[ky3]

mathematical proofs are difficult enough to follow without having to guess the action of the operators involved.

What Heaviside did was the sort of fast-and-loose syntactic manipulation that makes mathematicians queasy and/or indignant [1]. He treats the derivative operator just like it were an ordinary number X. And then he infers that 1/X must mean integration.

Compare to the naive argument for the positive integers 1+2+3+... summing to -1/12 that gets mathbabe's panties in a twist [2].

More details in Ch. 10 of Nahin's book.

[1] http://myreckonings.com/wordpress/2007/12/07/heavisides-oper...

[2] http://mathbabe.org/2014/01/21/if-its-hocus-pocus-then-its-n...