In 1611, Kepler proposed that the closest sphere packing has a maximum density of pi/(3sqrt(2)) approx 74%). This assertion is known as the Kepler conjecture Listen to Simon Singh describe it in this BBC Radio 4 program.

Buckminster Fuller (1975) claimed to have a proof, but it was really a description of face-centered cubic packing, not a proof of its optimality (Sloane 1998). A second putative proof of the Kepler conjecture was put forward by W.-Y. Hsiang (Cipra 1991, Hsiang 1992, 1993, Cipra 1993), but was subsequently determined to be flawed (Conway et al. 1994, Hales 1994, Sloane 1998). According to J. H. Conway, nobody who has read Hsiang’s proof has any doubts about its validity: it is nonsense….

Download the ram file of the Radio Program at…
BBC Radio 4 – Kepler Conjecture