The mathematician Heinrich Tietze 1880--1964. (Q2890550)

This is a biography of the Austrian-German topologist Heinrich Tietze (1880-1964), which is based on the author's PhD of 2010. Tietze spent most of his career in Munich and was a leading figure in the first years of modern topology both in its algebraic and set theoretic aspects. He was proud of his article on the various branches of topology which he had published in 1930, together with Leopold Vietoris, in the German Encyclopedia of mathematics and its applications. Tietze's ``Famous Problems of Mathematics'', based on popular lectures and published first in German in 1949 was very successful in broader circles and became known through an English translation (1959) also abroad.NEWLINENEWLINEThe biography comes in three parts of about equal length, reserving the first 100 pages to biographical information while using the second part to commentary, sometimes more briefly reporting than analyzing, on Tietze's mathematical work. Among other things Tietze\('\)s introduction in 1908 of the three-dimensional lens space is discussed and related to work by W. Wirtinger. The book is concluded with about 100 pages documents, including vitas, poems by Tietze, lists of his lectures and publications.NEWLINENEWLINETietze was -- together with his colleagues in Munich Oskar Perron and Constantin Carathéodory -- clearly no active supporter of the Nazi regime. More investigation of his role in this respect than provided in this book is desirable, although the latter is a valuable contribution to the biography of Tietze and to the early history of topology.