Frankl's union-closed conjecture

Polymath11 -- Frankl's union-closed conjecture

A family [math]\displaystyle{ \mathcal{A} }[/math] of sets is called union closed if [math]\displaystyle{ A\cup B\in\mathcal{A} }[/math] whenever [math]\displaystyle{ A\in\mathcal{A} }[/math] and [math]\displaystyle{ B\in\mathcal{A} }[/math]. Frankl's conjecture is a disarmingly simple one: if [math]\displaystyle{ \mathcal{A} }[/math] is a union-closed family of n sets, then must there be an element that belongs to at least n/2 of the sets? The problem has been open for decades, despite the attention of several people.