Related papers: Arnold Scholz: Between Mathematics and Politics
We review the possibilities and difficulties for statistical physicists if they apply their methods to biology, economics, or sociology.
This book covers the history of probability up to Kolmogorov with essential additional coverage of statistics up to Fisher. Based on my work of ca. 50 years, it is the only suchlike book. Gorrochurn (2016) is similar but his study of events…
This is a textbook about elementary number theory, with emphasis on classical topics around the Euklidean Algorithm.
What is the largest number accessible to the human imagination? The question is neither entirely mathematical nor entirely philosophical. Mathematical formulations of the problem fall into two classes: those that fail to fully capture the…
The language of operator algebras is of great help for the formulation of questions and answers in quantum statistical mechanics. In Chapter 1 we present a minimal mathematical introduction to operator algebras, with physical applications…
We are interested here in the program of reconstruction of quantum mechanics of the German physicist and philosopher Carl Friedrich von Weizs\"{a}cker, which still has some supporters today. In the major part of this article, we limit…
A sketch of some of the fundamental notions related to the nature of knowledge is offered, with special focus on the role of mathematics and my own opinions. No single idea exposed here is entirely original; indeed, this topic has been…
Some general considerations on the notion of entropy in physics are presented. An attempt is made to clarify the question of the differentiation between physical entropy (the Clausius-Boltzmann one) and quantities called entropies…
This tutorial paper presents a survey of results, both classical and new, linking inner functions and operator theory. Topics discussed include invariant subspaces, universal operators, Hankel and Toeplitz operators, model spaces, truncated…
Karl Stein was one of the pillars of the German school of several complex variables. In this article his scientific contributions are outlined in historical perspective.
The current work revisits the results of L.F. Meyers and R. See in [3], and presents the census-taker problem as a motivation to introduce the beautiful theory of numbers.
The history of computability theory and and the history of analysis are surprisingly intertwined since the beginning of the twentieth century. For one, \'Emil Borel discussed his ideas on computable real number functions in his introduction…
We present a new rigorous approach based on Orlicz spaces for the description of the statistics of large regular statistical systems, both classical and quantum. This approach has the advantage that statistical mechanics is much better…
We throw a brief glance at Galois' life, on the occasion of his 200th anniversary (written in German).
We revisit and further explore the celebrated Combinatorial Nullstellens\"atze of N. Alon in several different directions.
This is a free summary of a much longer article published in german in "Forschung Frankfurt". This article presents facts concerning the works of Max Dehn and the history of Frankfurt University. E. Hellinger, R. Moufang, C. L. Siegel, A.…
The traditional theoretical statistics course which develops the theoretical underpinnings of the discipline (usually following a probability course) is undergoing near-continuous revision in the statistics community. In particular, recent…
This is a translation of Heinz Bachmann's influential paper, wherein the Bachmann-Howard ordinal is defined, and some general considerations given on systems of ordinal functions. Permission to post has been granted by the editors of…
Some basic sociophysical notions are described by a physicist, tentatively for a sociologically-oriented reader.
In this paper we analyze both the scientific activities of Cahit Arf, a Turkish mathematician, and the social context in which he worked. We also discuss his work and social environment leading to the discovery of Arf invariant, Arf rings,…