young tableaux, beloved of combinatorialists, tolerated by representation theorists and geometers, seem at first glance to be an unruly combinatorial set. i'll define a simplicial complex in which they index the facets, and slightly more general objects (buch's ``set-valued tableaux'') label the other interior faces. the theorem that says we're on a right track: this simplicial complex is homeomorphic to a ball. i'll explain why this is surprising, useful, and shows why buch didn't discover the exterior faces too. finally, i'll explain how algebraic geometry forced these definitions on us (or, ``how i made my peace with young tableaux''). this work is joint with ezra miller and alex yong.