相关论文: Plane Geometry: An Elementary School Textbook (ca.…
By recasting metrical geometry in a purely algebraic setting, both Euclidean and non-Euclidean geometries can be studied over a general field with an arbitrary quadratic form. Both an affine and a projective version of this new theory are…
$p$-Adic mathematical physics is a branch of modern mathematical physics based on the application of $p$-adic mathematical methods in modeling physical and related phenomena. It emerged in 1987 as a result of efforts to find a…
The paper develops the idea that the dynamics of both classical and quantum processes is time reversible. It is shown how this classical analogy allows one to define the measure for the path integral in quantum mechanics.
This essay, originally published in the Sept 1990 Notices of the AMS, discusses problems of our mathematical education system that often stem from widespread misconceptions by well-meaning people of the process of learning mathematics. The…
It is shown that the conventional approach to microcosm investigations uses an incorrect supposition (incorrect space-time model) whose incorrectness is compensated by means of additional hypotheses, known as quantum mechanics principles.…
The century of complexity has come. The face of science has changed. Surprisingly, when we start asking about the essence of these changes and then critically analyse the answers, the result are mostly discouraging. Most of the answers are…
We show how the birth of perspective painting in the Italian Renaissance led to a new way of interpreting space that resulted in the creation of projective geometry. Unlike other works on this subject, we explicitly show how the craft of…
The alignments of galaxies across the large-scale structure of the Universe are known to be a source of contamination for gravitational lensing, but they can also probe cosmology and the physics of galaxy evolution in many ways. In this…
Finding patterns in data is one of the most challenging open questions in information science. The number of possible relationships scales combinatorially with the size of the dataset, overwhelming the exponential increase in availability…
In this paper we discuss the impact of the last Landau paper on physics and mathematics to date and make some predictions about its likely impact on sciences in new millennium.
The aim of this work is the mathematical analysis of the physical time-reversal operator and its definition as a geometrical structure\QTR{bf}{, }in such a way that it could be generalized to the purely mathematical realm. Rigorously, only…
We argue that quantum computing underwent an inflection point circa 2017. Long promised funding materialised which prompted public and private investments around the world. Techniques from machine learning suddenly influenced central…
We describe various errors in the mathematical literature, and consider how some of them might have been avoided, or at least detected at an earlier stage, using tools such as Maple or Sage. Our examples are drawn from three broad…
The notion of an unexpected curve in the plane was introduced in 2018, and was quickly generalized in several directions in a flurry of mathematical activity by many authors. In this expository paper we first describe some of the main…
The book is designed for a semester-long course in Foundations of Geometry and meant to be rigorous, conservative, elementary and minimalist. List of topics: Euclidean geometry: The Axioms / Half-planes / Congruent triangles / Perpendicular…
We present a pedagogical introduction to the recent advances in the computational geometry, physical implications, and data science of Calabi-Yau manifolds. Aimed at the beginning research student and using Calabi-Yau spaces as an exciting…
Physics is formulated in terms of timeless classical mathematics. A formulation on the basis of intuitionist mathematics, built on time-evolving processes, would offer a perspective that is closer to our experience of physical reality.
In 1710, George Berkeley, philospher and scientist, discovered that the directions in which we see (sightlines) are tilted 45 degrees towards the past from the directions in which we look. Looking north from the 3-d present we see to the…
This is a revised version of the notes from the week-long course I gave at the Centre de Recerca Matematica, Barcelona, in September of 2010. The aim is to give a working overview of recent methods and results in "Blaschkean integral…
Astrophysical studies require a knowledge of very accurate positions, motions and distances of stars. A brief overview is given of the significance and development of astrometry by ESA's two astrometric satellites, Hipparcos and Gaia,…