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I was always good at maths, just because primary/high school math was simple enough to find concrete examples for the abstract concepts, and that helped me a lot on exams.

Since then I tried to grasp more advanced concepts. But I always faced with pure overformalized, overgeneralized stuff with n's, m's, sets and spaces. And the only numbers in the whole paper were page numbers.

Conversely sometimes I can find an informal writings about the topic (probably written by a non-mathematician), that uses simple examples to demonstrate the concept, and it makes the whole topic easier to comprehend when I return to the previous formal thing.

As far as I know the human brain is very good at classifying and building models as long as it saw enough examples. But from my experience it isn't always trivial to create good examples when you are given only a definition.

I don't find proofs hard: just use the rules you know, a computer can do it nowadays. But definitions are magic: why do you define it that way? What does it express? Textbooks often don't answer these questions, but proceed assuming you already know everything about it inside out... And this is the point where I usually get lost, and I cannot proceed for weeks/months, eventually I give up and resign that I'm too stupid to comprehend it.

I understand that formalism is important in mathematics, but I still wonder why don't textbooks help the reader to get the point?

This often makes me research why mathematics hard...

I've recently found these lines [crackpot link deleted]

I really hope this isn't the truth...

Since then I tried to grasp more advanced concepts. But I always faced with pure overformalized, overgeneralized stuff with n's, m's, sets and spaces. And the only numbers in the whole paper were page numbers.

Conversely sometimes I can find an informal writings about the topic (probably written by a non-mathematician), that uses simple examples to demonstrate the concept, and it makes the whole topic easier to comprehend when I return to the previous formal thing.

As far as I know the human brain is very good at classifying and building models as long as it saw enough examples. But from my experience it isn't always trivial to create good examples when you are given only a definition.

I don't find proofs hard: just use the rules you know, a computer can do it nowadays. But definitions are magic: why do you define it that way? What does it express? Textbooks often don't answer these questions, but proceed assuming you already know everything about it inside out... And this is the point where I usually get lost, and I cannot proceed for weeks/months, eventually I give up and resign that I'm too stupid to comprehend it.

I understand that formalism is important in mathematics, but I still wonder why don't textbooks help the reader to get the point?

This often makes me research why mathematics hard...

I've recently found these lines [crackpot link deleted]

I really hope this isn't the truth...

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