I find the question http://mathoverflow.net/questions/98205/how-do-you-understand-algebra-if-you-are-very-much-of-an-analyst rather annoying, both in tone and in content. My first instinct was to vote to close it, with a snide remark. But of course snide remarks are never a good idea (even if sometimes I am unable to resist), and I just wanted to check whether there is some consensus that this question should be closed.

The line

I cannot even carry out simple algebraic computations(moving terms across, integration by parts) that come almost everyday in my work because a priori I don't see why I need such manipulations

suggests to me that the OP's problems lie less with a conceptual grasp of algebra, and more with some pretty basic deficiencies. Perhaps he is overstating things here, but still ...

It is actually a reasonable question if you understand what is asked (which is a non-trivial task given the way it is written). As a matter of fact, I often wondered pretty much the same thing though I wouldn't even try to formulate the underlying question exactly, much less to discuss it here. Anyway, it is closed by now, so the only point I want to make is that certain things are damn hard to express in words, so a ridiculous writeup doesn't necessarily mean a ridiculous chain of thought.