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Free translation of the original abstract in Spanish: Some of the most relevant milestones due to, or instigated by, mathematicians concerning the creation, development and advances of Cosmology as a scientific discipline are presented and…
The multi-layered nature of societal developments poses a challenge in the teaching and learning of history of mathematics. As an attempt to tackle this challenge we experimented with the use of Knowledge-Maps. The focus of our interest…
Scientometrics is the study of the quantitative aspects of the process of science as a communication system. It is centrally, but not only, concerned with the analysis of citations in the academic literature. In recent years it has come to…
I discuss some general aspects of the creation, interpretation, and reception of mathematics as a part of civilization and culture.
Science, being a social enterprise, is subject to fragmentation into groups that focus on specialized areas or topics. Often new advances occur through cross-fertilization of ideas between sub-fields that otherwise have little overlap as…
This paper has been withdrawn by the author. In this article I review W\"ust's recent handbook on mathematical physics from a philosophical standpoint. It emerges a structural approach to mathematics which evidences the utility of logic in…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
The development of a mathematics for living systems is one of the most challenging prospects of this century. The search began with the pioneering contribution of Ilia Prigogine, who developed methods from statistical physics to describe…
This text is based on an invited talk at the Dedekind Symposium at Braunschweig in October 2016. It summarizes views from my recent commented edition of Dedekinds two books on the foundations of mathematics.
Understanding the changing structure of science over time is essential to elucidating how science evolves. We develop diachronic embeddings of scholarly periodicals to quantify "semantic changes" of periodicals across decades, allowing us…
We partially update Grossman's 2005 survey of patterns in mathematical research using a sample of 401 profiles from MathSciNet. The mathematical landscape has changed substantially: single-paper authors have reduced from $43$ \% to $32.42$…
The first half of the 20th century in the history of Russian mathematics is striking with a combination of dramaticism, sometimes a tragedy, and outstanding achievements. The paper is devoted to St. Petersburg-Leningrad Mathematical School.…
The scientific status of physical cosmology has been the subject of philosophical debate ever since detailed mathematical models of the Universe emerged from Einstein's general theory of relativity. Such debates have revolved around whether…
Mathematical concepts and results have often been given a long history, stretching far back in time. Yet recent work in the history of mathematics has tended to focus on local topics, over a short term-scale, and on the study of ephemeral…
Physics research complements traditional approaches, such as mathematical (stochastic) finance and econometrics in quantitative economics and finance. In the early years of this millennium, we embarked on an interdisciplinary research…
The paper discusses the fundamental characteristics distinguishing the natural and social systems from each other. It considers in detail the basic approaches, prospects, and possibilities of constructing mathematical description for social…
We state the defining characteristic of mathematics as a type of symmetry where one can change the connotation of a mathematical statement in a certain way when the statement's truth value remains the same. This view of mathematics as…
The University of Strasbourg, fundamentally humanistic since its creation, has a complicated history, being sometimes German, sometimes French through the ages. If one focus, from 1871, on the area of mathematics, we can identify two…
Changing institutions is an integral part of an academic life. Yet little is known about the mobility patterns of scientists at an institutional level and how these career choices affect scientific outcomes. Here, we examine over 420,000…
Over the past six years, a detailed framework has been constructed to unravel the quantum nature of the Riemannian geometry of physical space. A review of these developments is presented at a level which should be accessible to graduate…