Friedrich Mohs, 1812: a mineral of higher number scratches one of lower number. The steps are not equal — corundum to diamond is a canyon. Pick two specimens (or a thumbnail and a steel file) and the plaque says who yields.
Reference set follows the classic Mohs scale (talc–diamond). Household proxies are field-kit approximations used in teaching collections, not laboratory Vickers numbers. Absolute hardness (sclerometer) rises roughly exponentially — diamond is ~4× corundum, not “one more”.