After the discovery in the early 60s of a proof for the Poincaré conjecture and other properties of simply connected manifolds of dimension greater than four, one of the biggest open problems, besides the three dimensional Poincaré conjecture, was the classification of closed simply connected four manifolds.
Matapos ang pagkatuklas sa maagang bahagi ng 60 s ng isang patunay para sa Poincaré haka-haka at iba pang pag-aari ng simpleng connected manifolds ng laki na mas malaki kaysa sa apat na, isa ng ang biggest buksan ang mga problema, maliban sa tatlong kalawakan Poincaré haka-haka, ay ang pag-uuri ng sarado lamang connected apat na manifolds.