Two main claims are associated with the Efficient Market Hypothesis (EMH). First of all, the price changes are nearly random in the financial markets. Secondly, the prices reflect the economic fundamentals. The relation between these two claims remains unclear in the actual literature. The purpose of this article is to show that this confusion is not new but began during the theoretical construction of EMH in the 1960s. The analysis is based on the reading of their 1965 papers and on the archives of Paul Samuelson from the Paul A. Samuelson Papers, David M. Rubenstein Rare Book Manuscript Library at Duke University.