Related papers: Richard Dedekind: Style and Influence
This draft book offers a comprehensive and rigorous treatment of the mathematical principles underlying modern deep learning. The book spans core theoretical topics, from the approximation capabilities of deep neural networks, the theory…
Remarks on mathematical proof and the practice of mathematics.
These are notes from a lecture course on symmetric spaces by the second author given at the University of Pittsburgh in the fall of 2010.
One of the variants for systematizing the activities of the historian of mathematics is proposed, as well as a scheme for organizing research and search work in the preparation of scientific articles and reports on the history of science.
This is a textbook about elementary number theory, with emphasis on classical topics around the Euklidean Algorithm.
As the etymology of the word shows, logic is intimately related to language, as exemplified by the work of philosophers from Antiquity and from the Middle-Age. At the beginning of the XX century, the crisis of the foundations of mathematics…
Science of science has become a popular topic that attracts great attentions from the research community. The development of data analytics technologies and the readily available scholarly data enable the exploration of data-driven…
In this paper, we propose that 'embodied mathematics' should be studied not only by reduction to the present individual bodily experience but in an historical context as well, as far as the origins of mathematics are concerned. Some early…
The purpose of this book is to give an exposition of geometry, from a point of view which complements Klein's Erlangen program. The emphasis is on extending the classical Euclidean geometry to the finite case, but it goes beyond that. After…
Here I am proposing a translation and discussion of the De Iride, one of the short scientific treatise written by Robert Grosseteste. In the first part of his Latin text we find reflection and refraction of light, described in a geometrical…
To be published in the proceedings of IAU Symposium 239 "Convection in Astrophysics" (ed. F. Kupka, I. W. Roxburgh, K. L. Chan). Content: 1. From Nice to Prague, 2. The triumph of 3-D simulations, 3. How to lower the cost - what else can be…
People sometimes change their opinions when they discuss things with other people. Researchers can use mathematics to study opinion changes in simplifications of real-life situations. These simplified settings, which are examples of…
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…
A brief overview of publications in approximation theory of functions known to the author and connected with scientific publications by V.~K.~Dzyadyk (1919--1998).
This paper is an exposition and review of the research related to the Riemann Hypothesis starting from the work of Riemann and ending with a description of the work of G. Spencer-Brown, culminating in his Denjoy proof of the RH.
The following three sections and appendices are taken from my thesis "The Foundations of Inference and its Application to Fundamental Physics" from 2021, in which I construct a theory of entropic inference from first principles. The…
This text (in Spanish) hopes to offer the reader a starting point to deliver good talks on mathematical topics.
This article serves as an introduction to the study of networks of social systems. First, we introduce the reader to key mathematical tools to study social networks, including mathematical representations of networks and essential…
Research output and impact is currently the focus of serious debate worldwide. Quantitative analyses based on a wide spectrum of indices indicate a clear advantage of US institutions as compared to institutions in Europe and the rest of the…
This is a draft of a chapter on mathematical logic and foundations for an upcoming handbook of computational proof assistants.