The ordered field R of real numbers can be constructed directly from the ring Z of integers without first manufacturing the field Q of rationals and without (explicitly) using Cauchy sequences or Dedekind cuts. This idea has avoided the wide publicity it deserves. I believed the original discoverer to be Steve Schanuel (SUNY, Buffalo, New York) who explained it to me while he was visiting Macquarie University last year. Peter Johnstone has recently told me that the construction was also proposed by Richard Lewis (Sussex, England). Does anyone know of any other independent discoverers?
