相关论文: Plane Geometry: An Elementary School Textbook (ca.…

Looking ahead to the next decade and imagining the landscape of astronomy in 2020, it is clear that astronomical surveys, large and small, plus extensive follow-up projects, will be a great engine of progress in our profession. Surveys have…

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…

Abstract axiomatic formulation of mathematical structures are extensively used to describe our physical world. We take here the reverse way. By making basic assumptions as starting point, we reconstruct some features of both geometry and…

Starting from the Italian unification in 1861, we describe the role of mathematics teaching in the Italian system of education giving an account of the main features of Italian mathematics education, and referring to the official syllabi,…

In this article, I discuss the relationship of mathematics to the physical world, and to other spheres of human knowledge. In particular, I argue that Mathematics is created by human beings, and the number $\pi$ can not be said to have…

We review some recent applications of machine learning to algebraic geometry and physics. Since problems in algebraic geometry can typically be reformulated as mappings between tensors, this makes them particularly amenable to supervised…

We use an information-theoretic measure of linguistic similarity to investigate the organization and evolution of scientific fields. An analysis of almost 20M papers from the past three decades reveals that the linguistic similarity is…

Identifying academic plagiarism is a pressing task for educational and research institutions, publishers, and funding agencies. Current plagiarism detection systems reliably find instances of copied and moderately reworded text. However,…

We consider several appearances of the notion of convexity in Greek antiquity, more specifically in mathematics and optics, in the writings of Aristotle, and in art. The final version of this article will appear in the book `Geometry in…

These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental…

The turn of the millennium was a time of optimism about an approach to noncommutative geometry inspired by rich mathematical objects called `quantum groups' and its applications to quantum spacetime. This would model quantum gravity effects…

Recent studies have shown that not only primary school students but also their future teachers reach science courses with pre-constructed and consistent models of the world surrounding them. These ideas include many misconceptions which…

While it is generally agreed that the nature of spacetime must be drastically different at the Planck scale, it has been a common practice to assume that spacetime is endowed with a full pseudo-Riemannian geometry regardless of the physical…

Abridged: The golden age of astrophysics is upon us with both grand discoveries (extra-solar planets, dark matter, dark energy) and precision cosmology. Fundamental understanding of the working of stars and galaxies is within reach, thanks…

When PageRank began to be used for ranking in Web search, a concern soon arose that older pages have an inherent --- and potentially unfair --- advantage over emerging pages of high quality, because they have had more time to acquire…

This paper seeks to develop a deeper understanding of the fundamental properties of neural text generations models. The study of artifacts that emerge in machine generated text as a result of modeling choices is a nascent research area.…

A survey is made of selected topics in flavour physics where real progress is expected in the coming half-decade, paying particular attention to those where New Physics signals may appear.

We study the possibility to undo the quantum mechanical evolution in a time reversal experiment. The naive expectation, as reflected in the common terminology ("Loschmidt echo"), is that maximum compensation results if the reversed dynamics…

We describe a prototype of a new experimental GeoGebra command and tool, Discover, that analyzes geometric figures for salient patterns, properties, and theorems. This tool is a basic implementation of automated discovery in elementary…

This contribution covers the topics presented by the authors at the {\it ``Fundamental Problems of Turbulence, 50 Years after the Marseille Conference 1961"} meeting that took place in Marseille in 2011. It focuses on some of the…