The concept of the indifference curve was the touchstone of the escape from cardinalism and the psychological foundations of demand and choice. Yet, once Hendrik S. Houthakker (1950) and Paul Samuelson (1950) recognized that the whole theory of the consumer could be derived from the strong axiom of revealed preferences (without supposing the existence of indifference curves from the outset), indifference curves survived mainly, if not exclusively, because they made it easy to teach and learn certain ideas and principles involving choices between certain prospects (intertemporal choice, the leisure-consumption trade-off). For such a role it is endowed with convenient mathematical properties allowing for the use of duality theorems.