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What essentially is the difference between a lemma and a theorem in mathematics? More specifically, suppose you come across a general result while solving a mathematical problem, what are the characteristics you would look for before categorizing it as a theorem or lemma?

EDIT: Does a difference of personal perspective count? Does the effort which goes into deriving a result also determine this distinction? I mean if the result is obtained by one person by a simple algebraic manipulation or trivial reasoning and by a complex derivation by another(let's suppose that this second person stumbles across this result while attacking a totally different problem from the first person), then I suppose the first person would call it a lemma and the second person a theorem? (Assuming that the result has great applications.)

PS: This question is the duplicate of another question (by Tamaroff) which is more comprehensive and has excellent answers. But as a result of Jim's last comment below, I have an important doubt, which I think needs to be cleared. This doubt has not come up in the question (by Tamaroff). So I think this post should not yet be closed. I have edited my question to include the doubt, which I raised in my comment below, in the question.

Nikhil Panikkar
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There is no functional difference. The difference is only in how you measure it's importance in context. If it's where you want to go it's a theorem, if it just helps you get there its a lemma.

And of course for everything that I or anyone else could say there is a counterexample. There really isn't a functional difference.

Jim
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  • Ok, so if you are say, solving problem A and in the process, if you get an intermediate result say B (which in addition is a minor result, you would categorize it as a lemma. – Nikhil Panikkar Feb 21 '13 at 07:11
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    If it is only of importance so far as solving the current problem I would call it a lemma. If it's important enough that you want anyone who's skimming your paper to stop and pay attention to it then it's a theorem. And if it's somewhere inbetween those two you could also call it a proposition :) – Jim Feb 21 '13 at 07:13
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    One mans lemma is anothers dissertation... – Jim Feb 21 '13 at 07:21
  • Ok, so there's a difference of personal perspective too. Does the effort which goes into deriving a result also determine this distinction? I mean if the result is obtained by one person by a simple algebraic manipulation or trivial reasoning and by a complex derivation by another(let's suppose that he stumbles across this result while attacking a totally different problem from the first person), then I suppose the first person would call it a lemma and the second person a theorem? – Nikhil Panikkar Feb 21 '13 at 11:21
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    The Lemma vs. Theorem thing often doesn't have anything to do with difficulty. There are plenty of examples of impressive theorems whose proof is very short and easy because most of the difficult work takes place in an earlier Lemma. – Jim Feb 21 '13 at 16:36