The de Bruijn-Erdös-Hanani theorem

Abstract: The paper is devoted to a somewhat idiosyncratic account of the theorem of de Bruijn-Erd\"{o}s and Hanani from the combinatorics of finite geometries and its various proofs. Among the proofs discussed are the original proofs by de Bruijn--Erd\"{o}s and Hanani and few others. It is explained how one of the proofs was discovered, and how another one could have been discovered.