Why it's important to check your work
Posted by Mike McClenathan
An anecdote: yesterday morning, I did a bunch of work typing up an explanation for the Q&A page, but then accidentally closed my browser and lost all my work before posting it. I was late for a train, so I didn't have time to retype it all. I figured that once I got to campus—school has started again for me, too—I'd have a chance to retype it. And I did.
For the first time that I'm aware of, I posted an incorrect answer on my Q&A. And it's not that I didn't know how to do the question. I did all the "hard" math correctly. But when it came time to add 1 + 5 + 10 + 10 + 5 + 1, I got 22 instead of 32. And I posted that. It was up for about 18 hours before I woke up today, half-dazed, and muttered wait...22 isn't a power of 2! (The super-fast solution I hinted at in that post is that the number of subsets of a set with n elements is 2n.) I got out of bed, changed one digit in a post, and went back to bed.
So what's the point? I'm good at math. I'm sure-footed, especially when it comes to SAT-style problems. I don't second guess myself. The fact that you're reading this means that I have a reputation for being an authority on the topic. And still, I managed to make a very silly mental math error, the kind that costs people dearly on tests. And I posted it without checking my work. It was the first time in nearly a year of running the Q&A, so it doesn't happen often, but I made a silly mistake and didn't catch it. Sometimes, everyone makes mistakes.
Maybe some readers saw that I did all the work right, and just assumed it was a typo. That's generous, and I thank them. But you know who won't be as generous? You know who doesn't care whether you did all the work right? You guessed it: the SAT. So do as I say, not as I failed to do yesterday.
Check your work if you have time.