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Comment by Peteris | Hacker News Reader

This is false. I studied Maths at Cambridge and learned some courses completely on my own.

Seconded. Math is one of the most easily self teachable subjects. The field of study is objects of mind (unless you're a platonist.) Literally no materials required except pen/paper, a brain and maybe a straightedge and compass. The point of math is not to do endless worked exercises. It's to understand mathematical objects and prove interesting things about them. You can generate unlimited problems for yourself by investigating some mathematical object at random.

Basically nothing you said actually made a case against anything I said, or for the thesis that it is easy to self teach. Just stating this for the record.

Could you explain briefly why this is the case? I don't understand.

Well, what was his argument? Based on his second reply, he seems to think that because it only depends on your ability to reason that it should be easy. But doesn't that trivialize the matter? As long as we have mathematical models, as we do in physics and in chemistry, then it should be just as easy to learn physics and chemistry.* So then what does he consider hard to learn? Are the social sciences hard to learn? The 'it is of the mind' is a non-argument to me. And I don't think he addressed anything I said.

Anyway, this is almost irrelevant to what I was saying. Even if you assume every person can reason well, I'm saying you could still be in error unless you seek validation and guidance. It's really easy to think you've given a solid argument for something, but actually be wrong. It happens to everyone.

*By the way, there is a definite trend in physics for math, instead of experimentation, to be leading the way towards discovery.

Well. There are no barriers to entry. If you have any inkling of logical ability, you should be able to tell when a proof is right. All it requires is critical thinking. Presumably humans come with that out of the box.

It's false that any of what I said can be true for some (or many) students? How do you determine if you're one of those students?

You're right, the above posters generalize way too much. They are either CS or Maths students and as such are already well-prepared for self-study! If you study Maths you already know what all the symbols like epsilon, e etc. mean, you can just gloss over a mathematical text and get the gist of it. Same goes for many (but not all!!!) CS-students, some unis lean a lot on algebra, some don't do much maths after the first two courses.

As such, I think it's ridiculous to go up to anyone and tell him/her to just "study by yourself", I could give a maths book to a biologist and that person would understand absolutely nothing without guidance.

Well, you could certainly do it when you start with "Maths 101" or something like that.

I was addressing the money issue and tacitly assuming that they could do the work. For just a Bachelor's and then just a Master's in engineering, they have a good chance of being able to judge correctly if they can do the work.

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