The forefront of monetary economics focuses on whether the currency should have material properties. The starting point of commodity currency theory is static exchange, the starting point of credit currency theory is the non-immediacy of exchange. Samuelson's "Intergenerational Exchange Puzzle" analyzes the properties and functions of money from the perspective of "intertemporal exchange" and rejects the currency from the "non-double coincidence of demand". Samuelson's "intergenerational exchange problem" is the key to unraveling the mystery of money.