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It is argued that the occurrence of disproportionately ("un-natural") large (or small) numbers, as well as deep cancellations, are comparatively natural traits of the way Nature is geared to operate in most complex systems. The idea is…
Some Goedel centenary reflections on whether incompleteness is really serious, and whether mathematics should be done somewhat differently, based on using algorithmic complexity measured in bits of information. [Enriques lecture given…
We aim to carry out an assessment of the scientific value of Oppenheimer's research on black holes in order to determine and weigh possible factors to explain its neglect by the scientific community, and even by Oppenheimer himself. Dealing…
It is a survey of the main results on abstract characterizations of algebras of $n$-place functions obtained in the last 40 years. A special attention is paid to those algebras of $n$-place functions which are strongly connected with groups…
On the occasion of the celebration of the first half-century of Yang--Mills theories, I am contributing a personal recollection of how the subject, in its early times, confronted physical reality, that is, its "phenomenology". There is…
Despite recent calls for including artificial intelligence (AI) literacy in K-12 education, not enough attention has been paid to studying youths' everyday knowledge about machine learning (ML). Most research has examined how youths…
Specialized intelligent systems can be found everywhere: finger print, handwriting, speech, and face recognition, spam filtering, chess and other game programs, robots, et al. This decade the first presumably complete mathematical theory of…
The growing disconnection of the majority of population from mathematics is becoming a phenomenon that is increasingly difficult to ignore. This paper attempts to point to deeper roots of this cultural and social phenomenon. It concentrates…
Riemannian metric learning is an emerging field in machine learning, unlocking new ways to encode complex data structures beyond traditional distance metric learning. While classical approaches rely on global distances in Euclidean space,…
We review the current status of dimensions, as the result of a long and controversial history that includes input from philosophy and physics. Our conclusion is that they are subjective but essential concepts which provide a kind of…
In this short review I present my personal reflections on Zeilinger-Brukner information interpretation of quantum mechanics (QM). In general, this interpretation is very attractive for me. However, its rigid coupling to the notion of…
We introduce several new functions that measure the distance between two points $x$ and $y$ in a domain $G\subsetneq\mathbb{R}^n$ by using the arithmetic or the logarithmic mean of the Euclidean distances from the points $x$ and $y$ to the…
The study of biharmonic submanifolds, initiated by B. Y. Chen and G. Y. Jiang independently, has received a great attention in the past 30 years with many important progress. This note attempts to give a short survey on the study of…
Logic has its origins in basic questions about the nature of the real world and how we describe it. This article seeks to bring out the physical and epistemological relevance of some of the more recent technical work in logic and…
This essay examines the relationship between artificial intelligence and the historical evolution of modern Mathematics. Rather than viewing AI as an external rupture, we argue that its effectiveness reveals a structural tendency already…
Deep neural networks have triggered a revolution in artificial intelligence, having been applied with great results in medical imaging, semi-autonomous vehicles, ecommerce, genetics research, speech recognition, particle physics,…
Over the past thirty years or so the authors have been teaching various programming for mathematics courses at our respective Universities, as well as incorporating computer algebra and numerical computation into traditional mathematics…
I am most honoured to have the privilege to present the Foreword to this fascinating and wonderfully varied collection of contributions, concerning the nature of computation and of its deep connection with the operation of those basic laws,…
The goal of this paper is to experiment new math concepts and theories, especially if they run counter to the classical ones. To prove that contradiction is not a catastrophe, and to learn to handle it in an (un)usual way. To transform the…
Can normal science-in the Kuhnian sense-add something substantial to the discussion about the measurement problem? Does an extended Wigner's-friend Gedankenexperiment illustrate new issues? Or a new quality of known issues? Are we led to…