
> 
> The Sylvester-Gallai theorem states that it is not possible to arrange a finite number
>  of points so that a line through every two of them passes through a
>  third unless they are all on a single line.
> 
> 
> 


Is there any modern research that generalizes this theorem or finds some unexpected relations between this theorem and other parts of mathematics? Could you point out some references (preferably survey papers)?



Generalization of Sylvester-Gallai theorem
Yes! See the beautiful recent [paper](http://arxiv.org/pdf/1208.4714v3.pdf) of Ben Green and Terry Tao, which shows that for large $n$, any collection of $n$ points not all collinear will have at least $n/2$ ordinary lines.


