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Weather forecasting. --- Artillery. --- Forcing (Model theory)

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This book offers an excursion through the developmental area of research mathematics. It presents some 40 papers, published between the 1870s and 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, Schröder, Bernstein, Borel, Zermelo, Poincaré, Russell, Peano, the Königs, Hausdorff, Sierpinski, Tarski, Banach, Brouwer and several others mainly of the Polish and the Dutch schools. In its attempt to present a diachronic narrative of one mathematical topic, the book resembles Lakatos’ celebrated book Proofs and Refutations. Indeed, some of the observations made by Lakatos are corroborated herein. The analogy between the two books is clearly anything but superficial, as the present book also offers new theoretical insights into the methodology of the development of mathematics (proof-processing), with implications for the historiography of mathematics.

Mathematics. --- Model theory. --- Set theory. --- Set theory --- Differential equations --- Logic, Symbolic and mathematical --- Differential equations. --- 517.91 Differential equations --- Category theory (Mathematics). --- Homological algebra. --- History. --- Mathematical logic. --- History of Mathematical Sciences. --- Mathematical Logic and Foundations. --- Category Theory, Homological Algebra. --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Syllogism --- Annals --- Auxiliary sciences of history --- Homological algebra --- Homology theory --- Category theory (Mathematics) --- Algebra, Homological --- Algebra, Universal --- Group theory --- Topology --- Functor theory --- Math --- Science --- Logic, Symbolic and mathematical. --- Algebra. --- Mathematical analysis