Uncovering the Importance of Lemmas in Mathematics

[Char. Limit]

What is a lemma?

I hear people talking about "lemmas" all the time. A great example is the math joke that ends with the devil saying "But I found this really interesting lemma..." This joke would likely be much funnier to me if I knew what a lemma (or Riemann's hypothesis, but if you want to, I don't necessarily need to know that) is.

All help appreciated.

 

[Hurkyl]

A lemma is a statement you can prove so that you can prove something else. The only reason we don't call them theorems is that they are typically aren't interesting enough to "deserve" that title.

 

[HallsofIvy]

You might also want to note "corrollary". A corrollary is a statement that is not important enough be called a "theorem" in its own right but follows easily from a given theorem.

"Lemmas" are used to prove a theorem so are proved before the theorem. "Corrollaries" are proved from the theorem an so are proved after the theorem.

 

[Char. Limit]

Thanks for the help.

 

[arildno]

There are SOME lemmas, though, that have shown themselves to be far more useful than the theorem originally sought to be proven by the aid of that lemma..

Zorn's lemma, for example.