Austrian-Hungarian contributions in the quest of defining the mathematical term ``dimension'' from the 1850's to the 1920's (Q2912564)

The article at hand wishes to present the mathematicians' attitude towards the concept of `dimension'. The idea that the author underlines is that the mathematician Bernhard Bolzano, in the first half of the nineteenth century, treated this notion in the best way possible at that time. The author also provides a brief overview of the evolution of the notion of `dimension' in terms of thoughts coming from the Austro-Hungarian mathematicians, starting with Bolzano, who looked for a philosophical point of view of this concept. He developed a profound thinking on the topic, which dealt with the use of `neighbourhood' of points and their `boundaries'. With the rise of topology, mathematicians tried to treat the problem with topological methods. Therefore, the Menger-Urysohn definition combines philosophical ideas with topological terms. An important progress came from Cantor's studies on cardinality. With the works of Cantor, Peano and Hilbert the `crisis of intuition' and the quest of defining the mathematical term `dimension' had begun. There have been several other attempts at rethinking the concept of dimension.NEWLINENEWLINEFor the entire collection see [Zbl 1245.01007].