In the scientific Nachlass of Richard Dedekind a small note was found with the following remarks: "Of all the tools created up until now by the human spirit for making his life, that is, the labour of thinking, easier, none has been as full of consequences and inseparably connected with his innermost nature as the concept of number. Arithmetic, whose only subject this concept is, has already become a science of immense proportions, and there is no doubt that its further development will have no bounds; equally immense is the field of its application, because every thinking human being, even if he is not clearly aware of this, is a creature of numbers, an arithmetican."
Richard Dedekind is considered 'one of the very great in the history of mathematics', one of the greatest number theorists. With his main works he moulded algebraic number theory and deeply influenced its development. It is not possible here to introduce the reader to the wealth of the results of his work, but we will attempt to outline his problems, his methods, his consistent realization of methodological principles, and mostly his position in the history of mathematics, by using some samples of his work.
We emphasize three basic themes in the mathematics of Dedekind: his view of numbers and mathematical concepts as free creations of human thought, the formation of concepts as a central moment of mathematical research, and the formation of sets, 'system formation' in the words of Dedekind, as a method for forming new concepts.