Math Academy pulled me out of the Valley of Despair
168 comments
·March 3, 2025Gimpei
nicf
I'm a private tutor who works with adults on proof-based math. I've often had a similar thought to the one you're expressing here --- I also found proofs pretty revelatory when I first exposed to them and wondered where this magical tool had been all my life --- but I wonder how well this experience would scale to the mass of students in high school math classes.
After teaching proof-writing to my students for several years now, I've seen a lot of variation in how quickly students take to the skill. Some of them have the same experience that it sounds like you and I had, where it "clicks" right away, some of them struggle for a while to figure out what the whole enterprise is even about, and everything in between. Basically everyone gets better at it over time, but for some that can mean spending a decent amount of time feeling kind of lost and frustrated.
And this is a very self-selected group of students: they're all grown-ups who decided to spend their money and spare time learning this stuff in addition to their jobs! For the kind of high school student who just doesn't really think of themselves as a "math person", who isn't already intrinsically motivated by the joy of discovering what makes integrals tick, I think it would be an even harder sell. High school math teachers have a hard job: they have to try to reach students at a pretty wide range of interest and ability levels, and sadly that often leads to a sort of lowest-common-denominator curriculum that doesn't involve a lot of risk-taking.
AntoniusBlock
A more rigourous approach was tried after WW2, when Americans feared the Soviets were edging ahead mathematically/scientifically. It was called "New Math" [0]. For an example of the type of textbook high school students were taught from, check out Dolciani's Modern Introductory Analysis (the 1960s and 1970s editions only; the later editions were dumbed down, especially when Dolciani died) [1], which starts with set theory, logic, field axioms, and proof writing techniques.
cultofmetatron
> I don’t understand why we can’t have more proof heavy math in high school.
proof based math requires critical thinking and its a lot harder to scale the teaching of critical thinking. We dont' pay enough for teachers of quality to be able to do this at the public school level. Its also much harder to test for in standardized tests.
zozbot234
> Its also much harder to test for in standardized tests.
You could test it using interactive proof verifiers. This would also make it a lot easier to teach, since proof verifiers can handle even very complex mathematical proof via the repeated application of a mere handful of rules. (The rules are also surprisingly similar to the familiar "plug and chug" workflow of school-level math, only with different underlying objects - lemmas and theorems as opposed to variables and expressions.)
Evil_Saint
I completely disagree. Proofs are very abstract. Learning to read them is a skill you have develop before you can learn anything from them.
BinaryMachine
Great post! It's always interesting to see the experiences of fellow peers going through Math Academy.
It took myself 2 1/2 months to complete Mathematics for Machine Learning on Math Academy last year (2024) working through reading material, taking notes, and completing all the exercises took all day everyday I loved it, this was after I completed Khan Academy (starting from the beginning of mathematics negative numbers, to the end differential equations) because I kept putting it off for years when I got to busy.
The main thing for me was learning not to get too frustrated when getting an answer wrong. If I made a mistake, I focused on understanding what went wrong, looking up youtube videos on the topic if it was confusing, and then trying again.
At the end of a lesson I wish I had someone to bounce questions off of but thats when I used chatGPT.
Congrats!
mikelikejordan
Thanks for reading my blog! M4ML is the next course for me after I complete MF3. What are you doing now on math academy!
BinaryMachine
Yeah! Unfortunately at the time I had gotten laid of from work so I had extra time just not extra $ to keep paying monthly subscription, also some courses still said coming soon at least the ones I wanted to take when I was taking M4ML.
Good Luck with M4ML its a great course! Covers a lot, I was impressed, wish there was some videos or more visuals but it doesn't hurt to use youtube. I took maybe 7 pages of notes on my github and each over 4000-8000 lines (I used the notes to do the step by step exercises it was easier for me to type notes and do the exercises on computer than pen and paper this is what I used to do).
I take the notes because I will probably forget, but I think its key to always be learning and keep practicing even when your done the course.
Once I get hired again I will def take Discrete Mathematics. In the mean time I've just read books on ML and LLMs, free online courses, youtube videos etc.
mikelikejordan
I understand the feeling. You'll get another job soon and be back to crushing math problems on math academy. Thanks I'm excited for M4ML a lot. I feel like I'll experience math in a way I never have before. Would you be willing to share your github of notes?
rcarr
I really want to do Math Academy and even briefly tried it a year ago. It's absolutely great but it's also very expensive. I know that math skills are invaluable, it's far cheaper than schooling, and that long term the investment is likely to pay for itself but when you're skint $49/month is still a pretty hefty sum, especially if you live outside of America. For context in the UK, a basic gym membership (£17/month) and a SIM only phone plan with unlimited data (£22/month on a two year contract) only costs £1 more in total than Math Academy (£38/month). I can't help but feel that the people who would benefit from it the most are also the people least likely to be able to afford it.
ohgr
Go on eBay and buy the following Open University book sets. They go for around £30-50 a pop: MU123 (basics), MST124 (more complex). 6 months worth of study in each book set. If you like it do MST125 (even more complex) and M140 (stats) after. That's the first year of a mathematics degree literally from the ground up through GCSE and A-level stuff. If you really like it, get a student loan and do the associated accredited degree.
£30 for 6 months is pretty damn cheap and you get to keep it forever!
ebay example of the latest edition for sale: https://www.ebay.co.uk/itm/197011707080
On archive.org too if you are happy with PDFs: https://archive.org/search?query=creator%3A%22The+MU123+Cour...
First MU123 book A: https://archive.org/details/BookAMU1232ndedOU2014/MU123-Book...
This is a proper accredited course developed over 50 years or so with its own textbooks and material from a respectable university, not a gamified subscription portal experiment put together by god knows who that can disappear in a puff of smoke at no notice.
NlightNFotis
I'm studying the Q31 (BSc Maths) on Open University.
I can second this recommendation. The maths books are _excellent_.
It's hard to explain how, but let me try: most of the maths textbooks I possess (plenty of them) are written with the assumption that you attend lectures at a classroom and use them for extra material/exercises/reference.
The OU books are written with the assumption that you learn from them as the primary material, so they go a lot further with regard to explaining things as well as producing them from first principles.
rahimnathwani
I just skimmed through MU123. The content and level is somewhere around the level of these two courses on Math Academy:
- 5th grade math
- prealgebra
The book does look high quality. But I'm surprised it covers these fundamentals, given it's for a university course.
NlightNFotis
Yeah, MU123 is basic (high school) mathematics. The reason for that is that the way the Open University works, they have no formal requirements to join, so they cannot assume that students know even the basic stuff (because they might have left school earlier, or they might be out of formal education for years, or be from a different domain, etc), so the aim of that course is to quickly help you catchup regardless your background.
If you are above this level, you would start with the "intensive start", which skips MU123 (allowing you to pick another module in its place) and then starts with MST124 (precalculus, trigonometry and single-var calculus, roughly), moving you on to MST125 (intro to proofs, number theory, more calculus, linear algebra, etc), in a faster pace.
AntoniusBlock
The OU maths books are indeed very good. This is the way to go.
suncherta
The way I come to look on such offers (monthly unlimited subscriptions) is not the net price itself, and not future supposed returns to it (who knows what they be, and they for sure will depend on many other things), but how many hours a week I am willing to spend on that service.
If you can and willing dedicate on average 2 hours a day (a big commitment but I think I was able to hold it for several month with them) the cost of mastering, say, Linear Algebra will be ~4 less then if you subscribe and will be spending ~30 minutes a day.
eps
> very expensive
I guess it depends on where you are at in the world, but in our neck of the woods $50/month is an absolute bargain compared to using a tutor. Not to mention you get to work at your own pace and to practice spaced repetition consistently.
raincole
It is. But I don't think there is an alternative way to make it sustainable. There are just not that many people who are serious about self-education, and you won't like it to cater to the less dedicated customers.
> I can't help but feel that the people who would benefit from it the most are also the people least likely to be able to afford it.
Even if it were $10/mo, the people who would benefit from it the most (around the world) still can't afford it.
criddell
Did you try contacting them and asking for a discount? Sometimes all you have to do is ask.
nsfmc
my read as a US person is that math academy is optimized towards students who would otherwise be well served by an in-person supplemental math program. at the earlier grades for math academy (grades 4-5 etc) the main competition i've encountered are in person programs like AoPS, Russian Math, or Kumon. The prices for those range between $450-$100/mo and for a student or student and parent combo that may be looking to supplement their math classes or for somebody who needs to home school for a period of time, mathacademy at $50/mo is a steal.
inglor_cz
I wonder if they could charge lower rates for people who live in poorer parts of the world.
$49/month is almost nothing to me now, but it would be prohibitively expensive for a 15 y.o. me in freshly independent Czechia.
I suspect it would also be prohibitively expensive for most 15 y.o.s in the developing world today, and these are the guys and gals who stand to gain the most.
david_allison
It's not just the price. You'll find a number of 15 year olds have no ability to spend money online.
gen_greyface
+1
I wish there was PPP for the subscription, i tried for a few months but stopped the subscription recently.
chrsig
I'll call out 3b1b and khan academy for me. Especially over covid. Made math fun again.
My middleschool principal thought it'd be a good idea to skip me over pre-algebra into alg 1.
Turns out that doesn't work great, and I still have confidence issues because I have a hard time remembering the properties of addition & multiplication by name. I know the rules.
whatshisface
A noun that only refers to one thing isn't a real word, so if you want to cure yourself of "the associative property" being meaningless, you could study other algebras where the rules are different.
chrsig
this was actually one of the things that really turned things around for me actually. it took probably 25 years in between.
rahimnathwani
My middleschool principal thought it'd be a good idea to skip me over pre-algebra into alg 1.
1. Read each sentence at half your normal reading pace
2. Skip every other chapter.
Sounds ridiculous, right?
That's my reaction when people propose grade skipping as the only solution for a child whose natural pace is 2x the 'standard' pace at which math is taught in school.
djeastm
Yes, it's ridiculous. They should really only grade-skip in math after giving the student take-home exercises during the current year that will serve as a replacement for the skipped grade. It's irresponsible to do otherwise, imo.
rahimnathwani
Agreed, but I'd rank the choices in this order. #3 is still better than #4.
1) Allow the child to go at their natural pace.
2) Grade skip every 2 years, with take-home exercises.
3) Grade skip every 2 years, without take-home exercises.
4) Force the child to go at the same pace as the rest of their same-age peers.
harrison_clarke
a lot of school is redundant, and the courses are often non-sequential
skipping chapters of a novel doesn't work very well, but it works great for the encyclopedia, and pretty well for a lot of textbooks
it's also not that hard to use khan academy or wikipedia to fill in the gaps, if you did miss something
eitally
The best solution is to offer accelerated math classes in public schools, in both elementary and middle. Mostly in middle school because elementary math can usually be handled through differentiated instruction by the teacher, unless the child is exceptionally advanced.
I really like the way my kid's middle school does it: accelerated 6th grade math covers the entirety of the 6th, 7th, and 8th grade standard math curriculum, which sets the kids up for algebra in 7th grade and geometry in 8th. Because the standard middle school math curriculum is essentially just advanced arithmetic, it's pretty straightforward to bundle this way. It also makes it easy to inject 7th graders who missed 6th grade accelerated math into the accelerated track if they pass the algebra qualifying test before 7th grade.
When I was growing up the G&T program started in 4th grade and cohorts from multiple schools were pulled into a school that ran the "gifted" program. Essentially all the kids were tracked from 4th grade through high school graduation and there was no real possibility for non-G&T kids to get into the "gifted" classes in middle school. In HS that just transitioned into APs and college dual-enrollment; by the time I graduated HS in '99, I had 22 credit hours of college classes banked, including dual-enrollment bio and calc 1 + 2, plus a bunch of humanities APs.
Today -- at least in our bay area public high school -- there's no tracking outside of math and the vast majority of classes can contain students in multiple grades. That absolutely was not the case when I was in school, and imho it's an improvement.
rahimnathwani
I'm thinking specifically about the USA math curriculum. It's pretty sequential until 8th grade or so.
Filling in gaps is fine for people with good study skills, but that excludes the vast majority of elementary school students.
abstractbill
Congrats on your progress!
Over the past few years, while homeschooling my daughters, I've come to see the way math is usually taught as horribly pathological. In the US, where we live now, it's often seen as a competitive activity -- almost like a sport. In the UK, where I grew up, that wasn't the case but still it was taught as this huge body of knowledge and skills with almost no motivation.
My daughters are so advanced in math and I really don't believe it's even mostly due to innate ability. It's because, just to take an easy random example, when we studied geometry our very first lesson was me pointing out that the word "geometry" just means "earth measuring", and it was useful for farmers to be able to do that. Or, when we proved the irrationally of sqrt(2), of course I entertained them with the tale of Hippasus being thrown into the sea by the Pythagoreans. For basically everything we've learned there are so many fun stories. It makes me sad that most students of math never get to hear them.
pipes
As a b and c grade student, who messed about, stumbled through a not very good info technology degree at university I definitely agree with this. The stories and lore are what makes me now so interested in programming and software engineering. I've pretty much taught myself everything programming related and that's what I work as too. I desperately want to learn math up to and including calculus as I feel like it's a hidden shame that I'm a programmer with not much math ability. I'm actually considering signing up for math academy.
pona-a
I am currently studying for our country's version of the SAT and, having tried Math Academy — having been convinced there is nothing anywhere as polished and developed on the market — I still had to cancel my subscription after the first month. The price just wasn't worth it; over a single year, it translates to a cost greater than one-on-one tutoring.
Small companies have to understand the value of local pricing — nobody is willing to pay above h percent of their salary for a service X, and there's only so much that rule can be bent. I understand that, at the end of the day, the company still has all their expenses in USA prices, but for digital services with no manufacturing or logistic costs, it can be better to make a modest profit than none at all.
ABS
I decided to try it 10 days ago exactly because of the pricing.
It would be impossible for me to have one-on-one tutoring for a year at only €465 ($499 but I'm in EU). And that's regardless of the tutoring quality
chamomeal
Wow that’s a pretty glowing review of the service. Sucks about the pricing though.
I haven’t really looked at math academy, but I was in school (including college) I probably learned 40% of math from khan academy, 40% from textbooks, and maybe 10% from lectures.
How does math academy compare to Khan academy?
pona-a
Math Academy uses spaced repetition for skills with tiny, to-the-point interactive lessons (typically following "theory, some exercises, theory, some more exercises" formula) based on an initial diagnostic test, where the skills are structured as a graph of dependencies.
I didn’t, at the time, appreciate how challenging a problem it was until I started researching Bayesian Knowledge Tracing. While their definition of a skill can be a bit narrow, thus putting more time into reviewing things I'd rather move on from, it does work from what I've observed.
I recall they had a course on Abstract Algebra and other more advanced subjects, so if you're really interested, the great thing about subscriptions is that you can afford to try it.
ChuckMcM
Always great to hear from people on the far side of the valley of despair. I don't think it is pointed out enough that people who fall off of "mount stupidity" can sometimes get really really stuck. In my experience when they do that at work it is quite traumatic.
Another good book for the author and others is "5 Elements of Effective Thinking" by Burger & Starbird. It thinks about thinking which can sometimes side step the depression of suddenly not thinking you know anything about anything that accompanies that big drop off mount stupid.
mikelikejordan
Thanks for reading my blog post! I'm going to pickup that book today and make sure to start reading it!
financypants
what do you mean by falling off mount stupidity, especially at work?
ChuckMcM
It was discussed in the article, but to be more explicit, sometimes a person who is sure of their understanding of things learns a new thing and that new thing opens their eyes to a huge amount of complexity they were missing. They go from feeling like they knew everything there was to know about a thing to feeling like they know little to nothing about the thing. (this is the "Falling off Mount Stupidity")
Depending on how senior they are at work, that can be quite traumatic. A lot of people in tech sort of base their self image on how smart they perceive themselves to be with respect to their peers. When that perception inverts their own world model makes them feel worthless.
In the two cases where people I was managing this occurred (that I knew of) their productivity dropped like a rock and they became seriously depressed. One I managed to get back on track, the other left tech and I have lost track of where they ended up.
null
mikelikejordan
Mount Stupidity is the peak of overconfidence greatly outpacing your competency level. So, falling off is essentially being humbled by expreiences that make you realize you do not know as much as you think you do, and your confidence takes a major dive as a result.
brm
Mount Stupidity relates to section two of the blog post where it references a concept related to the Dunning-Kruger effect.
tptacek
Math Academy is awesome, I'm fully hooked, but, repeating something I wrote elsewhere: it is a bleak existential confrontation with your ineptitude with fractions.
plutosmoon
you and me both buddy
tptacek
I'm signing up like, oh, I have a lot of gaps I can fill in with calculus, and it's like, no, you got a lot of gaps you need to fill in with simplifying cube root expressions. The best is every once in awhile it double checks to make sure I still know what multiplication is, with like Dick and Jane bought 10 apples problems. I have given it no reason to believe otherwise! But I trust the algorithm.
tptacek
Also, I go too fast through them and do stuff in my head that I should write down and make dumb mistakes, and when I get the "Incorrect" I'm like, yeah, I see exactly the dumb thing I did, let's move on, and it's like, no, let's do a next problem that's real nice and easy to make sure you get this and I'm like "stop patronizing me motherfucker".
danielecook
I’m doing math academy and I have two comments. First, the value of this site comes from its content which is very thorough. I think it’s a great way to learn math.
Second - I love the website. It reminds me of what I think of as the golden age of web design where sites were mostly server side rendered with a little jquery / Ajax sprinkled in, and more information density was preferred.
mikelikejordan
Hey everyone! This my blog. Just made an account on here so I could comment. Thank you all for the support and reading my story! :)
philips
I have enjoyed the challenge of relearning mathematics with Math Academy as well. I find the format and reviews extremely helpful- it is so refreshing to end a lesson or review early if you are getting all the answers right compared to the drudgery of my schooling experience where you are getting question after question that isn't introducing a new mental challenge.
My only desire is that their site worked on my phone- it would be nice to do a lesson when I have some free time and some paper.
bost-ty
I read this article because I wanted to learn more about their Math Academy experience, but I found the preamble and backstory a little long, which caused me to skim.
Re: Math Academy, I used the service for ~3 weeks last year from a post here on HN by the guy responsible for the AI/ML knowledge graph behind the platform (I believe his first name is Justin). I was "only" doing about 30-60 minutes a day (a little bit higher than their guidance, but low for someone not doing math otherwise IMO).
N.B. Due to substandard early instruction combined with being "gifted and talented", I was placed by the test into Math Foundations 1 (or 2?). For example, I still don't have an active/working mastery of the unit circle. So if you're a real whiz, YMMV.
I found Math Academy effective at showing me my weaknesses and sharpening those skills in the short term, but I probably didn't do it for long enough to benefit from the spaced repetition effects. I found the UI/UX better than Khan Academy (sans AI), and much less tedious (when I demonstrated understanding, the questions moved on or increased the complexity vs. doing the full problem set no matter what).
When I cancelled within the first month to receive my refund (see other commenters mentioning the high price), I was surprised to see my support email and refund request email both went to one of the founders (or owner?), Sandy Roberts, who was emailing me while also attending her daughter's college orientation (or helping her move, can't recall right now).
Cancelling was painless once I realized I was getting a response from someone at the platform --- so if you're interested in trying it, I can recommend giving it a shot. Maybe there's some sort of economy for them if more (adult) people sign up, because 50 USD still feels a bit steep.
Nifty3929
"other commenters mentioning the high price"
I understand that everybody has different financial circumstances, but personally I find it so odd how people prioritize their spending. $50/mo to level up your math game? Too much. 8x $6 lattes per month - totally worth it. $200k+ for a university education after which you STILL won't know basic math (or much else useful for most majors) - super totally worth it.
For me I'm just willing to pay a lot more than other folks are to learn interesting skills. Math, sailing, music, leatherworking, perfume making, whatever - to me that's such a good use of money.
bost-ty
Thanks for the reply, and I know I'm replying ~a day late to your comment.
The near-term costs vs. the long-term payoffs of learning the math skills I was learning were pretty clear (immediate costs, opaque long-term benefits other than being better at math in a general sense). I didn't have anywhere to apply the math, so I decided to spend my time learning more from sources like "Structure and Interpretation of Computer Programs", which is zero-cost to me.
I don't drink any $6 drinks of any sort; I also can't go back to change how much I did or didn't pay for a university education that did or didn't involve learning math for my major.
Other commenters I read who shared price concerns also didn't mention their latte habits or cost of their advanced degrees, so I didn't find this comment very helpful for making that comparison in my specific case.
littlekey
I agree with your overall point but I don't think those comparisons are very useful. Regardless of my monthly latte consumption, an extra 50/month is 50/month... the only real comparison imo is how much you'd be saving vs hiring a tutor or simply going through books yourself for free. I think it comes down to whether you have the drive to learn from books. If so then that's clearly the best move. But I'm willing to pay the 50 because this is the only approach that's worked for me so far. It's worth it but it still stings.
Nifty3929
Fair point. IOW, what you're saying is: If learning math is your goal, is this the best (or most cost effective) way to do it? Sure, for some it would be, but for others they'd be better off with books or some other alternative.
I had a similar experience where math went from being easy and fun to an intimidating and painful slog. My problem was just how focused most courses are on learning techniques for solving problems. I found all those endless substitutions that you learn in calculus to be infinitely dull and so it was difficult to do a good job. Ditto for the solution techniques for differential equations. Don’t get me started on matrix inverting. I think I had to do a 5x5 matrix once for a homework assignment. What a colossal waste of time.
Proof-based math classes came like a revelation to me. When I took Real Analysis, for the first time in over a decade, math was fun. You weren’t just memorizing and reapplying recipes. You were seriously thinking about unique problems and devising solutions. And all the while, you were learning where all these techniques actually came from and how everything connected together.
I don’t understand why we can’t have more proof heavy math in high school. Who cares whether you remember the arctan substitution or whatever in an integral; I’d always just use a solver for that anyway. I’d rather be learning about what an integral is in the first place.