Related papers: Arnold Scholz: Between Mathematics and Politics
A focused modernization of Sophus Lie's brilliant writings about the foundations of geometry that every contemporary geometer should have at least once a look at. Translated, updated, commented.
As David Berlinski writes (1997), the existence and nature of mathematics is a more compelling and far deeper problem than any of the problems raised by mathematics itself. Here we analyze the essence of mathematics making the main emphasis…
This is a short historical note concerning the evolution of Wetzel's problem and Erdos' solution.
This is a very basic introduction to some notions related to logic and complexity.
This paper has been withdrawn. With the advancement of statistical theory and computing power, data sets are providing a greater amount of insight into the problems of today. Statisticians have an ever increasing number of tools to attack…
The present article is devoted to the description of further investigations of the author of this article. These investigations (in terms of various representations of real numbers) include the generalized Salem functions and…
In the article we give an appreciation of Edward Nelson's multifaceted contribution to mathematics, and particularly to foundational theories of infinitesimals.
This is a introductory survey of some recent developments of "Galois ideas" in Arithmetic, Complex Analysis, Transcendental Number Theory and Quantum Field Theory, and of some of their interrelations.
This paper is devoted to Poincar\'e's work in probability. Though the subject does not represent a large part of the mathematician's achievements, it provides significant insight into the evolution of Poincar\'e's thought on several…
The nineteenth century Russian author Leo Tolstoy based his egalitarian views on sociology and history on mathematical and probabilistic views, and he also proposed a mathematical theory of waging war.
We review the work of Dominic Welsh (1938-2023), tracing his remarkable influence through his theorems, expository writing, students, and interactions. He was particularly adept at bringing different fields together and fostering the…
a 10-page biography of Raoul Bott followed by a 25-page discussion of his major papers
I am presenting a first-ever scientific collection of short sayings on probability and statistics expressed by most various men of science, many classics included, from antiquity to Kepler to our time. Quite understandably, the reader will…
In this short note we present some remarks and conjectures on two of Erd\"os's open problems in number theory.
In this essay, I attempt to provide supporting evidence as well as some balance for the thesis on `Transforming socio-economics with a new epistemology' presented by Hollingworth and Mueller (2008). First, I review a personal highlight of…
This is an updated version of the lectures notes for a course on condensed mathematics taught in the summer term 2019 at the University of Bonn. The material presented is joint work with Dustin Clausen. This is intended as a stable citable…
In this article, we are interested in the life and scientific work of the Belgian mathematician Paul Mansion. The year 2019 marks the centenary of his passing. We bring some new insights into Paul Mansion's work thanks to his scientific…
This article recounts the interaction of topology and singularity theory (mainly singularities of complex algebraic varieties) which started in the early part of this century and bloomed in the 1960's with the work of Hirzebruch, Brieskorn,…
In this article, we use the 75th anniversary of the publication of \emph{Introducci\'on al An\'alisis Matem\'atico} by Mario O. Gonz\'alez to study its importance. Besides, we give new biographical data from his author in the previous years…
Jonathan M. Borwein (1951-2016) was a prolific mathematician whose career spanned several countries (UK, Canada, USA, Australia) and whose many interests included analysis, optimisation, number theory, special functions, experimental…