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.

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ndriscoll 6 days ago | parent | next [-]

> 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.

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tptacek 6 days ago | parent [-]

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

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ndriscoll 6 days ago | parent [-]

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.

	▲	tptacek 6 days ago \| parent [-]
		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!

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6 days ago | parent | prev | next [-]

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mettamage 6 days ago | parent | prev [-]

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.