In part 9 and part 10 of this series of posts on Math Academy I provided some feedback on both the pedalogical and non-pedalogical aspects of Math Academy. In this last post I present my final thoughts on Math Academy and my quest to learn what an eigenvector is.

My current status

As of the time of writing, I’ve completed the Mathematical Foundations II course and am about 28% of the way through the Mathematical Foundations III course, having accumulated a total of over 3,600 XP thus far. I’ve settled down into a routine of doing at least 50 XP a day, sometimes a bit more than that. I have never gone a day without doing at least something.

If I maintain my current rate of progress, I hope to complete the Mathematical Foundations III course sometime in late May or June (but see my complaints in the prior post about progress estimates!), and will then start the Linear Algebra course. As I mentioned previously, my goal is to finish the Linear Algebra course before the end of 2025, and then to complete the Multivariable Calculus and Probability and Statistics courses by the end of 2026.

Is Math Academy worth the money?

Let’s start with the obvious topic, money. If I meet the goals discussed above by the ends of 2025 and 2026, I will end up spending over a thousand dollars on Math Academy. That’s a lot of money, even for someone like me with a well-paying job. Then I’ll be faced with the choice of paying for the service a while longer, to make sure I get any needed reviews and won’t forget what I learned. (See my suggestion in the last post for a reduced-price offering that just covers reviews.)

However, on balance I think it was and will be worth it. Learning mathematics is both a hobby for me and supports other hobbies I have, and I’ve spent similar amounts on hobbies in the past. And it’s certainly true that spending several years on a less costly approach (reading a textbook and doing its exercises) didn’t work out for me. So, I’m happy to pay for a service that looks like it will.

Do you actually learn anything?

I think I’m learning some mathematics with Math Academy, but am I really? Well, I now have a much better handle on some topics that I previously had never encountered or had trouble remembering. The most notable of these are the synthetic division method for polynomials, the various trigonometric identities, and differentiation of products and quotients of functions.

I still struggle remembering some things, like the derivatives of the secant and cosecant functions, but I hope that will get better in time. In the meantime I sometimes resort to deriving those from the derivatives for sine and cosine. (This works fine in lessons and reviews but kills performance on time-limited quizzes.)

One thing I will say is that the “scaffolding” aspect of the Math Academy system means that often what I’ve learned is the simplest possible case, and I would be at a loss dealing with more general cases. For example, the Mathematical Foundations II course teaches using synthetic division to divide a simple linear polynomial factor (e.g., x-3) into a polynomial of higher degree, but not how to divide an arbitrary polynomial into another.

I don’t see this as a drawback, though. It’s necessary to master simple cases before taking on more complex problems, and the confidence gained from knowing how to solve simple cases gives one a step up when it comes to learning about harder ones.

Does speed kill learning?

One criticism levied at Math Academy is that it overly emphasizes speed of learning. For example, this criticism shows up in Michael Pershan’s critique of the Math Academy system and in student quotes from an article about the original Math Academy program that he links to (“We do too much in not enough time”).

It’s certainly true that the developers of Math Academy put great weight on the speed of learning (“accelerates the learning process at 4X the speed of a traditional math class” is a key selling point). And at $49 a month there’s a built-in incentive to go as fast as possible, to get the most bang for the buck and avoid spending too much by stretching out your course time.

This emphasis on speed also shows up in the leagues and leaderboard system, which encourages students to compete on how fast they can pile up XP. Finally, it’s a common occurrence on X and similar forums to see people posting their XP totals in a way that’s reminiscent of people posting their high scores in a video game. It prompts the question: “OK, you did 7835 XP, but what mathematics did you actually learn?”

I’m sure that the Math Academy developers will respond that learning rapidly is perfectly compatible with learning well. Certainly The Math Academy Way doesn’t mention any drawbacks to trying to speed run through courses; at one point it raises the possibility of getting through a typical course in 5-6 weeks (at 100 XP a day), and treats that as an unambiguously positive thing to do. (An included table goes even further and shows that by doing 160 XP a day you could complete a typical Math Academy course in three weeks.)

However, after having breezed through most of the Mathematical Foundations II course in less than a month, I’ve decided to deliberately slow down my pace. With the Mathematical Foundations III course getting into more topics I have less previous experience with, I’m trying to stick to my original goal of 50 XP per day, as opposed to trying to push up to and past the 100 XP a day mark. I also have other things I want to do in my spare time, and I don’t want to get to a point where I’m doing so many math exercises that I get sick of the whole process.

What about this “understanding” thing?

Another point of contention is whether Math Academy is really helping students to understand mathematics, or whether it’s just teaching superficial procedural skills. (Michael Pershan harps on this, for example, as does Dan Meyer.) Other comments have criticized the Math Academy system because it’s so different from the heavily proof-based way of learning mathematics embodied in various advanced textbooks, in which students build up their knowledge of particular areas of mathematics almost from first principles.

I’m not an expert in mathematics education, so I can’t really speak to the debates about whether Math Academy promotes understanding or not. I do read the explanations embedded in Math Academy lessons, though, and I do try to build up a basic understanding of what I’m reading.

As for proofs, the Math Academy developers are certainly aware of student demands for a more proof-oriented approach (see for example a post by Justin Skycak) and are apparently working to add more courses in that vein. That may or may not satisfy those who want Math Academy to be more like the textbooks they’re used to.

However, as a former applied math and physics major, my approach to mathematics is primarily instrumental: I want to know how to do math in support of other things that I want to do. I am less interested in learning mathematics for its own sake, and am very much not interested in an approach to math that is overly abstract and proof-focused. From my point of view the Math Academy approach is therefore very congenial.

Who else might benefit from Math Academy?

It’s been a while since I had to worry about school instruction in mathematics, whether for me or anyone else, so I can’t speak to the issues around using Math Academy for home-schooled students or mathematically talented students. But as an adult student of mathematics I do have some thoughts about Math Academy’s approach to that segment of the market.

If you base your impressions on what Math Academy students post on X, Reddit, and other online venues, you could get the impression that the typical adult Math Academy user is what the sociologist Tressie McMillan Cottom snidely called a “roaming autodidact”: “a self-motivated, able learner . . . simultaneously embedded in technocratic futures and disembedded from place, culture, history, and markets . . . almost always conceived as western, white, educated and male.”

Assuming that’s the case, one can understand some of the current product focus of Math Academy the company, including introducing more proof-oriented courses, as mentioned above, and especially adding courses like Mathematics for Machine Learning that cater to the latest hotness. They are doing what Clayton Christensen claimed incumbent vendors do, namely going up-market and catering to their most demanding customers.

But in so doing, is Math Academy closing off other potential market opportunities and leaving them to possibly be exploited by others instead? Let’s go back to Benjamin Bloom’s original research and recall that what got people’s attention was not that he was able to take a 95+ percentile mathematically-talented student and turn him [sic] into the next John von Neumann. Rather it was the claim that Bloom’s methods could enable an average student to reach much higher levels of achievement.

There are a lot of otherwise-intelligent adults out there who left off their mathematics education fairly early due to encountering difficulties and suffering ensuing math anxiety. What Math Academy could offer them is a firm grounding in actual mathematics, as opposed to a simplified exposition high on verbosity and very light on equations (the mathematical equivalent of the “physics for poets” courses some institutions have).

Let’s consider an alternative customer persona:

She [sic] is a former humanities major now working in a relatively non-technical job in a company or industry with a tech focus. She feels the lack of the mathematics training she never got, or dropped out of early due to encountering difficulties. She’s motivated to remedy that lack, and has even tried taking a couple of community college mathematics courses, but it just didn’t work out for some reason—maybe it was the teacher or curriculum, maybe she couldn’t make the schedule work due to work or family responsibilites.

She makes a reasonably good salary for a humanities major, but not nearly as much as the technical professionals she works with. She’s moderately progressive in her politics, and checks social media posts on Bluesky when she has a few minutes, because that’s where her IRL and online friends are.

How might Math Academy cater to her and people like her (assuming that it wants to)?

First, meet her where she is. Extend the word of mouth marketing efforts beyond X and Reddit to alternative platforms like Bluesky, which currently has over 30 million registered users. (PS: If anyone from Math Academy wants to set up a Bluesky account I’d be happy to reskeet their skeets.)

Second, further tone down the “AI-powered” messaging, or just ditch it entirely. As I mentioned previously, it’s a potential turn-off for many people, and she may be one of them. (And even if she’s OK with it, her friends may give her grief for using anything having to do with “AI.”)

Finally, consider some alternative product packaging. She doesn’t want to march her way through every course Math Academy has to offer. She’d likely be interested only in the Mathematical Foundations courses, and possibly only the first one or two courses in that series. Given the other demands on her time, she’s leary about committing to spend $49 month after month. She might instead like to pay a flat rate (amount TBD) for a single course like Mathematical Foundations I, and have a generous time limit for completing it, say six to nine months. (A 3,000 XP course could be completed within six months at a pace of 30 XP a day, or within nine months at a pace of 20 XP a day.)

Whether such an offering would find much take-up with this hypothesized “ex-humanities major” market is an open question. However, I think it would be a more attractive offering to that market segment than what the current service provides. And even if relatively few people take Math Academy up on the offer, I think there could still be important intangible benefits to reaching out to adult learners beyond the current core user base of tech-savvy folks. It’s not something Math Academy necessarily needs to do now—after all, the service is still technically in beta—but it’s something that might be worth considering in the mid-term.

We have LLMs now, why bother learning math?

Speaking of “AI” and the latest hotness, one possible response to Math Academy is, “Why bother?” I can ask an LLM to explain pretty much any mathematical topic to me (even in poetic form if I’m so inclined), and as LLMs improve their various capabilities I can just point one to a mathematical problem and ask it to solve it for me. What’s the point of paying $49 a month to Math Academy and doing all that work, when I could pay less (or even nothing) to get on-demand mathematical expertise with little or no work required?

There are responses one could make regarding why internalizing mathematics knowledge is important, especially if your job involves tasks that are mathematical or quasi-mathematical in nature. But that’s not my situation, so I’ll leave it to others to make that particular case.

My response is simpler: I enjoy doing math-related activities (like hobby data science projects), just like I enjoy writing, and I have no interest in outsourcing those activities to anyone or anything else. If I wanted to play the guitar, I wouldn’t be satisfied with paying someone to play the guitar for me. I also wouldn’t care that other people can play the guitar much better than I ever could. I would just want the satisfaction of mastering the guitar myself and being able to play a song. That’s how it is with me and mathematics, and no conceivable LLM could change that particular equation.

(As it happens, I did ask an LLM to explain to me what an eigenvector is. The answer was like a condensed and simplified Wikipedia article, and reading it was unsatisfying. I want to play the guitar myself.)

Whither Math Academy?

Finally, what of Math Academy itself? When I got a copy of my transcript after completing Mathematical Foundations II, it listed my student ID as being above 12,000. Assuming that IDs are assigned sequentially and not randomly, that means that over 12,000 people have used the Math Academy system and enrolled in a Math Academy course.

If all those people were still subscribed to the service then Math Academy would have monthly revenue of about $600K or about a $7M a year run rate. In reality the number of current subscribers is presumably somewhat less than that (given that many subscribers may have stopped after a few months), but on the other hand the subscriber base seems to be growing reasonably rapidly. So, my Fermi estimate is that for 2025 Math Academy could be up to a $10M-a-year business with up to 20 employees.

As I mentioned before, I can’t speak to the market fit for home schoolers or mathematically talented youth. However, I think Math Academy has achieved good product/market fit for that group of people of which I’m a member: adult learners with at least some mathematical background, a desire or need to learn or re-learn math, and a reasonable amount of spending power, typically due to working in IT or other high-tech fields.

Math Academy is clearly catering to that market by its choice of courses to add, including the Mathematics for Machine Learning course and proposed computer science courses, expanding from its core mathematics curriculum into adjacent areas. It can further broaden the market by some of the sales and marketing initiatives already discussed, including PPP pricing for non-US students, group and family discounts, and the like. These measures will lower revenue per user, but will expand the total addressable market.

I suspect that Math Academy could grow its subscriber base to 10x its current size, and its revenue almost as much, and could do so on a relatively accelerated schedule. Given that it’s (presumably) cash-flow positive today and should stay that way barring misdirected overspending, it looks to be a business that will be around for the long haul.

What about the larger claims made on Math Academy’s behalf? There I remain unconvinced. I don’t believe that Math Academy and the ideas about mathematics education it embodies will have any significant impact on traditional educational institutions in the near or medium terms. (The reactions of people like Michael Pershan and Dan Meyer are early indicators of that.) There are people and organizations working to change that mindset (and new ones popping up all the time, like the just-established Center for Educational Progress), but I suspect their’s will be the work of a generation and perhaps longer.

Despite Math Academy’s claims to be research-grounded and evidence-based, I’m also skeptical that we’ll see much if any research focused on Math Academy itself, trying to determine whether its pedagogy really has any advantages over the alternatives. The Math Academy folks are clearly too busy to do this, and I’m not sure anyone else will be willing to take on the task. So, all we’ll have is anecdata, anecdata that will be untrustworthy given the selection effects inherent in who uses the service. (I should add that my own anecdata shouldn’t be trusted any more than anyone else’s.)

But, in the meantime, I’m happy to have a service that seems to work for me, happy enough that I just upgraded my Math Academy subscription from monthly to annual. So, with that I’ll end this series and go back to working through Mathematical Foundations III. If you’ve checked out even one or two of my posts on Math Academy, thank you for reading!