Ask HN: How to learn math from zero for adults?

I’m in a very similar position. I didn’t go to uni and somehow found myself in a programming career. In a few weeks I’ll be sitting A-level (UK advanced high school) Mathematics exams for the same reasons as you. I’m 32 years old.

I’ve found having formal exams to study for very motivating, and humbling. I thought I knew things I’d read in books, but it turns out I just recognised them when I came across the same topic again. Being able to recall concepts and use them without help under time pressure is a different level of mastery.

Can you sit high school exams as an adult in the US? There might be private exam centres in a city. That way you’ll _know_ you’ve learned the math(s) you need, on top of all the great learning resources linked here.

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Edit: Cambridge International do A-level exams, with centres accepting private candidates globally: https://www.cambridgeinternational.org/programmes-and-qualif...

I've done this and would echo the good advice you've already gotten about Khan Academy but I think the comments in this thread are skipping over the most important part: pace. Work slowly. Don't move on until you really "get" the concept you're working with. Some topics might "click" right away and others might take weeks of bashing your head against the wall until your brain makes sense of it. That's okay. It can definitely be tedious at times (so be kind to yourself!) but a lot of learning happens when you're struggling to make sense of something so it's worthwhile to lean into the trouble you're having and figure out what it is that you're struggling to understand.

The downside of formal education is that the teacher has a timeline that needs to be kept and the class will move on without you. It might not seem like a big deal in the moment but in math the foundation is so important because the concepts build on one another. Sometimes in really subtle ways. If you have the motivation (and it sounds like you do!) then the huge upside to self-paced learning is that you can build a really strong foundation and the more complicated advanced topics will be so much easier to master. Khan Academy is really good at breaking subjects down into tiny bites and then slowly building on what you've learned but if you don't quite understand a lesson or if you haven't properly paid attention don't be afraid to do it again. If you guessed the right answer but don't understand why your answer was right, don't be afraid to go back and do it again.

So just because one person here could do all of the Khan Academy 9th grade algebra in a week that doesn't mean you should set that timeline for yourself. Everyone is starting from a different place. So maybe it'll take you a day, or a week, or a month, or even months. But however long it takes is how long it takes.

* Subscribe to Beast Academy, and do the interesting problems (puzzle and challenge ones). Cost is $15/month, and you should be able to do this fast, so it shouldn't be too high

* Sign up for Alcumus. This is free. Set it to easy. Try problems in each section, and use this to identify gaps. If you find a gap, do a deep dive to address it. If you can't solve a problem independently, solve it using online resources (but put in the wrong answer / give up -- you don't want the ITS thinking you could do it).

* Watch videos on 3B1B, and sign up for Brilliant. Take a few courses.

* This will sound silly, but do sinerider, nandgame, and the fun Khan Academy courses (Advanced JavaScript and Pixar-in-a-Box), and things like this. Math is broad, and those give helpful exposure to a broader range of topics.

https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw

https://artofproblemsolving.com/alcumus/

I think in principle it boils down to two things: finding the right material, and proper time management because it is hard to do anything if you have a job and other responsibilities

I'll just mention: From a scientific perspective, this is absolutely the wrong advice.

If you couldn't understand something yesterday, that's very good evidence you won't make sense of it today. You should work hard, go deep, and try hard problems, but if you fail to understand something after putting in the effort, just move onto something else.

Learn a few unrelated things, and come back. Much of the time, if you come back in weeks or months, it will just click into place.

You also want to visit topics /many/ times. Truly understanding many topics in math should take months or years. You can do it a lot more efficiently if you visit a topic for e.g. 5 hours each every 6 months over 2 years than a single 80-hour cram. You'll put in less time and understand more deeply.

A good starting point for references is Bruner (and specifically under Spiral Curriculum), but there's a whole literature on this. There has been a slow transition from seeing math as a set of bricks which stack on each other to an interconnected network of knowledge. The spacing effect literature is good too.