Sign errors, and other tiny errors that are very easy to make, can totally mess up calculations and derivations. There are so many opportunities to make these sorts of mistakes that in even a moderately simple derivation there's a significant possibility of making at least one such mistake. This is why checking your results is so important. For example, after figuring out the roots of a quadratic, try putting them in and making sure that $y$ actually does $=0$! Now, most people hate sign errors, and this makes sense: It wastes time and reminds you that no matter how hard you try, Wolfram Alpha will always be better at math that you are, and you'll wonder why you're being put through this pain when you could just let a computer that doesn't make simple errors do the work for you!? (Answer: If you actually want to understand math, which is more and more important as you get into the advanced math used in science and engineering, you need to know what's going on under the hood, even if you can't do it as well as the computer can.)

But,strange as it may sound, I actually *love* these little
errors -- in moderation anyhow. I too can become frustrated if I'm
trying to a bunch of results and I am tired and so keep making
mistakes. But if I'm just doing math for fun, which I often do, I find
getting the wrong answer to actually be both fun and educational.

One reason that I like making mistakes is that I don't feel like checking my results was wasted effort. But the main reason I like making mistakes is that I like the detective work of figuring out what went wrong.

Math has many different kinds of pleasures. There is
the *"Tada!"* pleasure of figuring out a new technique and
seeing it work. Then there is the *"Cool!"* pleasure of
understanding how a new proof works, and the very
rarified *"Bam!"* pleasure of discovering a proof or derivation
for yourself that you've worked really hard on. (This can be so even
if the proof you've discovered is not a new one to the whole world;
rarely do you get to prove something that hasn't been proved before,
but it's still very satisfying to discover a proof that's new
to *you* even if it's not new to the world.)

Finding and fixing tiny errors, such as sign errors that led you down
the garden path to an incorrect result is a different kind of pleasure
-- something like *Aha!*, and then you get the *"Bam!"*
when the derivation concludes correctly. Another kind of pleasure that
error correction provides is the pleasure of telling
self-deprecating *"I was such an idiot!"* war stories, which
are good in classrooms to show your students that you're human too,
and that their mistakes aren't to be taken as a demonstration of their
failure, but rather as a demonstration of the success of checking
their results, and of their prowess as a mathematical detective.

As they say: *To Err is Human*. To able to fix your errs is one
of those small satisfactions that comes with being human.