The main challenge here lies in devising a mathematically acceptable proof of this impossibility, which is where the foundations for what we today know as graph theory.

Amir Dembo, Andrea Montanari, ISING MODELS ON LOCALLY TREE-LIKE GRAPHS, The Annals of Applied Probability, Vol. 20, No. 2 (April 2010), pp. 565-592 ...

Mathematicians have proved that copies of smaller graphs can always be used to perfectly cover larger ones. On January 8, three mathematicians posted a proof of a nearly 60-year-old problem in ...