"A formula is worth a thousand pictures." [1]

Also, draw a picture of the monster group (http://en.wikipedia.org/wiki/Monster_group), 11 dimensions of space time (http://en.wikipedia.org/wiki/M-theory), or explain how a picture of seven infinitely long cylinders can illustrate that each pair of those cylinders touches each other.

So, I disagree that "everyone ends up reasoning with drawings".

[1] https://www.utexas.edu/faculty/council/2002-2003/memorials/D...