[jinfiesto]

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.

[gems]

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.

[jinfiesto]

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.

[James_Duval]

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

[gems]

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.