Julius Petersen, Karl Weierstrass, Hermann Amandus Schwarz and Richard Dedekind on hypercomplex numbers (Q2762234)

The author gives a thorough analysis of Petersen's papers on hypercomplex numbers in the context of the relevant work of his contemporaries Weierstrass and Dedekind. After a short characterization of Danish mathematics at the end of the 19th century the author discusses Petersen's view on the foundation of mathematics, especially the nature of mathematical axioms, published in 1883 and Petersen's paper on the basic concepts of algebra from 1885. In the latter paper Petersen introduced ordinary complex numbers in an orthodox projective way as well as so-called ternions which are three-dimensional hypercomplex numbers. Since he gave no references it is an open question if Petersen knew of Weierstrass' paper of 1884. The background and the contents of this article which originated from a correspondence between H. A. Schwarz and K. Weierstrass in 1883 is also described in detail by the author. Then he considers Petersen's 1887 paper, tells the story of its publication in the ``Göttinger Nachrichten'' and brings out the central role played by the editor of this journal, H. A. Schwarz. Finally, the author has a look at Dedekind's papers of 1885 and 1887 treating the same topic and the different interpretation of a quote of Gauß by Dedekind and Weierstrass.NEWLINENEWLINEFor the entire collection see [Zbl 0970.00008].