I'll step in here. I've met people who are visual like me, and do math using their visual thinking. For me, algebra and such is like tetris or a legos but with

I'll step in here. I've met people who are visual like me, and do math using their visual thinking. For me, algebra and such is like tetris or a legos but with symbols. To this day, when I do algebra in my head, it involves visualizing symbols as if they are on a page and manipulating that picture. Others however are not visual, but yet they can do algebra fine using something like logical rules, and to be honest, often tend to be more accurate with it. It sounds like you're one of those people, so it's unfair for what the above poster said regarding everyone being "visual". I think it's not really a matter of ability, it's more about what methods people prefer and some people just don't prefer visualization. Funny side story: I think I can do the logical thing but it isn't my usual modus operandi, and I had to work on sharpening my "logical" side. I remember when I was in particle physics, and my office mate was so good at the algebra in QFT class and always very accurate. I on the other hand made frequently many little errors, but I'd always be able to "see the forest from the trees." I remember him once showing me the correct way to derive some transition amplitude that was in the homework, and just seeing it for the first time, I said "ah, that reduces to 1 + blah" because I could see that immediately; while he hadn't realized that even after working on it for a couple of hours. I think both types of people (left and right brain I guess) sort of complement each other in research, and we both have to approach math in our own ways.