Same for maps or navigating in cities and such. I can see the map overlay of the area as I travel down streets in my head even if I've never looked at an actual physical map of the area.
But algebra is still a mystery to me and I've tried several times over the years with computer programs and tutors. Apparently its just not something I am going to get.
I wish I could tell you what I saw and why it came to me. Brains are amazing and varied things. Some scary-smart people claim they see colors in numbers and that that simplifies existence. People are both funny and entertaining...and then we die.
Well, have you tried Book II of Euclid's Elements? This is nothing but familiar introductory algebra, but expressed in geometric form. Of course to Euclid, there was no other way.
If a straight line be bisected and a straight line be added to it in a straight line, the rectangle contained by the whole with the added straight line and the added straight line together with the square on the half is equal to the square on the straight line made up of the half and the added straight line.