Neatness and accuracy II

When I was at College, there was an American electrical engineering student with whom I was acquainted. She had spacial alignment problems. Whenever she wrote anything she wrote along an arc. She could write along a line for about the first half of the page, but then the text curved and ended up running parallel to the side of the page by the time she got to that side of the page.
Whereas it was possible to read what she'd written, and wasn't difficult to understand if it contained English words, when she wrote maths it was a nightmare to decipher. This is because, in Maths, the position of symbols is important. When adding, subtracting and multiplication, all the units are in the units column, all the tens are in the tens column and so on, in fractions some numbers are at the top and others are at the bottom.
Neatness is important in Maths to the extent that it is possible to know what column the digit is in and where it is located above or below other numbers, and of course to the extent that the numbers are legible. However, beyond that neatness is not a prime consideration.
Think of any film in which a "professor" is depicted. On the blackboard behind them there is almost always some calculation or other, complete with arrows linking one idea to another, and numbers highlighted by cirles. But nevertheless, the numbers are legible and in a clear relationship one to the other. It is a mix of neatness and exuberance, this is what mathematics is all about, a mixture of discipline and immagination.