§ 3. Ahnlichkeit einer Abbildung. Ahnliche Systeme § 4. Abbildung eines Systems in sich
selbst § 5. Das Endliche und Unendliche § 6. Einfach unendliche Systeme. Reihe der …

After an introductory section, this article will focus on four questions: How should the Kyoto
School be defined? What is meant by its central philosophical concept of “absolute …

The concept of infinity has a long and troubled history. Thus it is a promising concept with
which to explore rejection, disagreement, controversy and acceptance in mathematical …

The chief purpose of this book is to present, in detail, a compilation of proofs of the Cantor-
Bernstein Theorem (CBT) published through the years since the 1870s. Over 30 such proofs …

A long-standing tradition considers GEORG CANTOR (1845--1918) as the'creator'or founder
of set theory.~ This view, correct when restricted to transfinite set theory, stands in need of …

The celebrated “creation” of transfinite set theory by Georg Cantor has been studied in detail
by historians of mathematics. However, it has generally been overlooked that his research …

The first two of the twenty-three unsolved problems that David Hilbert famously proposed at
the 1900 International Congress of Mathematicians (ICM) in 1900 dealt with issues …

“No one shall expel us from the paradise which Cantor has created for us.” In this famous
sentence of 1926, Hilbert echoes (and negates) the expulsion of Adam from the Garden of …

This article looks at recent work in cognitive science on mathematical cognition from the
perspective of history and philosophy of mathematical practice. The discussion is focused on …

Natural Formalization proposes a concrete way of expanding proof theory from the meta-
mathematical investigation of formal theories to an examination of “the concept of the …