This book offers an excursion through the developmental area of research mathematics. The scenic route passes through some 40 papers, published between the 1870s to the 1970s, on proofs of the Cantor-Bernstein theorem and the related Bernstein division theorem. While the emphasis is placed on providing accurate proofs, similar to the originals, the discussion is broadened to include aspects that pertain to the methodology of the development of mathematics and to the philosophy of mathematics. Works of prominent mathematicians and logicians are reviewed, including Cantor, Dedekind, Schroder, Bernstein, Borel, Zermelo, Poincare, Russell, Pea, the Konigs, Hausdorff, Sierpinski, Tarski, Banach, Brouwer and several others mainly of the Polish or the Dutch schools. In its attempt to present a diachronic narrative of one mathematical topic, the book resembles the celebrated book of Lakatos Proofs and Refutations . Indeed, some of the observations made by Lakatos are corroborated herein. The analogy between the two books is clearly t superficial because the present book also offers new theoretical ideas regarding the methodology of the development of mathematics (proof-processing), with implications on the historiography of mathematics.
Date of Publication
English & Hebrew
Science Networks. Historical Studies
Series Part/Volume Number
Country of Publication
26 black & white illustrations, 3 colour illustrations, biography