This paper investigates the discovery of the truth-undefinability theorem. Although it is commonly attributed to Tarski, some historical data suggest that it was earlier discovered by Gödel. The author collects and comments several sources. It is argued that the historical issue requires taking into account various aspects, also including the philosophical background of Gödel and Tarski. The main thesis of the present paper is that the discussed theorem was explicitly formulated by Tarski.