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Comment by iliketosleep | Hacker News Reader

I disagree with the general statement that leaning maths is "pitifully slow without a teacher". So long as one has structure (e.g. some kind of syllabus) and has access to google, then learning can proceed very efficiently indeed. In addition, by being able to work through difficulties independently you can "be your own master" so to speak, earning the confidence to solve new and difficult problems without assistance.

Having said that, I have come across people who have absolutely no apitutude for maths and definitely need a teacher. In a matsh class, there's usually one one set of people who kind of just "get it" straight away, and another set who struggle despite studying hard.

As you said, there are many roads to Rome, and the best road may or may not involve a teacher depending on the individual.

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> I disagree with the general statement that leaning maths is "pitifully slow without a teacher".

How do you check your work then? I remember specific experiences in college math classes where I thought I understood something, took a test, and then got something wrong. And it was because of a misunderstanding of something I thought I understood. I have those misunderstandings occasionally in math. And that can make self-teaching really difficult. At least with cs/software development you can check your understanding by writing code.

By downloading question papers that have worked solutions. If you get something wrong, check your solution against the worked solution and then error in your understanding should become apparent. This works well up to about college level, after which it's harder to find resources.

That's a good solution, but college-level mathematics was specifically where I had issues learning the material myself. I remember taking an upper-level college class for my cs degree that focused heavily on proof-based mathematics. I decided I wanted a tutor. Online tutoring for the highschool/lower level college classes was easy to find. But not for upper-level proof based math classes that were TA'd by grad students. I finally found one company that was willing to tutor me. They advertised tutors from ivy-league grad schools and started billing at over 100/hr. Fortunately I found a grad student to to tutor me at my university for a much more reasonable price. But I definitely noticed a difference in the type of tutoring offered. I'm much less confident self-teaching myself mathematics if it involves proofs, or material that would show up in grad school or an upper-level undergrad class.

I think for most people though, not having a teacher doesn't mean "pitifully slow", it means they will eventually forfeit the endeavor. The option to self-study has always been there, and now Khan Academy is here too, but I think there's a reason why we haven't seen an education revolution just yet, and I think it's because an interactive teacher who monitors your state and thinks about the road ahead is key.

There are even a lot of math teachers who feel anxiety about basic math. Why don't they simply self-study?

They feel anxiety about basic math because they've lost touch with the basics, and this is a massive problem. They could and should go back and review the basics; otherwise they will not make great teachers.

An author of a book is still a teacher... we’re just debating the personalization of the teaching at this point.

But then this recommendation becomes vacuous. No one is recommending learning math by deriving everything yourself.

Exactly. What’s really being referred to? Lower cost and more scheduling flexibility perhaps?

Maybe, but I think people do mean a literal human, and I do think books were always available, and if that alone were the key... then I hesitatingly make the simple argument that it would've already been done. One might make a similar argument about why Khan Academy isn't a blowout success in the US.

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