The mole and Avogadro's number are two important concepts of science that provide a link between the properties of individual atoms or molecules and the properties of bulk matter. It is clear that an early theorist of the idea of these two concepts was Avogadro. However, the research literature shows that there is a controversy about the subjects of when and by whom the mole concept was first introduced into science and when and by whom Avogadro's number was first calculated. Based on this point, the following five matters are taken into consideration in this paper. First, in order to base the subject matter on a strong ground, the historical development of understanding the particulate nature of matter is presented. Second, in 1811, Amedeo Avogadro built the theoretical foundations of the mole concept and the number 6.022 X 10(23) mol(-1). Third, in 1865, Johann Josef Loschmidt first estimated the number of molecules in a cubic centimetre of a gas under normal conditions as 1.83X10(18). Fourth, in 1881, August Horstmann first introduced the concept of gram-molecular weight in the sense of today's mole concept into chemistry and, in 1900, Wilhelm Ostwald first used the term mole instead of the term `gram- molecular weight'. Lastly, in 1889, Karoly Than first determined the gram-molecular volume of gases under normal conditions as 22,330 cm(3). Accordingly, the first value for Avogadro's number in science history should be 4.09 X 10(22) molecules/grammolecular weight, which is calculated by multiplying Loschmidt's 1.83 X10(18) molecules/ cm(3) by Than's 22,330 cm(3) / gram-molecular weight. Hence, Avogadro is the originator of the ideas of the mole and the number 6.022 9 10 23 mol(-1), Horstmann first introduced the mole concept into science/ chemistry, and Loschmidt and Than are the scientists who first calculated Avogadro's number. However, in the science research literature, it is widely expressed that the mole concept was first introduced into chemistry by Ostwald in 1900 and that Avogadro's number was first calculated by Jean Baptiste Perrin in 1908. As a result, in this study, it is particularly emphasised that Horstmann first introduced the mole concept into science/ chemistry and the first value of Avogadro's number in the history of science was 4.09 9 10 22 molecules/ gram-molecular weight and Loschmidt and Than together first calculated this number.