Etydhv

I am writing a paper for a class that has to include a proof. I have started out by listing what I want to prove as a theorem and then I'll go through the process of proving it. However, the code I am using below puts everything on one line and the text portion of the theorem ends up running off the page. I tried putting in "" after the equation to put the text onto the line below it but that doesn't seem to work. Any ideas as to how I can fix this issue?

begintheorem 
[ 
G(x)=sum_kgeq0C_kx^k=frac1-sqrt1-4x2x,\ 
where G(x) is the generating function for the catalan number sequence. 
] 
endtheorem

First off, I wouldn't place the string where G(x) is the generating function for the catalan number sequence. inside a displayed equation. Second, one cannot have line breaks inside [ ... ]. If you need to create a multi-line displayed equation, use a suitable environment provided by the amsmath package, such as align, gather, and multline.

documentclassarticle
usepackageamsthm
newtheoremtheoremTheorem
begindocument

begintheorem 
Bla bla bla dots
[ 
G(x)=sum_kgeq0C_kx^k=frac1-sqrt1-4x2x,,
] 
where $G(x)$ is the generating function for the catalan number sequence. 
endtheorem
enddocument

If you really wish the "where G(x) is the generating function for the catalan number sequence"-phrase to belong to the equation, which would affect the size of vertical gap/the vertical spacing between the equation and that phrase, you can, e.g., use a gather- or a split-environment:

documentclassarticle
usepackageamsmath
newtheoremtheoremTheorem
begindocument
begintheorem
This is a theorem. This is a theorem. This is a theorem. This is a theorem. This is a theorem.
This is a theorem. This is a theorem. This is a theorem. This is a theorem. This is a theorem.
begingather*
G(x)=sum_kgeq0C_kx^k=frac1-sqrt1-4x2x,\
textwhere (G(x)) is the generating function for the catalan number sequence.%
endgather*
This is a theorem. This is a theorem. This is a theorem. This is a theorem. This is a theorem.
This is a theorem. This is a theorem. This is a theorem. This is a theorem. This is a theorem.
beginequation*beginsplit
&G(x)=sum_kgeq0C_kx^k=frac1-sqrt1-4x2x,\
&textwhere (G(x)) is the generating function for the catalan number sequence.%
endsplitendequation*
This is a theorem. This is a theorem. This is a theorem. This is a theorem. This is a theorem.
This is a theorem. This is a theorem. This is a theorem. This is a theorem. This is a theorem.
endtheorem
enddocument

And in some situations a simple minipage-environment might be your friend:

documentclassarticle
usepackageamsmath
newtheoremtheoremTheorem
begindocument
begintheorem
This is a theorem. This is a theorem. This is a theorem. This is a theorem. This is a theorem.
This is a theorem. This is a theorem. This is a theorem. This is a theorem. This is a theorem.
[%
G(x)=sum_kgeq0C_kx^k=frac1-sqrt1-4x2x,
text%
 beginminipage[t]4cm%
 where (G(x)) is the generating function for the catalan number sequence.%
 endminipage%
%
]
This is a theorem. This is a theorem. This is a theorem. This is a theorem. This is a theorem.
This is a theorem. This is a theorem. This is a theorem. This is a theorem. This is a theorem.
endtheorem
enddocument