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What are general guidelines for checking your proofs? I believe this is important for graduate students like me. I already know what we need to do to prove something, but you always have to check everything before you send it out. Even to your own advisor.

I've developed myself some strategies by trial and error, and got a lot of advice from my advisor. But this is always a very tedious work. Normally, when you finish with something, you just want to go on to the next problem, but you still have to stick to the current problem until everything is perfect. Here I present an example of my own list of tricks:

Fill in the details. A lot of mistakes are in places were you write "it is clear that...", "without loss of generality...", etc. Try some numbers. Try extreme cases, like "what happens when I set $n=1$ or $n=1000$". Keep a clean notebook. Write every day on it, and compare it with your rough notes. I try to write also in latex, I've found many mistakes this way.

What are the general strategies that you apply for checking your proofs?

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