The rare first English translation of the final major publication by the Russian-born German mathematician Georg Cantor (1845-1918), the culmination of his foundational work on transfinite set theory.
Cantor ‘is one of the most imaginative and controversial figures in the history of mathematics. Toward the end of the nineteenth century his study of continuity and the infinite eventually forced him to depart radically from standard interpretations and use of infinity in mathematics’ (Dauben, p. 1).
Originally published in German as a two-part paper titled Beitrage zur Begrundung der transfiniten Mengenlehre (1895-1897) in the journal Mathematische Annalen, the work stands as Cantor’s ‘last great summation of his set theory’. ‘In its abstractness, in its independence from point sets and physical examples, the Beitrage represented Cantor’s last effort to present mathematicians with the basic elements of his transfinite set theory. … Following publication of the Beitrage and its translation almost immediately into Italian and French, Cantor’s ideas became widely known and circulated among mathematicians the world over. What is more important, the value of his transfinite set theory was quickly recognized, and soon Cantor’s ideas were stimulating heated polemics between widely divided camps of mathematical opinion. Though Cantor never seemed able to avoid controversy and division over the nature of his work, he was, after 1895, increasingly defended by younger and more energetic mathematicians. No longer was he left to face the opposition alone. … For him, the crusade was nearly over, and though the theoretical difficulties were by no means satisfactorily resolved, recognition that Cantor had contributed something of lasting significance to the world of mathematics had been achieved’ (Dauben, p. 158, 218).
The earliest of any of Cantor’s works to appear in English, the present translation was undertaken by the British logician Philip Jourdain (1879-1919), who also provided a substantial introduction to the text. A transatlantic publishing endeavour, the sheets of the first edition were printed in Great Britain, with the American issue bound in blue cloth lettered in gilt and the present UK issue bound in green cloth lettered in black.
See: Joseph Warren Dauben, Georg Cantor: His Mathematics and Philosophy of the Infinite.
