John Conway and Neil Sloane collaborated often (at least 55 times by mathscinet's count). One observation they made together answered a previously unanswered question in lattice theory, namely whether there are lattices which are generated by their minimal vectors which have the additional property that the minimal vectors do not contain a basis for the lattice.

They showed that such lattices appear in dimensions as small as $d=11$ by an explicit construction. Later Jacques Martinet and Achill Schürmann discovered a new example in dimension $d=10$ and proved that phenomenon cannot happen for $d\leq 9$ settling the question of for which dimensions lattices of the above type may exist.

John Conway and Neil Sloane collaborated often (at least 55 times by MathSciNet's count). One observation they made together answered a previously unanswered question in lattice theory, namely whether there are lattices which are generated by their minimal vectors which have the additional property that the minimal vectors do not contain a basis for the lattice.

They showed that such lattices appear in dimensions as small as $d=11$ by an explicit construction. Later Jacques Martinet and Achill Schürmann discovered a new example in dimension $d=10$ and proved that phenomenon cannot happen for $d\leq 9$ settling the question of for which dimensions lattices of the above type may exist.