened. Push through it.

What you describe is entirely normal in my experience learning lots of stuff and teaching many others. It might help you to let go of the idea that learning is a linear process where you master one topic and move on to the next. As I learn more I'm continually getting a deeper understanding of basic material I "mastered" decades ago. I often tell my students I don't think their understanding is complete but it is sufficient to move on, and the later material will help them get a better understanding. And it does!

> that learning is a linear process where you master one topic and move on to the next.

It's closer to true in mathematics than most other places, but not very close to true.

It's amazing the "layer cake model" of mathematics learning is such a strong idea even among many mathematics teachers.

On the other hand, sometimes a missing concept like cancellation in fractions or just poor proficiency in arithmetic rears its head and makes doing later stuff very hard. Once a student gets used to being and staying confused, it's often game over.

> Once a student gets used to being and staying confused, it's often game over.

I think this is a very good insight, that somehow eluded me. Many many people are OK being confused about things, and I never considered that it's something they learn, but it makes so much sense.

Sounds like you'd really like MA. It will drill you on things until you actually know them. There's no green checkmark as such either - everything will be tested again spaced repetition style. You will be slowed down until you can actually use the previous concepts properly.

Mostly sympathetic here, but your duolingo comment is a bit too harsh. Anecdotal counterpoint: my high-schooler used duolingo last summer to skip a year of instruction and get into AP Spanish as a junior, and got into the Spanish National Honors Society, and earned a fluency certificate. (I know most high school language classes churn out students who can't speak a lick, but her school is excellent and she has working fluency - which she credits largely to using duolingo to catch up.) IOW, YMMV.

You can, but you will spend a lot of time figuring out what it is that you need to study and where your weak points are. MathAcademy does that for you so you can spend your precious studying time on, well, what you need to study.

I think it’s very expensive, and the correct price should be €$25/ month at most, imho, but its spaced repetition system definitely provides value over self study.

You can discover your weaknesses yourself by doing problem sets then checking solutions. You'll notice what kinds of questions you keep getting wrong, then you make a note to study that area again or you do more problems in that area. You don't need a computer algorithm for this.

You don't NEED anything really. But it's helpful to have a computer algorithm for this. Processing that yourself is meta effort not everyone has the extra time for or will be diligent enough about.

Right, and then you’re expending mental energy on figuring out how to teach math (to yourself) instead of on the math itself. This is not wrong, and will likely even teach you a thing or two (and in fact it was how self-teaching math worked before this came along) but, to me at least, MathAcademy seems to be more efficient in getting you to do just the math and nothing else.

I also have to suspect that the depth of the knowledge you get from reading real textbooks (and working the problems) is more profound than you're ever going to get from a MOOC, no matter how well put together.

I'm a bit behind you - I'm just finishing up my (third lol) re-read of my old undergraduate calculus textbook but one of these days I'm going to get around to real analysis. I'm pretty sure that a really good understanding of calculus still puts me in the top 5% of American adults.

$49 seems a surprisingly high amount for something aimed at students and learners - I appreciate the content may be good, but it's effectively 3 times a Netflix subscription.

It's meant to be something you stick with in the "long term" by its nature, and yet an annual subscription is $500 - this is just completely unrealistic for any student. Someone in a lower end job hoping to "up skill" is going to really struggle with this.

I believe their rationale is that a private tutor costs more than this per lesson, and they're targeting the people who will pay for a tutor once/twice a week for themselves or their children.

I tend to agree with you, it seems like they could be wayyy more competitive on price but I also understand where they're coming from.

They’re not a private tutor, though. They don’t explain very much and there certainly isn’t a way to ask questions. As I said elsewhere, to me they’re about twice as expensive as they should be.

> They don’t explain very much

That's not really the case. Each separate step of each lesson is explained and practiced many times. Repeated failures across multiple students are noticed and explanations reworked. If it's not enough, you can report your issues. And there are MA communities to check with if you really get stuck for some random reason.

I’m currently doing the Calculus I course and while there are explanations interspersed throughout the problems, these mostly seem to be the bare minimum you need to work the problems. When I compare it to the calculus textbook I keep alongside it (Stewart’s “Calculus Early Transcendentals”) it barely seems enough.

The explanations are very limited compared to actual maths lessons, though: in my experience they were very often something like "it turns out that the formula for this is...".

IMO it's scaffolded and explained a bit more than an average mathematics lesson, though teachers vary a lot.

There's a whole lot of "here's the formula" and not so much "here's the derivation" in most classrooms.

The math classes that I taught: I tried to do a lot more of the why, either rigorously or using proof by gesticulation. But there were still absolutely times that I just handed something over and was like "do this, for now."

Yes, they are not a private tutor, and they do not claim to be. That is just the market they are going after.

They believe they can help people reach better outcomes for less. Whether they're correct or not is another question.

Private tutors are much more expensive and not uniformly effective. Math Academy is an extremely low-risk bet for parents of math students (you'll know before the first usage period whether it's working out). I like the business model here a lot --- I also just think it's like something concocted in a mad scientists lab to annoy HN people, who always have a really hard time intuiting market/pricing segmentation.

I get why some people would not want to pay this, but it’s also not at all unreasonable to pay 50 USD.

It might be 3x a Netflix subscription, but Netflix is, for many, just wasting our time, whereas learning math could mean you can get a better job (higher salary, more interesting projects, future proofing yourself), then suddenly the 50 dollars per month is negligible.

I also get that in the end all this is available for free scattered around the internet and libraries, but having guidance, having a system that helps you actually do the learning is also very valuable.

There are cases where it's not the student who is paying. Definitely all the younger students, since that's covered by parents by default. I got it covered for a while under work's learning budget. I'm sure there are other groups I can't think of right now.

Having once been poor I understand you, but this is missing the bigger picture. If you're going to improve at mathematics you need to put serious time into it.

Instead of an hour of extra work every day, you're doing math instead. At minimum wage that's around two grand lost over a year. Even if MathAcademy was free.

Also, I recall seeing MathAcademy being free if you can demonstrate financial need.

The latest trend in educational software seems to be relatively high pricing. See e.g., Mentava, which sells for $500 USD/mo (not a typo). AoPS online courses are $28/lesson (though Beast Academy can be had for $100/yr). By comparison, this ($49) is in the realm of reasonable.

If this kind of pricing helps these services be sustainable over the long term, it's probably not a bad thing.

I forget where I originally saw this, but someone put together a document titled "How to Take all the Math Classes You Need." (https://docs.google.com/document/d/1G-hSdO5Tm9Nc6E4GobZZlwD0...)

While it assumes a level of competence of basic algebra, it essentially mimics a self-study math major and provides links to lecture recordings, widely used textbooks, problem sets, and answer banks to said problem sets. You obviously have to be self-motivated, but it beats paying $50 per month for the service OP's post links to.

> but it beats paying $50 per month for the service OP's post links to.

I used this with my kids.

The $50 a month to make it easy is worth it for many people, and is downright cheap compared to many approaches.

Now, there's other options-- Khan is also great and free. But always having a bite-sized chunk to do, immediate feedback, spaced repetition, etc-- it's pretty good.

I recently stopped my MathAcademy subscription: I went from halfway through Math Foundations II through to near the end of Linear Algebra. I stopped because I realised I wasn't really learning maths, I was just learning to answer the questions by rote.

The way that they pretty much completely omit all the explanation, proofs and discussion you get in traditional maths education really limits its utility once you get to more advanced content. I think the reason for a lot of the positive reviews is that their approach works really well early on when you're revising the basic end-of high-school stuff.

So until mathematical foundations 3?

I did 100% of MF II and III, plus 80% of Linear Algebra: https://mathacademy.com/courses/linear-algebra.

MF II and III were great for revision of late high school maths, yes.

I'm surprised Kahn Academy hasn't been mentioned. It's free and from my experience pretty good. Though I'm not a parent or teacher so I can't speak from either of those viewpoints.

Khan Academy last I checked went up to High School. MathAcademy goes up to undergrad math.

High enough for you ?

https://www.khanacademy.org/math/calculus-2

I stand corrected. Can’t edit my original post, though.

Khan hides it well, though - it’s listed smack in the middle of sixth grade math and high school math courses. I skimmed through the list (again) and found some college math but not all. Maybe this is a new offering?

The last I checked, most high schoolers don't take Diff Eq classes.

https://www.khanacademy.org/math/multivariable-calculus https://www.khanacademy.org/math/differential-equations https://www.khanacademy.org/math/linear-algebra

If you need to get into math and are not really motivated I can recommend 3blue1Brown by Grant Sanderson (https://www.3blue1brown.com/). The best part is not only, that he explains math problems in an easy way, but also show how to approach math problems in general. I think it’s one of the best sources to start with Math.

Not sure I’d want to use it as my only resource, but as supplementary material it’s excellent. He really explains concepts well (some better than others though, though this is likely a ymmv issue).

If you are recommending 3B1B from a pov of someone who has already once been past college level math, it's certainly commendable, but does not help someone who has not.

I used math academy for several months. I was curious and wanted to try it out since it’s a problem I’ve also worked on in the past. Th system is good, the fractional spaced repetition is a nice system and really reduces the spaced repetition overhead. Still IMHO, it provides nowhere near the value of the $50 a month pricing. But again I also know a lot of higher level mathematics and can work my way through a topology book on my own, so I’m probably not in the target audience. Still, I would think that even for people wanting to get into math or high school students this would still be a very steep price.

This could’ve been written by me, it so closely matches my own experience. I know too well the “hit with a bag of bricks” realization that much of your professional life has been more or less you winging it. Math has that tendency of shining a bright ugly light on your real capability. It’s deeply humbling.

I’ve been using MathAcademy, trying to do at least one lesson each night after the kid is asleep. But instead of rote memorization, I sit with each problem until I truly and deeply understand it.

It’s going to be a long time before I’m mathematically competent, but there’s nowhere to go but up.

Yeah, that’s my thinking now as well. It’s going to take an incredibly long time but truly understanding each problem is probably the only way to go.

Which is where this beats self study using books, I think. With a book, I can sort of wing it and think I understand something when I only do so very superficially whereas when you do the problems you truly learn what you understand and what you do not. And MathAcademy is only problems, so …

Oh another monthly subscription with no accredited learning.

If you want to actually learn mathematics, buy Open University book sets and work through them. MU123 -> MST124 -> MST125 -> M208 -> MST224. Diversion of M140 if you want stats. They are written by actual professionals, the course is accredited and if you like it you can turn that into an actual qualification as well. All the textbooks are in-house written over the space of over 40 years (!) and designed for self-learning.

The whole set is on github somewhere as well if I remember - search for it.

It shows this 3/4 the way down on their homepage (https://mathacademy.com/):

> Math Academy's courses are fully accredited by the Accrediting Commission for Schools, Western Association of Schools and Colleges. www.acswasc.org

It matters who as well as that.

OU are accredited by Institute of Mathematics and its Applications, Institute of Physics and Royal Statistical Society for example (I am a member of two of these).

But if you self study using the OU books, you yourself will not be accredited.

You have to give them ~£23k for that honour.

Did that a number of years back. Was worth it.

Worth it in the personal sense, or career-wise? I'd love to do a maths degree, but being mid-40s with family, mortgage, career etc makes it hard to see myself doing it for real.

I finished it when I was 47 and have a full time job, 3 kids and a care responsibility for a sick parent. Planning is the word :)

Paying that money was worth it? Why not just self-study then?

The fact that you did the whole journey with that amount of responsibilities is impressive!

Correct but you know the material is good.

I’m interested in learning math, theoretical physics, electronic engineering, welding, and AI/ML.

But, when you don’t even focus on basic self-care, you sleep terribly, suffer depression, ADD, etc., you’ll never get past just browsing someone’s page of links to educational material to actually developing the habits you need to learn.

If someone could solve that, I’d pay them $50/mo.

For ADD I recommend "Delivered from Distraction" by Edward Hallowell, it has a lot of advice about finding ADD specific strategies for learning things and developing habits. I can't really think of a way to summarize, I strongly recommend just reading it.

I'm also on foundations 3 at this point and love the system. I combine it with Anki to reinforce the retention of older material, and I find the price very reasonable for something that helps me learn math consistently.

As for the price, I see people mentioning text books as a cheaper alternative, but Math Academy includes review work, tests, and retakes when necessary. It takes care of the organizing and evaluating that is related to but not the same as the learning. You can focus on being a student, without having to also be the teacher.

I would love a full depth, accredited system that didn't cost thousands of dollars.

I'm at 10k points after a couple months. Previous experience was self-teaching linear algebra, which I needed for cryptography work, and I managed well enough to help my daughter cruise through a proofs-heavy linear algebra course at UIUC; I'd have aced it if I took it. I started doing MathAcademy for two reasons: to replace an NYT crossword habit with something more rewarding, and because I have (had) no calculus. I do about 250 points per week.

Math Academy is --- so far --- probably one of the better dollars-for-skills trades I've made in my adult life, easily outstripping every book I've ever bought.

I have a lot of gripes!

* The gamification is really annoying as an adult learner. There are lots of little cues in the system to keep moving forward, which pushes me past what feels like the limits of retention. There is no credential Math Academy can give me that I give a shit about, so moving faster for the sake of it is a bad trade for me.

* Along similar lines, I really wish it was easier to get more explicit review. Part of the premise of Math Academy is that the spaced repetition comes in large part from units that build on each other; you're making relentless forward progress with reviews baked into new material. I've at times had to have o4-mini make me problem sets, which seems dumb since I'm paying for exactly that from Math Academy.

* "Foundations", the adult learning series, is premised as being a curriculum stripped of stuff high school students learn solely because they'll be tested on it. They could strip it more. I got that sense in Foundations II but wasn't confident enough to call it out; now I'm doing linear algebra stuff and, I mean --- I object on moral grounds to inverting a matrix with determinants!

The flip side though: I have a decent grip on calc now, after just a couple months of doing this rather than crosswords. My trig, another weak spot, is annoyingly better (also I now know I authentically hate trig). The gripes are just gripes; my overall experience is, it does what it says on the tin.

I read people (and reviews, including expert reviews) complain about Math Academy's spartan approach to explanation/exposition/proofs. It's a super fair concern. For my part, I pair Math Academy with GPT; GPT is better than any online math education resource at explaining and handholding. I don't need explanations; what I need is a focused, structured curriculum: do this, then this, here's the problem sets, here's a graded quiz. I know how to read a book already; books didn't teach me any math --- university linear algebra course homework problem sets did. This is a better version of that.

Yea I also combine it with ChatGPT and Claude. It helps for extra context and at a high school level, I can still do the checking myself. Sometimes it's simply that I have 0 clue about what keywords to even search for. ChatGPT helps with the discoverability of that.

> I object on moral grounds to inverting a matrix with determinants!

The determinant of a linear map is the induced effect it has on volumes. So it makes sense that it appears when inverting a map: if the forward map scales volumes by detA the the inverse needs to scale them by 1/detA. It also makes sense as an invertibility criterion: you can invert a map iff it didn't collapse the space down to a lower dimension iff it doesn't reduce volumes to 0.

Of course this is presented completely opaquely at a low level with the even more opaque cofactor matrix stuff. So the trouble is that we really need to incorporate wedge products and some of the underlying geometry better at the lower level.

That first paragraph is more valuable than a unit of determinant matrix inversion problems.

I generally agree, though I think that's kind of a rejection of approaches like MA entirely (with the caveat that I've never used MA, so I'm assuming what it is based on discussions I've read): mathematics naturally gives you spaced repetition from new concepts building upon previous concepts, so calculation problems are mostly needed as a "check whether you are truly following along", and doing an entire unit of any type of calculation is somewhat pointless once you reach a certain maturity level unless there's some specific insight you're supposed to get from each example calculation.

I see exactly what you're saying and I agree: the kind of understanding your exposition gives is different than the kind of upskilling Math Academy can promise. My only thing here is (a) there's value in both approaches and (b) everything I've read about self-teaching math is that you can't get fluency without grinding problem sets.

I buy that you need both (and: I supplement MA with ChatGPT, which is pretty great at Socratically working through concepts), but also I cringe whenever people say "oh, you want to understand eigenvectors, just watch the 3blue1brown videos", because, those videos are great, and watching them in isolation gets you approximately 0% closer to being able to do (or appreciate) a PCA.

I think a set of videos like Strang's 18.06 and Math Academy (but for arbitrary subjects, like Calc II or undergrad Stat) would be a pretty killer combination. Are a killer combination, is what I mean to say. But I've only been at it a few months!

I did a summer of khan academy over a decade ago.

I was switching from liberal arts to NLP and wanted to train my math muscle. I went with their “world of Math” which was a feature to go over all math problems “in order”. When stuck you could view the associated video.

I don’t think they have that feature anymore.

As khan Academy goes from preschool through high school, you start out by counting pictures of elephants and other exercises meant for young children to get comfortable with numbers, which was definitely too early a place to start.

I thought it was fun to see how such exercises looked and I didn’t really now how far I wanted to skip so I just powered through.

I think it was really good with the above caveat. My other two cents are: going from way too easy problems to problems you actually have to work on is jarring in terms of pacing. All in all I enjoyed it.

It’s love to know how it compares to MathAcademy. I think Khan Academy is of really high quality and to go from free to $50/month requires a lot of added value.

That's a great find, as I'm in a somewhat similar place - (re)-learning maths at a not so young age, with kids, and doing it for the same reasons as the author. There is plenty of material out there for free (including a lot of complete courses from top universities), but not a lot of that is structured and I was often finding myself 'not knowing what I don't know'. Surprisingly, I've found chatGPT quite good for helping in that.

My current method is watching a lot of videos and taking notes - it's great in the beginning when it's mostly rediscovering what I already knew, but anything that's really new - it takes orders of magnitude more time. And that's very hard without some structure in learning.

I'm definitely giving Math Academy a try - looks great for what I need.

> It was at the same time depressing (I’m dumb), liberating (I don’t have to pretend I’m not dumb anymore) and exciting (I have a chance to be not dumb anymore).

> Learning is hard work, and if you don’t respect the process, it won’t happen.

These two ideas resonate well with me. My experience in pursuit of steady and sustainable growth in any area of interest has had these in common. You have articulated them well enough for me to realize that. I appreciate that.

I am also at a similar point in life that sits at the intersection of building consistent habits that support goals and balancing priorities like family life. “It’s a marathon, not a sprint” has never been more applicable.

I understand such blog spam is yet another plug for another thing where you need to swipe your card at some point for some questionable benefit. At this rate I would have thought that we are able to smell the crap as consumers, but there seems to be enough people who are willing to experiment with that.

For those who really want to "learn math" as autodidacts, nothing comes close to the Open University textbooks that are freely available in your libraries and also with some clever searching online. That material is refined over decades to support the autodidact use case.

The post you're complaining about is someone's personal blog, which appears to go back at least a decade.

Since you created an account just to complain about this, do you have a rule for what people can or can't blog about? Do you only accept posts about OSS and free materials?

I will surely be critical when a founder of a company is blogging about positive results of using his product on a $49/month questionable learning resource.

You do know the blogger isn't the one who created the product, right...?

I have tried Math Academy after seeing a post here a few years ago (I think it was to Justin's blog? --- he's referred to early on in TFA).

Echoing what others say: it was very cool, went quickly at first, but within a few weeks, progress slowed because I just couldn't ingest the new information as quickly, even when doing two "blocks" a day.

It is superior to the free tier of Khan Academy.

I don't know if it's superior to textbooks and problem sets in a self-study capacity.

I found it better than the (highly rated) math education I partially received in HS.

I really want to backfill my math one day, so I've slowly collected tools like this for "when I have the time" (scheduled in 2 years lol). I'm unclear why I'd use this tool instead of Khan Academy, which is free and seems to have developed a solid reputation for the like, decade or more its been around.

I’ve never understood why people post daily updates to social media. Who wants to see that?

I really love the free khan academy, https://www.khanacademy.org/

It has some higher level mathematics, but crucially has some lever stuff to make sure your understanding is rock solid.

I'm doing Math academy and learning Mathematica at the same time. I've made the pragmatic decision to do as much with mathematica as possible. This makes learning math vastly more fun and faster.

Claude is pretty good at explaining how to solve problems with and without using Mathematica.

I'd love to read a blog post about that. I used a bit of Mathematica at uni back in the day.

Not a lot to blog about. As I go through the problems I just figure out how to do them using mathematica. I love using Solve[]

As a kid, I started to get really into computer graphics. But, the textbooks I got as a 15 year old from Borders Books were full of calculus that was literally greek to me. I was also not really enjoying my public school math education. One day I brought the book to my math teacher and he was dismissive and basically said, 'you're not going to understand any of this – it's college and beyond."

Such a giant missed opportunity that makes me more angry now as an adult with my own kids.

In the end, I'm self-taught in so many areas that it means throughout the years I've had to confront gaps and work to fill them in. And there's definitely a healthy amount of 'learn to unlearn' because, sometimes you're lucky enough to find a book or a person who explains things to you in a totally different way that makes it all click.

Anyway – it's never too late; big fan of life-long learning and continual self-improvement.

Reminder for the broke people like me, Khan Academy is free and very good

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