I've heard several times (such as this one) that it's dangerous to learn/prove/teach mathematics through images. I've also read somewhere that showing mathematics through images helps one's intuition because we understand better through images, due to our long date use of the vision sense. I can conceive that this information should be half-true - there might be things that can be taught with images and things that can not. From here, I have two doubts:
- What can and what can't be learned/proved/taught with images and why?
- Using mathematics this way isn't the same as geometrical thinking?
I'm also open to books/articles on this topic.